From 5be9bbeafb7250c92fcc3dbb0a1c6e0acac63111 Mon Sep 17 00:00:00 2001 From: Dylan Roy <249851642+d6g8k5htny-coder@users.noreply.github.com> Date: Thu, 8 Oct 2026 10:11:23 -0700 Subject: [PATCH 1/4] Materialize P-C companion B against independently pinned landed inventory A --- .github/workflows/downstream-gate.yml | 22 +- .../P_C/PROOF_SLICE.json | 20838 ++++++++++++++++ .../proof_dependencies_20261008/P_C/README.md | 37 +- ...885c19e07c5286d25065c1163aedae9dc6792.json | 9 + tests/test_proof_slice_check.py | 29 +- 5 files changed, 20910 insertions(+), 25 deletions(-) create mode 100644 reviews/proof_dependencies_20261008/P_C/PROOF_SLICE.json create mode 100644 reviews/proof_dependencies_20261008/P_C/records/comment-6064435898-139ffd12d0daa6d0dfaa4c3a1e6885c19e07c5286d25065c1163aedae9dc6792.json diff --git a/.github/workflows/downstream-gate.yml b/.github/workflows/downstream-gate.yml index 7b2daba12..b8a495406 100644 --- a/.github/workflows/downstream-gate.yml +++ b/.github/workflows/downstream-gate.yml @@ -98,7 +98,7 @@ jobs: }, indent=2) + '\n') print('DOWNSTREAM_GATE_PASSED') PYTHON - - name: P-C inventory A source-bound conformance + - name: P-C paired A/B source-bound conformance env: PYTHONDONTWRITEBYTECODE: '1' GIT_NO_LAZY_FETCH: '1' @@ -107,6 +107,7 @@ jobs: test "$(git --no-replace-objects --no-lazy-fetch rev-parse HEAD)" = "$GITHUB_SHA" test "$(git --no-replace-objects --no-lazy-fetch rev-parse --is-shallow-repository)" = false git --no-replace-objects --no-lazy-fetch cat-file -e '9fd261135b41daf1e377f9ef2db193fee6ec36be^{commit}' + git --no-replace-objects --no-lazy-fetch cat-file -e '92a45e1749936a19ebfe31e803289e0f4683d754^{commit}' git --no-replace-objects --no-lazy-fetch cat-file -e "$GITHUB_SHA^{commit}" out="$RUNNER_TEMP/downstream-gate-results" mkdir -p "$out" @@ -115,17 +116,28 @@ jobs: python3 -B -S - "$out" <<'PC_TEST_EVIDENCE' import pathlib, re, sys # Conventional unittest output checks, not hostile-producer authentication. - expected_count = 93 + expected_count = 94 out = pathlib.Path(sys.argv[1]) for mode in ('normal', 'optimized'): stderr = (out / f'proof-slice-tests-{mode}.stderr').read_text(encoding='utf-8') summary = re.search(r'\nRan ([1-9][0-9]*) tests in [0-9]+\.[0-9]{3}s\n\nOK\n\Z', stderr) if summary is None or int(summary.group(1)) != expected_count or 'skipped=' in stderr: raise RuntimeError('P-C focused tests have incomplete or unsuccessful execution: ' + mode) - print('P_C_FOCUSED_TESTS_PASSED: normal and optimized, 93 methods each, no skips') + print('P_C_FOCUSED_TESTS_PASSED: normal and optimized, 94 methods each, no skips') PC_TEST_EVIDENCE - python3 -B -S tools/proof_slice_check.py --repo . --inventory-commit "$GITHUB_SHA" --inventory-path reviews/proof_dependencies_20261008/P_C/EXPECTED_INVENTORY.json > "$out/proof-slice-inventory-normal.json" 2> "$out/proof-slice-inventory-normal.stderr" - python3 -B -O -S tools/proof_slice_check.py --repo . --inventory-commit "$GITHUB_SHA" --inventory-path reviews/proof_dependencies_20261008/P_C/EXPECTED_INVENTORY.json > "$out/proof-slice-inventory-optimized.json" 2> "$out/proof-slice-inventory-optimized.stderr" + python3 -B -S tools/proof_slice_check.py --repo . --expected-commit 92a45e1749936a19ebfe31e803289e0f4683d754 --expected-path reviews/proof_dependencies_20261008/P_C/EXPECTED_INVENTORY.json --companion-commit "$GITHUB_SHA" --companion-path reviews/proof_dependencies_20261008/P_C/PROOF_SLICE.json > "$out/proof-slice-paired-normal.json" 2> "$out/proof-slice-paired-normal.stderr" + python3 -B -O -S tools/proof_slice_check.py --repo . --expected-commit 92a45e1749936a19ebfe31e803289e0f4683d754 --expected-path reviews/proof_dependencies_20261008/P_C/EXPECTED_INVENTORY.json --companion-commit "$GITHUB_SHA" --companion-path reviews/proof_dependencies_20261008/P_C/PROOF_SLICE.json > "$out/proof-slice-paired-optimized.json" 2> "$out/proof-slice-paired-optimized.stderr" + python3 -B -S - "$out" <<'PC_PAIRED_SCOPE' + import json, os, pathlib, sys + for mode in ('normal', 'optimized'): + report = json.loads((pathlib.Path(sys.argv[1]) / f'proof-slice-paired-{mode}.json').read_text()) + if not (report['valid'] is True and report['phase'] == 'paired' + and report['validation_scope'] == 'pc-pilot-fixed-source' + and report['fixed_source_commit'] == '9fd261135b41daf1e377f9ef2db193fee6ec36be' + and report['inputs']['inventory']['commit'] == '92a45e1749936a19ebfe31e803289e0f4683d754' + and report['inputs']['companion']['commit'] == os.environ['GITHUB_SHA']): + raise RuntimeError('P-C requires independently pinned, pilot-scoped paired validation') + PC_PAIRED_SCOPE - name: Retain evidence even on failure if: always() uses: actions/upload-artifact@043fb46d1a93c77aae656e7c1c64a875d1fc6a0a diff --git a/reviews/proof_dependencies_20261008/P_C/PROOF_SLICE.json b/reviews/proof_dependencies_20261008/P_C/PROOF_SLICE.json new file mode 100644 index 000000000..6b533db4b --- /dev/null +++ b/reviews/proof_dependencies_20261008/P_C/PROOF_SLICE.json @@ -0,0 +1,20838 @@ +{ + "schema": "proof-slice/v0-provisional-5", + "artifact_kind": "source_companion", + "id": "P-C-SOURCE-COMPANION-20261008", + "read_at": "2026-10-08T17:07:50Z", + "author": { + "provider": "OpenAI", + "agent": "Codex implement_proof_slice_inventory", + "session": null, + "exposure": "Actual receiver pc-companion-b-author-20261008; runtime session identifier is not attested. Actual Stage B materializer; prior Stage A author and source/design discussion exposure. Descriptive serialization only; no original-proof-author or independent applicability-review identity is claimed." + }, + "scientific_effect": "NONE", + "status_authority": false, + "independence_credit": 0, + "root": { + "statement_id": "UNIFORM-MATRIX-CAP-LIFETIME-20260924-v1::Theorem-C", + "source_statement": { + "source_id": "P", + "lines": [ + 47, + 52 + ], + "locator": "Theorem C (1.3), statement and retained scope", + "precision": "exact_lines" + }, + "entry_unit_ids": [ + "B53" + ], + "graph_node": null, + "museum_card": null, + "semantics": { + "model": { + "text": "The recorded model is a centered stationary variance-one Gaussian field on the fixed flat torus R^d/(L Z^d), with the normalized periodized Gaussian covariance K_L. No nonperiodic covariance or isotropic GOE substitution is made.", + "source_refs": [ + { + "source_id": "P", + "lines": [ + 11, + 16 + ], + "locator": "Fixed torus and normalized periodized covariance", + "precision": "exact_lines" + } + ], + "record_refs": [ + { + "record_id": "R6049443374", + "locator": "## Mandatory reading boundary" + }, + { + "record_id": "R6053473777", + "locator": "### Source-bound decision table / 3. P-C root and coefficient" + } + ], + "unknown_refs": [] + }, + "observables": [ + { + "text": "nu_cand^all(ell) counts all ordered maximum/index-(d-1)-saddle pairs with positive height difference ell, in expectation per unit volume.", + "source_refs": [ + { + "source_id": "P", + "lines": [ + 47, + 52 + ], + "locator": "Theorem C candidate-pair observable", + "precision": "exact_lines" + } + ], + "record_refs": [ + { + "record_id": "R6049443374", + "locator": "## Mandatory reading boundary" + }, + { + "record_id": "R6053473777", + "locator": "### Source-bound decision table / 3. P-C root and coefficient" + } + ], + "unknown_refs": [] + }, + { + "text": "nu_eld^all(ell) counts actual finite ordinary superlevel-H0 persistence bars, in expectation per unit volume. It remains distinct from candidate-pair density; the essential global-maximum class is excluded.", + "source_refs": [ + { + "source_id": "P", + "lines": [ + 47, + 52 + ], + "locator": "Theorem C finite ordinary-bar observable", + "precision": "exact_lines" + } + ], + "record_refs": [ + { + "record_id": "R6049443374", + "locator": "## Mandatory reading boundary" + }, + { + "record_id": "R6053473777", + "locator": "### Source-bound decision table / 3. P-C root and coefficient" + } + ], + "unknown_refs": [ + "UNKNOWN-U3" + ] + } + ], + "normalization": { + "text": "Expectation per unit volume with ordered endpoint roles, ordinary sphere measure d-sigma and no unordered-pair factor 1/2. The exact normalized periodized covariance is retained.", + "source_refs": [ + { + "source_id": "P", + "lines": [ + 317, + 319 + ], + "locator": "Ordered-role spatial and height Jacobians; per-unit midpoint volume", + "precision": "exact_lines" + } + ], + "record_refs": [ + { + "record_id": "R6049548422", + "locator": "### 3. Applicability (instruction 3): text-level results / Ordinary dσ sphere, no 1/2" + }, + { + "record_id": "R6049548422", + "locator": "### 3. Applicability (instruction 3): text-level results / Per-volume convention" + } + ], + "unknown_refs": [] + }, + "parameters": { + "text": "Dimension d>=2 and side length L>0 are fixed. Theorem C includes all birth heights, all positive scaled-gap marks and all spatial separations on that torus. Compact-window hypotheses remain local hypotheses of the intermediate statements, not restrictions silently imposed on the unrestricted root.", + "source_refs": [ + { + "source_id": "P", + "lines": [ + 11, + 16 + ], + "locator": "Fixed d,L and compact intermediate windows", + "precision": "exact_lines" + }, + { + "source_id": "P", + "lines": [ + 47, + 52 + ], + "locator": "Unrestricted root parameters", + "precision": "exact_lines" + } + ], + "record_refs": [ + { + "record_id": "R6049443374", + "locator": "## Mandatory reading boundary" + }, + { + "record_id": "R6053473777", + "locator": "### Source-bound decision table / 3. P-C root and coefficient" + } + ], + "unknown_refs": [] + }, + "limit_order": { + "text": "For the unrestricted near term, integrate at fixed ell and then let ell decrease to zero by dominated convergence at each fixed b,k,u, with r=(ell/k)^(1/3). The bounded far contribution vanishes after multiplication by ell^(1/3). Section 15 evaluates the coefficient after this limit. Compact-case uniform limits and Section 12 cumulative statements retain their separate domains.", + "source_refs": [ + { + "source_id": "P", + "lines": [ + 417, + 433 + ], + "locator": "Unrestricted cutoff, domination and limiting density", + "precision": "exact_lines" + }, + { + "source_id": "P", + "lines": [ + 445, + 445 + ], + "locator": "Near/far combination and conclusion", + "precision": "exact_lines" + } + ], + "record_refs": [ + { + "record_id": "R6049548422", + "locator": "### 3. Applicability (instruction 3): text-level results / Limit order" + }, + { + "record_id": "R6049548422", + "locator": "### 3. Applicability (instruction 3): text-level results / **N3:**" + } + ], + "unknown_refs": [] + }, + "conclusion": { + "text": "P records the leading asymptotics nu_cand^all(ell) ~ c_{d,L} ell^(-1/3) and nu_eld^all(ell) ~ c_{d,L} ell^(-1/3), with positive finite c_{d,L}. B53 is the root entry. B65/(15.2) is its exact angular/cone coefficient source reference, not an additional root entry or numerical certificate.", + "source_refs": [ + { + "source_id": "P", + "lines": [ + 47, + 52 + ], + "locator": "Theorem C statement and limitations", + "precision": "exact_lines" + }, + { + "source_id": "P", + "lines": [ + 445, + 445 + ], + "locator": "B53 concludes Theorem C", + "precision": "exact_lines" + }, + { + "source_id": "P", + "lines": [ + 476, + 478 + ], + "locator": "B65 coefficient representation (15.2)", + "precision": "exact_lines" + } + ], + "record_refs": [ + { + "record_id": "R6053473777", + "locator": "### Source-bound decision table / 3. P-C root and coefficient" + }, + { + "record_id": "R6049443374", + "locator": "B53" + }, + { + "record_id": "R6049443374", + "locator": "B65" + } + ], + "unknown_refs": [] + }, + "exclusions": [ + { + "text": "No unrestricted compact-window O(ell^(2/3)) difference estimate, elementary closed form or numerical enclosure is asserted by this root.", + "source_refs": [ + { + "source_id": "P", + "lines": [ + 52, + 52 + ], + "locator": "Theorem C exclusions", + "precision": "exact_lines" + } + ], + "record_refs": [ + { + "record_id": "R6049443374", + "locator": "## Mandatory reading boundary" + }, + { + "record_id": "R6053473777", + "locator": "### Source-bound decision table / 3. P-C root and coefficient" + } + ], + "unknown_refs": [] + }, + { + "text": "Earlier P sections 1–9, the external Kac-Rice base and unnamed input mechanisms remain imported/unexpanded in this descriptive slice. The source inventory and its unknown annotations do not establish mathematical applicability, necessity or sufficiency.", + "source_refs": [], + "record_refs": [ + { + "record_id": "R6049443374", + "locator": "## Mandatory reading boundary" + }, + { + "record_id": "R6049548422", + "locator": "### UNKNOWN" + } + ], + "unknown_refs": [ + "UNKNOWN-U1", + "UNKNOWN-U2", + "UNKNOWN-U4", + "UNKNOWN-U7" + ] + }, + { + "text": "R, C52, C50/C51 witness routes, CUB and formal acceptance remain separate. No whole-torus root, witness premise, scientific status or formal coverage is inferred.", + "source_refs": [], + "record_refs": [ + { + "record_id": "R6049443374", + "locator": "Explicit unknowns and omission/applicability exit" + }, + { + "record_id": "R6051274124", + "locator": "1. Decision and exact scope" + } + ], + "unknown_refs": [] + } + ] + }, + "reading_boundaries": [ + { + "id": "READ-CAP", + "source_id": "CAP", + "consumed_lines": [ + [ + 11, + 28 + ], + [ + 49, + 167 + ] + ], + "excluded_lines": [ + [ + 30, + 47 + ] + ], + "reason": { + "text": "Only the deterministic theorem and sections 2–5 are consumed. The narrower fixed-axis 2D SIDE24 probabilistic corollary at30–47 is excluded despite the older broad1–168 label; later numerical imports are unexpanded. CAP enters through the recorded Theorem-A/Section-8 inputs, not as an automatic independent P-C premise.", + "source_refs": [], + "record_refs": [ + { + "record_id": "R6049548422", + "locator": "4. Consumption boundaries / CAP (N6)" + }, + { + "record_id": "R6049640627", + "locator": "N1–N7 are retained" + } + ], + "unknown_refs": [] + } + }, + { + "id": "READ-E1", + "source_id": "E1", + "consumed_lines": [ + [ + 8, + 40 + ] + ], + "excluded_lines": [ + [ + 1, + 7 + ], + [ + 41, + 44 + ] + ], + "reason": { + "text": "Present descriptive selection: complete P-section-5 congruence correction, transformed Hessian, determinant normalization, limiting matrices and unchanged-formula statement. Identity metadata and the historical review request remain authenticated but excluded. This is a reading correction, not an independent probability result or acceptance.", + "source_refs": [], + "record_refs": [ + { + "record_id": "R6057972030", + "locator": "Source reasons and limits / E1" + } + ], + "unknown_refs": [] + } + }, + { + "id": "READ-E2", + "source_id": "E2", + "consumed_lines": [ + [ + 9, + 131 + ] + ], + "excluded_lines": [ + [ + 1, + 8 + ], + [ + 132, + 147 + ] + ], + "reason": { + "text": "Present descriptive selection includes external-citation/finding context9–21, complete P-section-9 replacement23–110 and conditional disposition/scope limits112–131. Armentano–Azaïs–León v3 Theorems2.2/7.1 remain unexpanded external imports; compact off-diagonal and continuous/lower-semicontinuous-base hypotheses remain. The full-Borel extension retains the actual global elder/type mark, full determinant accounting and diagonal exhaustion importing P sections3/5/10 rather than re-proving them. Contact covariance, normalizer, TheoremA, unrestricted domination/coefficient and numerical/scientific gates stay separate.", + "source_refs": [], + "record_refs": [ + { + "record_id": "R6057972030", + "locator": "Source reasons and limits / E2" + }, + { + "record_id": "R6049548422", + "locator": "4. Consumption boundaries / E2 / (b) N2" + } + ], + "unknown_refs": [] + } + }, + { + "id": "READ-REC", + "source_id": "REC", + "consumed_lines": [ + [ + 10, + 64 + ], + [ + 83, + 210 + ], + [ + 215, + 225 + ] + ], + "excluded_lines": [ + [ + 1, + 9 + ], + [ + 65, + 82 + ], + [ + 211, + 214 + ], + [ + 226, + 309 + ] + ], + "reason": { + "text": "Present descriptive selection retains reading rules and model/scoped statements, attributed source/review ledger context83–131, residual qualifications133–166, historical sections11–12 review168–205, and retained consumer-scope context207–210/215–225. W1 gives joint convergence in law via Slutsky. The embedding radius bounds TheoremA r_*, not every P13 covariance r0; separate quantitative R12 is not a P-C premise. ACCEPT/provider, machine-binding and spot-check text remains historical provenance, not this materializer’s verdict or execution. The planar lower-bound composition66–69, section3 synopsis71–81, outbound consumers211–214 and later register/check instructions are excluded. REC is not an independent replacement proof of every interface, and its broad historical CAP label cannot override the CAP exclusion.", + "source_refs": [], + "record_refs": [ + { + "record_id": "R6057972030", + "locator": "Source reasons and limits / REC" + }, + { + "record_id": "R6049548422", + "locator": "4. Consumption boundaries / REC (N1)" + }, + { + "record_id": "R6049640627", + "locator": "N1–N7 are retained" + } + ], + "unknown_refs": [] + } + } + ] + }, + "sources": [ + { + "id": "P", + "identity": { + "repository": "d6g8k5htny-coder/Math-", + "commit": "9fd261135b41daf1e377f9ef2db193fee6ec36be", + "path": "imports/lifetime_parent_20260925/UNIFORM_MATRIX_CAP_AND_LIFETIME.md", + "git_blob": "dfed3b8d318a3ab1950957f393307733a4bef3f2", + "bytes": 40261, + "sha256": "9350ad6eaba6626b93c3dedeef9e2ff816e5cdf1c8318e85fb27499141c84bc7" + } + }, + { + "id": "CAP", + "identity": { + "repository": "d6g8k5htny-coder/Math-", + "commit": "9fd261135b41daf1e377f9ef2db193fee6ec36be", + "path": "imports/lifetime_parent_20260925/MARKED_CYLINDER_CAP_PROOF.md", + "git_blob": "0633aca3c2a2882b0de4399da0a75d64c2e6b2e1", + "bytes": 15160, + "sha256": "0bf922b9203c29088b12388807aa0e2ecd020485eb0f6e919679841b5b2636fc" + } + }, + { + "id": "E1", + "identity": { + "repository": "d6g8k5htny-coder/Math-", + "commit": "9fd261135b41daf1e377f9ef2db193fee6ec36be", + "path": "imports/lifetime_parent_20260925/ERRATUM_CONGRUENCE.md", + "git_blob": "213594d6ca6a86fb938110f4d166d9ce275a02d0", + "bytes": 1782, + "sha256": "bad7ef609c4ad8c41ad6af562c1b6807921e19a9d556ed793ad1a0db6e202028" + } + }, + { + "id": "E2", + "identity": { + "repository": "d6g8k5htny-coder/Math-", + "commit": "9fd261135b41daf1e377f9ef2db193fee6ec36be", + "path": "reviews/d1_section9_borel_repair_20260925/REPAIR.md", + "git_blob": "fe9b9ce4999908bb3814b500ee2d0ceb0c6f704a", + "bytes": 9062, + "sha256": "845abf9f9c99d672c2a10a887b5a2e7206a3d2de3d876f35f75ff6e2dc13e62f" + } + }, + { + "id": "REC", + "identity": { + "repository": "d6g8k5htny-coder/Math-", + "commit": "9fd261135b41daf1e377f9ef2db193fee6ec36be", + "path": "reviews/d1_chain_reconciliation_20260928/RECONCILIATION.md", + "git_blob": "75da2597971510f843f8d90c743950cb8c177342", + "bytes": 23312, + "sha256": "451b9d7ffee072a73fc904cab891b6693e3f233808b89df10cce1b57036b65da" + } + } + ], + "records": [ + { + "id": "R6049443374", + "identity": { + "kind": "github_comment_snapshot", + "repository": "d6g8k5htny-coder/main", + "issue": 281, + "comment_id": "6049443374", + "url": "https://github.com/d6g8k5htny-coder/main/issues/281#issuecomment-6049443374", + "updated_at": "2026-10-08T00:13:18Z", + "body_bytes": 22410, + "body_sha256": "3726784e264a844dddab7f982419e751da96b7bb6661a1689518db9a6522c9f0" + }, + "performer": { + "provider": "OpenAI", + "agent": "Codex root", + "session": "01a103c8-7a8e-7461-8e9f-36e3b02757c5", + "exposure": "Source/discussion exposed as recorded; organizational-independence credit 0. Original descriptive inventory, 66 units and originally listed 109 uses; source/review exposed, no applicability acceptance." + }, + "role": "inventory", + "scope": "Original descriptive inventory, 66 units and originally listed 109 uses; source/review exposed, no applicability acceptance." + }, + { + "id": "R6049548422", + "identity": { + "kind": "github_comment_snapshot", + "repository": "d6g8k5htny-coder/main", + "issue": 281, + "comment_id": "6049548422", + "url": "https://github.com/d6g8k5htny-coder/main/issues/281#issuecomment-6049548422", + "updated_at": "2026-10-08T00:22:13Z", + "body_bytes": 10976, + "body_sha256": "1c22188ec6395aceadbf5a34b0da5f83de95c84a6c619159f33aac23ca8f5466" + }, + "performer": { + "provider": "Grok Bot", + "agent": "Grok Bot agent 10", + "session": null, + "exposure": "Source/discussion exposed as recorded; organizational-independence credit 0. Historical separate omission/applicability read at its recorded scope; non-Claude/nonauthor support; no full proof or current-target review." + }, + "role": "omission_read", + "scope": "Historical separate omission/applicability read at its recorded scope; non-Claude/nonauthor support; no full proof or current-target review." + }, + { + "id": "R6049640627", + "identity": { + "kind": "github_comment_snapshot", + "repository": "d6g8k5htny-coder/main", + "issue": 281, + "comment_id": "6049640627", + "url": "https://github.com/d6g8k5htny-coder/main/issues/281#issuecomment-6049640627", + "updated_at": "2026-10-08T00:30:12Z", + "body_bytes": 2756, + "body_sha256": "ec0677b5e6e0630e444d8ae94cc4fc4572848241786e30e391897e068b9937dc" + }, + "performer": { + "provider": "OpenAI", + "agent": "Codex root", + "session": "01a103c8-7a8e-7461-8e9f-36e3b02757c5", + "exposure": "Source/discussion exposed as recorded; organizational-independence credit 0. Original inventory author additions A1–A6, U66.3 reclassification and dated responses; no accepted mathematical edge." + }, + "role": "author_response", + "scope": "Original inventory author additions A1–A6, U66.3 reclassification and dated responses; no accepted mathematical edge." + }, + { + "id": "R6051274124", + "identity": { + "kind": "github_comment_snapshot", + "repository": "d6g8k5htny-coder/main", + "issue": 281, + "comment_id": "6051274124", + "url": "https://github.com/d6g8k5htny-coder/main/issues/281#issuecomment-6051274124", + "updated_at": "2026-10-08T03:00:28Z", + "body_bytes": 34493, + "body_sha256": "29e9a4db8bae928f9f7b9b5286db1cdf722e7ceb90b108fd09d53082b72edaba" + }, + "performer": { + "provider": "OpenAI", + "agent": "design_proof_dependency_view", + "session": null, + "exposure": "Source/discussion exposed as recorded; organizational-independence credit 0. Original provisional contract; retained for statement-key provenance and unchanged scope, superseded only by explicit successor rules." + }, + "role": "design", + "scope": "Original provisional contract; retained for statement-key provenance and unchanged scope, superseded only by explicit successor rules." + }, + { + "id": "R6053473777", + "identity": { + "kind": "github_comment_snapshot", + "repository": "d6g8k5htny-coder/main", + "issue": 281, + "comment_id": "6053473777", + "url": "https://github.com/d6g8k5htny-coder/main/issues/281#issuecomment-6053473777", + "updated_at": "2026-10-08T06:02:42Z", + "body_bytes": 12576, + "body_sha256": "1b5012b601bcefbb493a1f27b7e8526326ef0f0f44374f4862f211787d83943f" + }, + "performer": { + "provider": "OpenAI", + "agent": "validate_proof_slice_sources", + "session": null, + "exposure": "Source/discussion exposed as recorded; organizational-independence credit 0. Descriptive five-choice source assessment, including entry B53, B65 role, contained spans and existing grouping; not original-author assent." + }, + "role": "omission_read", + "scope": "Descriptive five-choice source assessment, including entry B53, B65 role, contained spans and existing grouping; not original-author assent." + }, + { + "id": "R6053539516", + "identity": { + "kind": "github_comment_snapshot", + "repository": "d6g8k5htny-coder/main", + "issue": 281, + "comment_id": "6053539516", + "url": "https://github.com/d6g8k5htny-coder/main/issues/281#issuecomment-6053539516", + "updated_at": "2026-10-08T06:07:18Z", + "body_bytes": 3027, + "body_sha256": "edcf2e3d34f606c66fcb6f5391342802d9cb44cb35a6b59f5151a93e44641cc5" + }, + "performer": { + "provider": "OpenAI", + "agent": "Codex coordinator", + "session": null, + "exposure": "Source/discussion exposed as recorded; organizational-independence credit 0. Candidate-preparation disposition and A/B boundary; not a source implication review." + }, + "role": "design", + "scope": "Candidate-preparation disposition and A/B boundary; not a source implication review." + }, + { + "id": "R6054305355", + "identity": { + "kind": "github_comment_snapshot", + "repository": "d6g8k5htny-coder/main", + "issue": 281, + "comment_id": "6054305355", + "url": "https://github.com/d6g8k5htny-coder/main/issues/281#issuecomment-6054305355", + "updated_at": "2026-10-08T06:55:28Z", + "body_bytes": 4059, + "body_sha256": "fb29f57919825c8e9f1fa80e241a0a1736e70b7565e101badc3de9730052bc66" + }, + "performer": { + "provider": "OpenAI", + "agent": "prepare_proof_slice_records", + "session": null, + "exposure": "Source/discussion exposed as recorded; organizational-independence credit 0. Frozen candidate delivery: all 66/115 choices and 45 owner groups; actual candidate preparer, not original inventory author." + }, + "role": "inventory", + "scope": "Frozen candidate delivery: all 66/115 choices and 45 owner groups; actual candidate preparer, not original inventory author." + }, + { + "id": "R6054567951", + "identity": { + "kind": "github_comment_snapshot", + "repository": "d6g8k5htny-coder/main", + "issue": 281, + "comment_id": "6054567951", + "url": "https://github.com/d6g8k5htny-coder/main/issues/281#issuecomment-6054567951", + "updated_at": "2026-10-08T07:09:22Z", + "body_bytes": 15086, + "body_sha256": "d49e298d4bb3d585385028834f0f6db7dfb1de5accc955fac1b6c9f43cd30ca0" + }, + "performer": { + "provider": "OpenAI", + "agent": "validate_proof_slice_sources", + "session": null, + "exposure": "Source/discussion exposed as recorded; organizational-independence credit 0. Separate exact candidate descriptive source-data read; supports 112 premise/2 context/1 check and 42 mappings, preserving three then-unresolved cases." + }, + "role": "omission_read", + "scope": "Separate exact candidate descriptive source-data read; supports 112 premise/2 context/1 check and 42 mappings, preserving three then-unresolved cases." + }, + { + "id": "R6055287391", + "identity": { + "kind": "github_comment_snapshot", + "repository": "d6g8k5htny-coder/main", + "issue": 281, + "comment_id": "6055287391", + "url": "https://github.com/d6g8k5htny-coder/main/issues/281#issuecomment-6055287391", + "updated_at": "2026-10-08T07:48:50Z", + "body_bytes": 7084, + "body_sha256": "420b04f3b14335559eccda7cf0bd3ae7ee88da8f532b9eac0e99ebb65a7140ef" + }, + "performer": { + "provider": "OpenAI", + "agent": "prepare_proof_slice_records", + "session": null, + "exposure": "Source/discussion exposed as recorded; organizational-independence credit 0. Actual continuing descriptive custodian selection of the three joint-contribution targets; not mathematical sufficiency or original-author assent." + }, + "role": "author_response", + "scope": "Actual continuing descriptive custodian selection of the three joint-contribution targets; not mathematical sufficiency or original-author assent." + }, + { + "id": "R6055282954", + "identity": { + "kind": "github_comment_snapshot", + "repository": "d6g8k5htny-coder/main", + "issue": 281, + "comment_id": "6055282954", + "url": "https://github.com/d6g8k5htny-coder/main/issues/281#issuecomment-6055282954", + "updated_at": "2026-10-08T07:48:38Z", + "body_bytes": 5854, + "body_sha256": "ee7bb9469d3aaecc8bd5afc6c8e463f6767132e91645fa5b4c36650a2f81700c" + }, + "performer": { + "provider": "OpenAI", + "agent": "validate_proof_slice_sources", + "session": null, + "exposure": "Source/discussion exposed as recorded; organizational-independence credit 0. Continuing separate source-reader agreement with the three source-selected joint contribution sets; design/source scope only." + }, + "role": "omission_read", + "scope": "Continuing separate source-reader agreement with the three source-selected joint contribution sets; design/source scope only." + }, + { + "id": "R6057972030", + "identity": { + "kind": "github_comment_snapshot", + "repository": "d6g8k5htny-coder/main", + "issue": 281, + "comment_id": "6057972030", + "url": "https://github.com/d6g8k5htny-coder/main/issues/281#issuecomment-6057972030", + "updated_at": "2026-10-08T10:34:25Z", + "body_bytes": 6711, + "body_sha256": "cd622caf140c346e07ec8775644789b4e82c648389c8beb161975ea76a6fd298" + }, + "performer": { + "provider": "OpenAI", + "agent": "prepare_proof_slice_records", + "session": null, + "exposure": "Source/discussion exposed as recorded; organizational-independence credit 0. Present bounded E1/E2/REC consumed/excluded range selection, with explicit reading/provenance roles; not claimed as an earlier author choice." + }, + "role": "author_response", + "scope": "Present bounded E1/E2/REC consumed/excluded range selection, with explicit reading/provenance roles; not claimed as an earlier author choice." + }, + { + "id": "R6064435898", + "identity": { + "kind": "github_comment_snapshot", + "repository": "d6g8k5htny-coder/main", + "issue": 281, + "comment_id": "6064435898", + "url": "https://github.com/d6g8k5htny-coder/main/issues/281#issuecomment-6064435898", + "updated_at": "2026-10-08T16:31:05Z", + "body_bytes": 2785, + "body_sha256": "139ffd12d0daa6d0dfaa4c3a1e6885c19e07c5286d25065c1163aedae9dc6792" + }, + "performer": { + "provider": "OpenAI", + "agent": "Codex implement_proof_slice_inventory", + "session": null, + "exposure": "Actual receiver pc-companion-b-author-20261008; runtime session identifier is not attested. Actual Stage B materializer; prior Stage A author and source/design discussion exposure. Descriptive serialization only; no original-proof-author or independent applicability-review identity is claimed." + }, + "role": "design", + "scope": "Actual bounded Stage B custody/pickup and literal landed-A pin. This is not source-data review, applicability review or theorem acceptance." + } + ], + "inventory_binding": { + "expected_inventory": { + "repository": "d6g8k5htny-coder/Math-", + "commit": "92a45e1749936a19ebfe31e803289e0f4683d754", + "path": "reviews/proof_dependencies_20261008/P_C/EXPECTED_INVENTORY.json", + "git_blob": "252f1f36bd8ddb4f6fe00c17dc1486836fe13198", + "sha256": "bb764b4a5b440c63c176006e4187f8a9a38833cbc6086905123887f4397c17d3", + "bytes": 102233 + }, + "extraction_record": { + "record_id": "R6049443374", + "locator": "## Frozen source and extraction convention" + }, + "correction_records": [ + { + "record_id": "R6049640627", + "locator": "I accept A1–A6 as proposed additive uses" + }, + { + "record_id": "R6055287391", + "locator": "My explicit descriptive selection" + }, + { + "record_id": "R6057972030", + "locator": "Exact arrays for the existing ReadingBoundary fields" + } + ] + }, + "units": [ + { + "id": "B01", + "source": { + "source_id": "P", + "lines": [ + 312, + 312 + ], + "locator": "P lines312", + "precision": "exact_lines" + }, + "section": 10, + "description": { + "text": "Defines π_r; leads to (10.1). Earlier P proof imported/unexpanded.", + "source_refs": [ + { + "source_id": "P", + "lines": [ + 312, + 312 + ], + "locator": "P lines312", + "precision": "exact_lines" + } + ], + "record_refs": [ + { + "record_id": "R6049443374", + "locator": "### B01 — P lines312" + } + ], + "unknown_refs": [] + }, + "uses": [ + { + "id": "U01.1", + "kind": "premise", + "binding": { + "consumer_statement_id": "UNIFORM-MATRIX-CAP-LIFETIME-20260924-v1::Theorem-C", + "consumer_unit_id": "B01", + "consumer_source": { + "source_id": "P", + "lines": [ + 312, + 312 + ], + "locator": "P lines312", + "precision": "exact_lines" + }, + "supplier_ids": [ + "S-U01.1-P" + ], + "claimed_interface": { + "text": "P §3 (3.1)/(3.3): contact observation and target.", + "source_refs": [], + "record_refs": [ + { + "record_id": "R6049443374", + "locator": "B01/U01.1" + } + ], + "unknown_refs": [] + }, + "parameter_mapping": { + "text": "Recorded occurrence: P §3 (3.1)/(3.3): contact observation and target.\n\nLiteral consuming expression at P lines312:\nLet pi_r(R;v_r) denote the density of U_r at (3.3). Since U_r=T_r O_r,\n\nAdditional supplier-to-consumer substitutions beyond this retained wording/expression are unexpanded in this companion; no extra map is inferred.", + "source_refs": [ + { + "source_id": "P", + "lines": [ + 312, + 312 + ], + "locator": "P lines312", + "precision": "exact_lines" + } + ], + "record_refs": [ + { + "record_id": "R6049443374", + "locator": "B01/U01.1" + } + ], + "unknown_refs": [] + }, + "context": { + "text": "Recorded owning-block description: Defines π_r; leads to (10.1). Earlier P proof imported/unexpanded.", + "source_refs": [ + { + "source_id": "P", + "lines": [ + 312, + 312 + ], + "locator": "P lines312", + "precision": "exact_lines" + } + ], + "record_refs": [ + { + "record_id": "R6049443374", + "locator": "### B01 — P lines312" + } + ], + "unknown_refs": [] + }, + "source_reading": [] + }, + "provenance": [ + { + "record_id": "R6049443374", + "locator": "B01/U01.1" + } + ], + "applicability_reviews": [], + "unknown_refs": [] + }, + { + "id": "U01.2", + "kind": "premise", + "binding": { + "consumer_statement_id": "UNIFORM-MATRIX-CAP-LIFETIME-20260924-v1::Theorem-C", + "consumer_unit_id": "B01", + "consumer_source": { + "source_id": "P", + "lines": [ + 312, + 312 + ], + "locator": "P lines312", + "precision": "exact_lines" + }, + "supplier_ids": [ + "S-U01.2-UNNAMED" + ], + "claimed_interface": { + "text": "unnamed invertible-linear observation density rule.", + "source_refs": [], + "record_refs": [ + { + "record_id": "R6049443374", + "locator": "B01/U01.2" + } + ], + "unknown_refs": [] + }, + "parameter_mapping": { + "text": "Recorded occurrence: unnamed invertible-linear observation density rule.\n\nLiteral consuming expression at P lines312:\nLet pi_r(R;v_r) denote the density of U_r at (3.3). Since U_r=T_r O_r,\n\nAdditional supplier-to-consumer substitutions beyond this retained wording/expression are unexpanded in this companion; no extra map is inferred.", + "source_refs": [ + { + "source_id": "P", + "lines": [ + 312, + 312 + ], + "locator": "P lines312", + "precision": "exact_lines" + } + ], + "record_refs": [ + { + "record_id": "R6049443374", + "locator": "B01/U01.2" + } + ], + "unknown_refs": [] + }, + "context": { + "text": "Recorded owning-block description: Defines π_r; leads to (10.1). Earlier P proof imported/unexpanded.", + "source_refs": [ + { + "source_id": "P", + "lines": [ + 312, + 312 + ], + "locator": "P lines312", + "precision": "exact_lines" + } + ], + "record_refs": [ + { + "record_id": "R6049443374", + "locator": "### B01 — P lines312" + } + ], + "unknown_refs": [] + }, + "source_reading": [] + }, + "provenance": [ + { + "record_id": "R6049443374", + "locator": "B01/U01.2" + } + ], + "applicability_reviews": [], + "unknown_refs": [] + }, + { + "id": "U01.3", + "kind": "premise", + "binding": { + "consumer_statement_id": "UNIFORM-MATRIX-CAP-LIFETIME-20260924-v1::Theorem-C", + "consumer_unit_id": "B01", + "consumer_source": { + "source_id": "P", + "lines": [ + 312, + 312 + ], + "locator": "P lines312", + "precision": "exact_lines" + }, + "supplier_ids": [ + "S-U01.3-P" + ], + "claimed_interface": { + "text": "P3(3.2) exact determinant", + "source_refs": [], + "record_refs": [ + { + "record_id": "R6049640627", + "locator": "paragraph beginning \"I accept A1–A6 as proposed additive uses\" / U01.3" + } + ], + "unknown_refs": [] + }, + "parameter_mapping": { + "text": "Recorded occurrence: P3(3.2) exact determinant\n\nLiteral consuming expression at P lines312:\nLet pi_r(R;v_r) denote the density of U_r at (3.3). Since U_r=T_r O_r,\n\nAdditional supplier-to-consumer substitutions beyond this retained wording/expression are unexpanded in this companion; no extra map is inferred.", + "source_refs": [ + { + "source_id": "P", + "lines": [ + 312, + 312 + ], + "locator": "P lines312", + "precision": "exact_lines" + } + ], + "record_refs": [ + { + "record_id": "R6049640627", + "locator": "paragraph beginning \"I accept A1–A6 as proposed additive uses\" / U01.3" + } + ], + "unknown_refs": [] + }, + "context": { + "text": "Recorded owning-block description: Defines π_r; leads to (10.1). Earlier P proof imported/unexpanded.", + "source_refs": [ + { + "source_id": "P", + "lines": [ + 312, + 312 + ], + "locator": "P lines312", + "precision": "exact_lines" + } + ], + "record_refs": [ + { + "record_id": "R6049443374", + "locator": "### B01 — P lines312" + } + ], + "unknown_refs": [] + }, + "source_reading": [] + }, + "provenance": [ + { + "record_id": "R6049640627", + "locator": "paragraph beginning \"I accept A1–A6 as proposed additive uses\" / U01.3" + }, + { + "record_id": "R6049548422", + "locator": "2. Input-use challenges (instruction 2): additive amendments / A1" + } + ], + "applicability_reviews": [], + "unknown_refs": [] + } + ], + "premise_groups": [ + { + "id": "G-B01", + "combination": "ALL", + "conclusion": "B02", + "premise_use_ids": [ + "U01.1", + "U01.2", + "U01.3" + ], + "basis": [ + { + "record_id": "R6049443374", + "locator": "### B01 — P lines312" + }, + { + "record_id": "R6054305355", + "locator": "## COMPLETE / own RELEASE — P-C candidate kinds and group table" + } + ] + } + ], + "related_unit_ids": [] + }, + { + "id": "B02", + "source": { + "source_id": "P", + "lines": [ + 314, + 315 + ], + "locator": "P lines314–315", + "precision": "exact_lines" + }, + "section": 10, + "description": { + "text": "(10.1) conclusion; parent uses are B01 and P §3 det T_r. This display is not a second derivation.", + "source_refs": [ + { + "source_id": "P", + "lines": [ + 314, + 315 + ], + "locator": "P lines314–315", + "precision": "exact_lines" + } + ], + "record_refs": [ + { + "record_id": "R6049443374", + "locator": "### B02 — P lines314–315" + } + ], + "unknown_refs": [] + }, + "uses": [], + "premise_groups": [], + "related_unit_ids": [] + }, + { + "id": "B03", + "source": { + "source_id": "P", + "lines": [ + 317, + 317 + ], + "locator": "P lines317", + "precision": "exact_lines" + }, + "section": 10, + "description": { + "text": "Four distinct factor uses. No probability-normalized sphere or 1/2 factor.", + "source_refs": [ + { + "source_id": "P", + "lines": [ + 317, + 317 + ], + "locator": "P lines317", + "precision": "exact_lines" + } + ], + "record_refs": [ + { + "record_id": "R6049443374", + "locator": "### B03 — P lines317" + } + ], + "unknown_refs": [] + }, + "uses": [ + { + "id": "U03.1", + "kind": "premise", + "binding": { + "consumer_statement_id": "UNIFORM-MATRIX-CAP-LIFETIME-20260924-v1::Theorem-C", + "consumer_unit_id": "B03", + "consumer_source": { + "source_id": "P", + "lines": [ + 317, + 317 + ], + "locator": "P lines317", + "precision": "exact_lines" + }, + "supplier_ids": [ + "S-U03.1-UNNAMED" + ], + "claimed_interface": { + "text": "unnamed midpoint/ordered-separation linear Jacobian=1.", + "source_refs": [], + "record_refs": [ + { + "record_id": "R6049443374", + "locator": "B03/U03.1" + } + ], + "unknown_refs": [] + }, + "parameter_mapping": { + "text": "Recorded occurrence: unnamed midpoint/ordered-separation linear Jacobian=1.\n\nLiteral consuming expression at P lines317:\nUse midpoint z, directed separation h=r u, birth b, and gap mark k. The change from the ordered pair (M,S) to (z,h) has absolute determinant one. Polar separation contributes r^(d-1) dr d sigma(u), where sigma is ordinary, NOT probability-normalized, surface area on S^(d-1). The height change (f(M),f(S))=(b,b-k r^3), at fixed r, contributes r^3 db dk. There is no factor 1/2: maximum/saddle pairs are ordered by their different roles.\n\nAdditional supplier-to-consumer substitutions beyond this retained wording/expression are unexpanded in this companion; no extra map is inferred.", + "source_refs": [ + { + "source_id": "P", + "lines": [ + 317, + 317 + ], + "locator": "P lines317", + "precision": "exact_lines" + } + ], + "record_refs": [ + { + "record_id": "R6049443374", + "locator": "B03/U03.1" + } + ], + "unknown_refs": [] + }, + "context": { + "text": "Recorded owning-block description: Four distinct factor uses. No probability-normalized sphere or 1/2 factor.", + "source_refs": [ + { + "source_id": "P", + "lines": [ + 317, + 317 + ], + "locator": "P lines317", + "precision": "exact_lines" + } + ], + "record_refs": [ + { + "record_id": "R6049443374", + "locator": "### B03 — P lines317" + } + ], + "unknown_refs": [] + }, + "source_reading": [] + }, + "provenance": [ + { + "record_id": "R6049443374", + "locator": "B03/U03.1" + } + ], + "applicability_reviews": [], + "unknown_refs": [] + }, + { + "id": "U03.2", + "kind": "premise", + "binding": { + "consumer_statement_id": "UNIFORM-MATRIX-CAP-LIFETIME-20260924-v1::Theorem-C", + "consumer_unit_id": "B03", + "consumer_source": { + "source_id": "P", + "lines": [ + 317, + 317 + ], + "locator": "P lines317", + "precision": "exact_lines" + }, + "supplier_ids": [ + "S-U03.2-UNNAMED" + ], + "claimed_interface": { + "text": "unnamed Euclidean polar Jacobian with ordinary dσ.", + "source_refs": [], + "record_refs": [ + { + "record_id": "R6049443374", + "locator": "B03/U03.2" + } + ], + "unknown_refs": [] + }, + "parameter_mapping": { + "text": "Recorded occurrence: unnamed Euclidean polar Jacobian with ordinary dσ.\n\nLiteral consuming expression at P lines317:\nUse midpoint z, directed separation h=r u, birth b, and gap mark k. The change from the ordered pair (M,S) to (z,h) has absolute determinant one. Polar separation contributes r^(d-1) dr d sigma(u), where sigma is ordinary, NOT probability-normalized, surface area on S^(d-1). The height change (f(M),f(S))=(b,b-k r^3), at fixed r, contributes r^3 db dk. There is no factor 1/2: maximum/saddle pairs are ordered by their different roles.\n\nAdditional supplier-to-consumer substitutions beyond this retained wording/expression are unexpanded in this companion; no extra map is inferred.", + "source_refs": [ + { + "source_id": "P", + "lines": [ + 317, + 317 + ], + "locator": "P lines317", + "precision": "exact_lines" + } + ], + "record_refs": [ + { + "record_id": "R6049443374", + "locator": "B03/U03.2" + } + ], + "unknown_refs": [] + }, + "context": { + "text": "Recorded owning-block description: Four distinct factor uses. No probability-normalized sphere or 1/2 factor.", + "source_refs": [ + { + "source_id": "P", + "lines": [ + 317, + 317 + ], + "locator": "P lines317", + "precision": "exact_lines" + } + ], + "record_refs": [ + { + "record_id": "R6049443374", + "locator": "### B03 — P lines317" + } + ], + "unknown_refs": [] + }, + "source_reading": [] + }, + "provenance": [ + { + "record_id": "R6049443374", + "locator": "B03/U03.2" + } + ], + "applicability_reviews": [], + "unknown_refs": [] + }, + { + "id": "U03.3", + "kind": "premise", + "binding": { + "consumer_statement_id": "UNIFORM-MATRIX-CAP-LIFETIME-20260924-v1::Theorem-C", + "consumer_unit_id": "B03", + "consumer_source": { + "source_id": "P", + "lines": [ + 317, + 317 + ], + "locator": "P lines317", + "precision": "exact_lines" + }, + "supplier_ids": [ + "S-U03.3-UNNAMED" + ], + "claimed_interface": { + "text": "height-mark map (b,b−kr³) Jacobian r³.", + "source_refs": [], + "record_refs": [ + { + "record_id": "R6049443374", + "locator": "B03/U03.3" + } + ], + "unknown_refs": [] + }, + "parameter_mapping": { + "text": "Recorded occurrence: height-mark map (b,b−kr³) Jacobian r³.\n\nLiteral consuming expression at P lines317:\nUse midpoint z, directed separation h=r u, birth b, and gap mark k. The change from the ordered pair (M,S) to (z,h) has absolute determinant one. Polar separation contributes r^(d-1) dr d sigma(u), where sigma is ordinary, NOT probability-normalized, surface area on S^(d-1). The height change (f(M),f(S))=(b,b-k r^3), at fixed r, contributes r^3 db dk. There is no factor 1/2: maximum/saddle pairs are ordered by their different roles.\n\nAdditional supplier-to-consumer substitutions beyond this retained wording/expression are unexpanded in this companion; no extra map is inferred.", + "source_refs": [ + { + "source_id": "P", + "lines": [ + 317, + 317 + ], + "locator": "P lines317", + "precision": "exact_lines" + } + ], + "record_refs": [ + { + "record_id": "R6049443374", + "locator": "B03/U03.3" + } + ], + "unknown_refs": [] + }, + "context": { + "text": "Recorded owning-block description: Four distinct factor uses. No probability-normalized sphere or 1/2 factor.", + "source_refs": [ + { + "source_id": "P", + "lines": [ + 317, + 317 + ], + "locator": "P lines317", + "precision": "exact_lines" + } + ], + "record_refs": [ + { + "record_id": "R6049443374", + "locator": "### B03 — P lines317" + } + ], + "unknown_refs": [] + }, + "source_reading": [] + }, + "provenance": [ + { + "record_id": "R6049443374", + "locator": "B03/U03.3" + } + ], + "applicability_reviews": [], + "unknown_refs": [] + }, + { + "id": "U03.4", + "kind": "premise", + "binding": { + "consumer_statement_id": "UNIFORM-MATRIX-CAP-LIFETIME-20260924-v1::Theorem-C", + "consumer_unit_id": "B03", + "consumer_source": { + "source_id": "P", + "lines": [ + 317, + 317 + ], + "locator": "P lines317", + "precision": "exact_lines" + }, + "supplier_ids": [ + "S-U03.4-P" + ], + "claimed_interface": { + "text": "P §1: maximum/saddle roles are ordered.", + "source_refs": [], + "record_refs": [ + { + "record_id": "R6049443374", + "locator": "B03/U03.4" + } + ], + "unknown_refs": [] + }, + "parameter_mapping": { + "text": "Recorded occurrence: P §1: maximum/saddle roles are ordered.\n\nLiteral consuming expression at P lines317:\nUse midpoint z, directed separation h=r u, birth b, and gap mark k. The change from the ordered pair (M,S) to (z,h) has absolute determinant one. Polar separation contributes r^(d-1) dr d sigma(u), where sigma is ordinary, NOT probability-normalized, surface area on S^(d-1). The height change (f(M),f(S))=(b,b-k r^3), at fixed r, contributes r^3 db dk. There is no factor 1/2: maximum/saddle pairs are ordered by their different roles.\n\nAdditional supplier-to-consumer substitutions beyond this retained wording/expression are unexpanded in this companion; no extra map is inferred.", + "source_refs": [ + { + "source_id": "P", + "lines": [ + 317, + 317 + ], + "locator": "P lines317", + "precision": "exact_lines" + } + ], + "record_refs": [ + { + "record_id": "R6049443374", + "locator": "B03/U03.4" + } + ], + "unknown_refs": [] + }, + "context": { + "text": "Recorded owning-block description: Four distinct factor uses. No probability-normalized sphere or 1/2 factor.", + "source_refs": [ + { + "source_id": "P", + "lines": [ + 317, + 317 + ], + "locator": "P lines317", + "precision": "exact_lines" + } + ], + "record_refs": [ + { + "record_id": "R6049443374", + "locator": "### B03 — P lines317" + } + ], + "unknown_refs": [] + }, + "source_reading": [] + }, + "provenance": [ + { + "record_id": "R6049443374", + "locator": "B03/U03.4" + } + ], + "applicability_reviews": [], + "unknown_refs": [] + } + ], + "premise_groups": [ + { + "id": "G-B03", + "combination": "ALL", + "conclusion": "B03", + "premise_use_ids": [ + "U03.1", + "U03.2", + "U03.3", + "U03.4" + ], + "basis": [ + { + "record_id": "R6049443374", + "locator": "### B03 — P lines317" + }, + { + "record_id": "R6054305355", + "locator": "## COMPLETE / own RELEASE — P-C candidate kinds and group table" + } + ] + } + ], + "related_unit_ids": [] + }, + { + "id": "B04", + "source": { + "source_id": "P", + "lines": [ + 319, + 319 + ], + "locator": "P lines319", + "precision": "exact_lines" + }, + "section": 10, + "description": { + "text": "Claimed candidate intensity per midpoint volume; formula follows in B05.", + "source_refs": [ + { + "source_id": "P", + "lines": [ + 319, + 319 + ], + "locator": "P lines319", + "precision": "exact_lines" + } + ], + "record_refs": [ + { + "record_id": "R6049443374", + "locator": "### B04 — P lines319" + } + ], + "unknown_refs": [] + }, + "uses": [ + { + "id": "U04.1", + "kind": "premise", + "binding": { + "consumer_statement_id": "UNIFORM-MATRIX-CAP-LIFETIME-20260924-v1::Theorem-C", + "consumer_unit_id": "B04", + "consumer_source": { + "source_id": "P", + "lines": [ + 319, + 319 + ], + "locator": "P lines319", + "precision": "exact_lines" + }, + "supplier_ids": [ + "S-U04.1-E2" + ], + "claimed_interface": { + "text": "E2 §9.4: candidate marked pair Kac–Rice with full determinant weight.", + "source_refs": [], + "record_refs": [ + { + "record_id": "R6049443374", + "locator": "B04/U04.1" + } + ], + "unknown_refs": [ + "UNKNOWN-U2" + ] + }, + "parameter_mapping": { + "text": "Recorded occurrence: E2 §9.4: candidate marked pair Kac–Rice with full determinant weight.\n\nLiteral consuming expression at P lines319:\nConsequently the candidate intensity per unit midpoint volume is\n\nAdditional supplier-to-consumer substitutions beyond this retained wording/expression are unexpanded in this companion; no extra map is inferred.", + "source_refs": [ + { + "source_id": "P", + "lines": [ + 319, + 319 + ], + "locator": "P lines319", + "precision": "exact_lines" + } + ], + "record_refs": [ + { + "record_id": "R6049443374", + "locator": "B04/U04.1" + } + ], + "unknown_refs": [ + "UNKNOWN-U2" + ] + }, + "context": { + "text": "Recorded owning-block description: Claimed candidate intensity per midpoint volume; formula follows in B05.\n\nSource-attributed reading/scope qualifications:\nE2 §9.4 uses the actual global elder/type Borel mark, the full-pin density and one determinant product weight W_r; there is no second determinant factor or local-cap substitution for the global mark. Its external Armentano–Azaïs–León base remains imported/unexpanded. The near-diagonal exhaustion at E2:110 imports P §§3/5/10 estimates rather than reproving them; the remaining off-diagonal/unbounded-mark/coefficient obligations are separate.\n\nThe historical N2 observation records both the E2 §9.4 consumption and its import of P §§3/5/10. The source asserts the P10 bound from P3/5; those earlier sections are unexpanded here. No noncircularity or present applicability verdict is added.\n\nReferenced UNKNOWN annotations retain their historical observation/response scope; they are not current failure or acceptance verdicts.", + "source_refs": [ + { + "source_id": "P", + "lines": [ + 319, + 319 + ], + "locator": "P lines319", + "precision": "exact_lines" + }, + { + "source_id": "E2", + "lines": [ + 94, + 110 + ], + "locator": "§9.4 global elder/type mark and imported diagonal exhaustion", + "precision": "exact_lines" + }, + { + "source_id": "E2", + "lines": [ + 121, + 131 + ], + "locator": "Separate obligations retained by E2", + "precision": "exact_lines" + }, + { + "source_id": "E2", + "lines": [ + 110, + 110 + ], + "locator": "Imported parent estimates in near-diagonal exhaustion", + "precision": "exact_lines" + } + ], + "record_refs": [ + { + "record_id": "R6049443374", + "locator": "### B04 — P lines319" + }, + { + "record_id": "R6049548422", + "locator": "4. Consumption boundaries / E2" + }, + { + "record_id": "R6057972030", + "locator": "Exact arrays for the existing ReadingBoundary fields / E2 row; Source reasons and limits / E2" + }, + { + "record_id": "R6049548422", + "locator": "4. Consumption boundaries / E2 / (b) N2" + }, + { + "record_id": "R6049640627", + "locator": "U2" + } + ], + "unknown_refs": [ + "UNKNOWN-U2", + "UNKNOWN-U4" + ] + }, + "source_reading": [ + { + "boundary_id": "READ-E2", + "supplier_ids": [ + "S-U04.1-E2" + ], + "applies_to": [ + { + "source_id": "E2", + "lines": [ + 94, + 110 + ], + "locator": "§9.4 global elder/type mark and imported diagonal exhaustion", + "precision": "exact_lines" + }, + { + "source_id": "E2", + "lines": [ + 121, + 131 + ], + "locator": "Separate obligations retained by E2", + "precision": "exact_lines" + } + ], + "explanation": { + "text": "E2 §9.4 uses the actual global elder/type Borel mark, the full-pin density and one determinant product weight W_r; there is no second determinant factor or local-cap substitution for the global mark. Its external Armentano–Azaïs–León base remains imported/unexpanded. The near-diagonal exhaustion at E2:110 imports P §§3/5/10 estimates rather than reproving them; the remaining off-diagonal/unbounded-mark/coefficient obligations are separate.", + "source_refs": [ + { + "source_id": "E2", + "lines": [ + 94, + 110 + ], + "locator": "§9.4 global elder/type mark and imported diagonal exhaustion", + "precision": "exact_lines" + }, + { + "source_id": "E2", + "lines": [ + 121, + 131 + ], + "locator": "Separate obligations retained by E2", + "precision": "exact_lines" + } + ], + "record_refs": [ + { + "record_id": "R6049548422", + "locator": "4. Consumption boundaries / E2" + }, + { + "record_id": "R6057972030", + "locator": "Exact arrays for the existing ReadingBoundary fields / E2 row; Source reasons and limits / E2" + } + ], + "unknown_refs": [ + "UNKNOWN-U4" + ] + } + }, + { + "boundary_id": "READ-E2", + "supplier_ids": [ + "S-U04.1-E2" + ], + "applies_to": [ + { + "source_id": "E2", + "lines": [ + 110, + 110 + ], + "locator": "Imported parent estimates in near-diagonal exhaustion", + "precision": "exact_lines" + } + ], + "explanation": { + "text": "The historical N2 observation records both the E2 §9.4 consumption and its import of P §§3/5/10. The source asserts the P10 bound from P3/5; those earlier sections are unexpanded here. No noncircularity or present applicability verdict is added.", + "source_refs": [ + { + "source_id": "E2", + "lines": [ + 110, + 110 + ], + "locator": "Imported parent estimates in near-diagonal exhaustion", + "precision": "exact_lines" + } + ], + "record_refs": [ + { + "record_id": "R6049548422", + "locator": "4. Consumption boundaries / E2 / (b) N2" + }, + { + "record_id": "R6049640627", + "locator": "U2" + } + ], + "unknown_refs": [ + "UNKNOWN-U2" + ] + } + } + ] + }, + "provenance": [ + { + "record_id": "R6049443374", + "locator": "B04/U04.1" + } + ], + "applicability_reviews": [], + "unknown_refs": [ + "UNKNOWN-U2", + "UNKNOWN-U4" + ] + } + ], + "premise_groups": [ + { + "id": "G-B04", + "combination": "ALL", + "conclusion": "B05", + "premise_use_ids": [ + "U04.1" + ], + "basis": [ + { + "record_id": "R6049443374", + "locator": "### B04 — P lines319" + }, + { + "record_id": "R6054305355", + "locator": "## COMPLETE / own RELEASE — P-C candidate kinds and group table" + } + ] + } + ], + "related_unit_ids": [] + }, + { + "id": "B05", + "source": { + "source_id": "P", + "lines": [ + 321, + 322 + ], + "locator": "P lines321–322", + "precision": "exact_lines" + }, + "section": 10, + "description": { + "text": "(10.2) definition/conclusion A_r=12π_r Z_r/r²; binds B01–B04, not an additional input-use.", + "source_refs": [ + { + "source_id": "P", + "lines": [ + 321, + 322 + ], + "locator": "P lines321–322", + "precision": "exact_lines" + } + ], + "record_refs": [ + { + "record_id": "R6049443374", + "locator": "### B05 — P lines321–322" + } + ], + "unknown_refs": [] + }, + "uses": [], + "premise_groups": [], + "related_unit_ids": [] + }, + { + "id": "B06", + "source": { + "source_id": "P", + "lines": [ + 324, + 324 + ], + "locator": "P lines324", + "precision": "exact_lines" + }, + "section": 10, + "description": { + "text": "Lead-in to the exponent ledger, not a separate premise.", + "source_refs": [ + { + "source_id": "P", + "lines": [ + 324, + 324 + ], + "locator": "P lines324", + "precision": "exact_lines" + } + ], + "record_refs": [ + { + "record_id": "R6049443374", + "locator": "### B06 — P lines324" + } + ], + "unknown_refs": [] + }, + "uses": [], + "premise_groups": [], + "related_unit_ids": [] + }, + { + "id": "B07", + "source": { + "source_id": "P", + "lines": [ + 326, + 327 + ], + "locator": "P lines326–327", + "precision": "exact_lines" + }, + "section": 10, + "description": { + "text": "Unnamed power-sum step yields radial exponent 1; repeated uses retained.", + "source_refs": [ + { + "source_id": "P", + "lines": [ + 326, + 327 + ], + "locator": "P lines326–327", + "precision": "exact_lines" + } + ], + "record_refs": [ + { + "record_id": "R6049443374", + "locator": "### B07 — P lines326–327" + } + ], + "unknown_refs": [] + }, + "uses": [ + { + "id": "U07.1", + "kind": "premise", + "binding": { + "consumer_statement_id": "UNIFORM-MATRIX-CAP-LIFETIME-20260924-v1::Theorem-C", + "consumer_unit_id": "B07", + "consumer_source": { + "source_id": "P", + "lines": [ + 326, + 327 + ], + "locator": "P lines326–327", + "precision": "exact_lines" + }, + "supplier_ids": [ + "S-U07.1-UNITS" + ], + "claimed_interface": { + "text": "B03 spatial exponent d−1.", + "source_refs": [], + "record_refs": [ + { + "record_id": "R6049443374", + "locator": "B07/U07.1" + } + ], + "unknown_refs": [] + }, + "parameter_mapping": { + "text": "Recorded occurrence: B03 spatial exponent d−1.\n\nLiteral consuming expression at P lines326–327:\n spatial (d-1) + height-mark 3 + pin -(d+3)\n + determinant-normalizer 2 = 1.\n\nAdditional supplier-to-consumer substitutions beyond this retained wording/expression are unexpanded in this companion; no extra map is inferred.", + "source_refs": [ + { + "source_id": "P", + "lines": [ + 326, + 327 + ], + "locator": "P lines326–327", + "precision": "exact_lines" + } + ], + "record_refs": [ + { + "record_id": "R6049443374", + "locator": "B07/U07.1" + } + ], + "unknown_refs": [] + }, + "context": { + "text": "Recorded owning-block description: Unnamed power-sum step yields radial exponent 1; repeated uses retained.", + "source_refs": [ + { + "source_id": "P", + "lines": [ + 326, + 327 + ], + "locator": "P lines326–327", + "precision": "exact_lines" + } + ], + "record_refs": [ + { + "record_id": "R6049443374", + "locator": "### B07 — P lines326–327" + } + ], + "unknown_refs": [] + }, + "source_reading": [] + }, + "provenance": [ + { + "record_id": "R6049443374", + "locator": "B07/U07.1" + } + ], + "applicability_reviews": [], + "unknown_refs": [] + }, + { + "id": "U07.2", + "kind": "premise", + "binding": { + "consumer_statement_id": "UNIFORM-MATRIX-CAP-LIFETIME-20260924-v1::Theorem-C", + "consumer_unit_id": "B07", + "consumer_source": { + "source_id": "P", + "lines": [ + 326, + 327 + ], + "locator": "P lines326–327", + "precision": "exact_lines" + }, + "supplier_ids": [ + "S-U07.2-UNITS" + ], + "claimed_interface": { + "text": "B03 height exponent 3.", + "source_refs": [], + "record_refs": [ + { + "record_id": "R6049443374", + "locator": "B07/U07.2" + } + ], + "unknown_refs": [] + }, + "parameter_mapping": { + "text": "Recorded occurrence: B03 height exponent 3.\n\nLiteral consuming expression at P lines326–327:\n spatial (d-1) + height-mark 3 + pin -(d+3)\n + determinant-normalizer 2 = 1.\n\nAdditional supplier-to-consumer substitutions beyond this retained wording/expression are unexpanded in this companion; no extra map is inferred.", + "source_refs": [ + { + "source_id": "P", + "lines": [ + 326, + 327 + ], + "locator": "P lines326–327", + "precision": "exact_lines" + } + ], + "record_refs": [ + { + "record_id": "R6049443374", + "locator": "B07/U07.2" + } + ], + "unknown_refs": [] + }, + "context": { + "text": "Recorded owning-block description: Unnamed power-sum step yields radial exponent 1; repeated uses retained.", + "source_refs": [ + { + "source_id": "P", + "lines": [ + 326, + 327 + ], + "locator": "P lines326–327", + "precision": "exact_lines" + } + ], + "record_refs": [ + { + "record_id": "R6049443374", + "locator": "### B07 — P lines326–327" + } + ], + "unknown_refs": [] + }, + "source_reading": [] + }, + "provenance": [ + { + "record_id": "R6049443374", + "locator": "B07/U07.2" + } + ], + "applicability_reviews": [], + "unknown_refs": [] + }, + { + "id": "U07.3", + "kind": "premise", + "binding": { + "consumer_statement_id": "UNIFORM-MATRIX-CAP-LIFETIME-20260924-v1::Theorem-C", + "consumer_unit_id": "B07", + "consumer_source": { + "source_id": "P", + "lines": [ + 326, + 327 + ], + "locator": "P lines326–327", + "precision": "exact_lines" + }, + "supplier_ids": [ + "S-U07.3-UNITS" + ], + "claimed_interface": { + "text": "B02 pin exponent −(d+3).", + "source_refs": [], + "record_refs": [ + { + "record_id": "R6049443374", + "locator": "B07/U07.3" + } + ], + "unknown_refs": [] + }, + "parameter_mapping": { + "text": "Recorded occurrence: B02 pin exponent −(d+3).\n\nLiteral consuming expression at P lines326–327:\n spatial (d-1) + height-mark 3 + pin -(d+3)\n + determinant-normalizer 2 = 1.\n\nAdditional supplier-to-consumer substitutions beyond this retained wording/expression are unexpanded in this companion; no extra map is inferred.", + "source_refs": [ + { + "source_id": "P", + "lines": [ + 326, + 327 + ], + "locator": "P lines326–327", + "precision": "exact_lines" + } + ], + "record_refs": [ + { + "record_id": "R6049443374", + "locator": "B07/U07.3" + } + ], + "unknown_refs": [] + }, + "context": { + "text": "Recorded owning-block description: Unnamed power-sum step yields radial exponent 1; repeated uses retained.", + "source_refs": [ + { + "source_id": "P", + "lines": [ + 326, + 327 + ], + "locator": "P lines326–327", + "precision": "exact_lines" + } + ], + "record_refs": [ + { + "record_id": "R6049443374", + "locator": "### B07 — P lines326–327" + } + ], + "unknown_refs": [] + }, + "source_reading": [] + }, + "provenance": [ + { + "record_id": "R6049443374", + "locator": "B07/U07.3" + } + ], + "applicability_reviews": [], + "unknown_refs": [] + }, + { + "id": "U07.4", + "kind": "premise", + "binding": { + "consumer_statement_id": "UNIFORM-MATRIX-CAP-LIFETIME-20260924-v1::Theorem-C", + "consumer_unit_id": "B07", + "consumer_source": { + "source_id": "P", + "lines": [ + 327, + 327 + ], + "locator": "P327: determinant-normalizer exponent", + "precision": "exact_lines" + }, + "supplier_ids": [ + "S-U07.4-UNITS", + "S-U07.4-P" + ], + "claimed_interface": { + "text": "P §5 / B05 determinant exponent 2.", + "source_refs": [], + "record_refs": [ + { + "record_id": "R6049443374", + "locator": "B07/U07.4" + } + ], + "unknown_refs": [] + }, + "parameter_mapping": { + "text": "Recorded occurrence: P §5 / B05 determinant exponent 2.\n\nLiteral consuming expression at P327: determinant-normalizer exponent:\n + determinant-normalizer 2 = 1.\n\nAdditional supplier-to-consumer substitutions beyond this retained wording/expression are unexpanded in this companion; no extra map is inferred.", + "source_refs": [ + { + "source_id": "P", + "lines": [ + 327, + 327 + ], + "locator": "P327: determinant-normalizer exponent", + "precision": "exact_lines" + } + ], + "record_refs": [ + { + "record_id": "R6049443374", + "locator": "B07/U07.4" + } + ], + "unknown_refs": [] + }, + "context": { + "text": "Recorded owning-block description: Unnamed power-sum step yields radial exponent 1; repeated uses retained.", + "source_refs": [ + { + "source_id": "P", + "lines": [ + 326, + 327 + ], + "locator": "P lines326–327", + "precision": "exact_lines" + } + ], + "record_refs": [ + { + "record_id": "R6049443374", + "locator": "### B07 — P lines326–327" + } + ], + "unknown_refs": [] + }, + "source_reading": [] + }, + "provenance": [ + { + "record_id": "R6049443374", + "locator": "B07/U07.4" + } + ], + "applicability_reviews": [], + "unknown_refs": [] + } + ], + "premise_groups": [ + { + "id": "G-B07", + "combination": "ALL", + "conclusion": "B07", + "premise_use_ids": [ + "U07.1", + "U07.2", + "U07.3", + "U07.4" + ], + "basis": [ + { + "record_id": "R6049443374", + "locator": "### B07 — P lines326–327" + }, + { + "record_id": "R6054305355", + "locator": "## COMPLETE / own RELEASE — P-C candidate kinds and group table" + } + ] + } + ], + "related_unit_ids": [] + }, + { + "id": "B08", + "source": { + "source_id": "P", + "lines": [ + 329, + 329 + ], + "locator": "P lines329", + "precision": "exact_lines" + }, + "section": 10, + "description": { + "text": "Explicit earlier-section import pair.", + "source_refs": [ + { + "source_id": "P", + "lines": [ + 329, + 329 + ], + "locator": "P lines329", + "precision": "exact_lines" + } + ], + "record_refs": [ + { + "record_id": "R6049443374", + "locator": "### B08 — P lines329" + } + ], + "unknown_refs": [] + }, + "uses": [ + { + "id": "U08.1", + "kind": "premise", + "binding": { + "consumer_statement_id": "UNIFORM-MATRIX-CAP-LIFETIME-20260924-v1::Theorem-C", + "consumer_unit_id": "B08", + "consumer_source": { + "source_id": "P", + "lines": [ + 329, + 329 + ], + "locator": "P lines329", + "precision": "exact_lines" + }, + "supplier_ids": [ + "S-U08.1-P" + ], + "claimed_interface": { + "text": "P §3: uniform nonsingular contact limit.", + "source_refs": [], + "record_refs": [ + { + "record_id": "R6049443374", + "locator": "B08/U08.1" + } + ], + "unknown_refs": [] + }, + "parameter_mapping": { + "text": "Recorded occurrence: P §3: uniform nonsingular contact limit.\n\nLiteral consuming expression at P lines329:\nBy Sections 3 and 5,\n\nAdditional supplier-to-consumer substitutions beyond this retained wording/expression are unexpanded in this companion; no extra map is inferred.", + "source_refs": [ + { + "source_id": "P", + "lines": [ + 329, + 329 + ], + "locator": "P lines329", + "precision": "exact_lines" + } + ], + "record_refs": [ + { + "record_id": "R6049443374", + "locator": "B08/U08.1" + } + ], + "unknown_refs": [] + }, + "context": { + "text": "Recorded owning-block description: Explicit earlier-section import pair.", + "source_refs": [ + { + "source_id": "P", + "lines": [ + 329, + 329 + ], + "locator": "P lines329", + "precision": "exact_lines" + } + ], + "record_refs": [ + { + "record_id": "R6049443374", + "locator": "### B08 — P lines329" + } + ], + "unknown_refs": [] + }, + "source_reading": [] + }, + "provenance": [ + { + "record_id": "R6049443374", + "locator": "B08/U08.1" + } + ], + "applicability_reviews": [], + "unknown_refs": [] + }, + { + "id": "U08.2", + "kind": "premise", + "binding": { + "consumer_statement_id": "UNIFORM-MATRIX-CAP-LIFETIME-20260924-v1::Theorem-C", + "consumer_unit_id": "B08", + "consumer_source": { + "source_id": "P", + "lines": [ + 329, + 329 + ], + "locator": "P lines329", + "precision": "exact_lines" + }, + "supplier_ids": [ + "S-U08.2-P" + ], + "claimed_interface": { + "text": "P §5: typed full-normalizer limit (read E1+REC W1).", + "source_refs": [], + "record_refs": [ + { + "record_id": "R6049443374", + "locator": "B08/U08.2" + } + ], + "unknown_refs": [] + }, + "parameter_mapping": { + "text": "Recorded occurrence: P §5: typed full-normalizer limit (read E1+REC W1).\n\nLiteral consuming expression at P lines329:\nBy Sections 3 and 5,\n\nAdditional supplier-to-consumer substitutions beyond this retained wording/expression are unexpanded in this companion; no extra map is inferred.", + "source_refs": [ + { + "source_id": "P", + "lines": [ + 329, + 329 + ], + "locator": "P lines329", + "precision": "exact_lines" + } + ], + "record_refs": [ + { + "record_id": "R6049443374", + "locator": "B08/U08.2" + } + ], + "unknown_refs": [] + }, + "context": { + "text": "Recorded owning-block description: Explicit earlier-section import pair.\n\nSource-attributed reading/scope qualifications:\nE1 is a reading correction to P §5, not an additional probability result or counted premise. Read the Hessian congruence as D_r=diag(r^(-1/2),I), with det(D_r H_i D_r)=det(H_i)/r.\n\nREC W1 distinguishes the vanishing correction in probability from A_M converging in law; the joint limit is in law via Slutsky and continuous mapping off the determinant-zero null set. No common-space convergence in probability to the limiting A_0 is asserted here.", + "source_refs": [ + { + "source_id": "P", + "lines": [ + 329, + 329 + ], + "locator": "P lines329", + "precision": "exact_lines" + }, + { + "source_id": "E1", + "lines": [ + 21, + 40 + ], + "locator": "Corrected congruence and normalization", + "precision": "exact_lines" + }, + { + "source_id": "REC", + "lines": [ + 153, + 161 + ], + "locator": "W1 convergence-in-law wording correction", + "precision": "exact_lines" + } + ], + "record_refs": [ + { + "record_id": "R6049443374", + "locator": "### B08 — P lines329" + }, + { + "record_id": "R6049548422", + "locator": "4. Consumption boundaries / E1" + }, + { + "record_id": "R6053473777", + "locator": "Source-bound decision table / 4. Reading boundary" + }, + { + "record_id": "R6049548422", + "locator": "3. Applicability / Typed/full normalizer" + } + ], + "unknown_refs": [] + }, + "source_reading": [ + { + "boundary_id": "READ-E1", + "supplier_ids": [ + "S-U08.2-P" + ], + "applies_to": [ + { + "source_id": "E1", + "lines": [ + 21, + 40 + ], + "locator": "Corrected congruence and normalization", + "precision": "exact_lines" + } + ], + "explanation": { + "text": "E1 is a reading correction to P §5, not an additional probability result or counted premise. Read the Hessian congruence as D_r=diag(r^(-1/2),I), with det(D_r H_i D_r)=det(H_i)/r.", + "source_refs": [ + { + "source_id": "E1", + "lines": [ + 21, + 40 + ], + "locator": "Corrected congruence and normalization", + "precision": "exact_lines" + } + ], + "record_refs": [ + { + "record_id": "R6049548422", + "locator": "4. Consumption boundaries / E1" + }, + { + "record_id": "R6053473777", + "locator": "Source-bound decision table / 4. Reading boundary" + } + ], + "unknown_refs": [] + } + }, + { + "boundary_id": "READ-REC", + "supplier_ids": [ + "S-U08.2-P" + ], + "applies_to": [ + { + "source_id": "REC", + "lines": [ + 153, + 161 + ], + "locator": "W1 convergence-in-law wording correction", + "precision": "exact_lines" + } + ], + "explanation": { + "text": "REC W1 distinguishes the vanishing correction in probability from A_M converging in law; the joint limit is in law via Slutsky and continuous mapping off the determinant-zero null set. No common-space convergence in probability to the limiting A_0 is asserted here.", + "source_refs": [ + { + "source_id": "REC", + "lines": [ + 153, + 161 + ], + "locator": "W1 convergence-in-law wording correction", + "precision": "exact_lines" + } + ], + "record_refs": [ + { + "record_id": "R6049548422", + "locator": "3. Applicability / Typed/full normalizer" + }, + { + "record_id": "R6053473777", + "locator": "Source-bound decision table / 4. Reading boundary" + } + ], + "unknown_refs": [] + } + } + ] + }, + "provenance": [ + { + "record_id": "R6049443374", + "locator": "B08/U08.2" + } + ], + "applicability_reviews": [], + "unknown_refs": [] + } + ], + "premise_groups": [ + { + "id": "G-B08", + "combination": "ALL", + "conclusion": "B09", + "premise_use_ids": [ + "U08.1", + "U08.2" + ], + "basis": [ + { + "record_id": "R6049443374", + "locator": "### B08 — P lines329" + }, + { + "record_id": "R6054305355", + "locator": "## COMPLETE / own RELEASE — P-C candidate kinds and group table" + } + ] + } + ], + "related_unit_ids": [] + }, + { + "id": "B09", + "source": { + "source_id": "P", + "lines": [ + 331, + 331 + ], + "locator": "P lines331", + "precision": "exact_lines" + }, + "section": 10, + "description": { + "text": "(10.3) positive contact A_0 conclusion paired with B08.", + "source_refs": [ + { + "source_id": "P", + "lines": [ + 331, + 331 + ], + "locator": "P lines331", + "precision": "exact_lines" + } + ], + "record_refs": [ + { + "record_id": "R6049443374", + "locator": "### B09 — P lines331" + } + ], + "unknown_refs": [] + }, + "uses": [], + "premise_groups": [], + "related_unit_ids": [] + }, + { + "id": "B10", + "source": { + "source_id": "P", + "lines": [ + 333, + 333 + ], + "locator": "P lines333", + "precision": "exact_lines" + }, + "section": 10, + "description": { + "text": "Unnamed descent to u/sphere; does not posit a global continuous transverse frame.", + "source_refs": [ + { + "source_id": "P", + "lines": [ + 333, + 333 + ], + "locator": "P lines333", + "precision": "exact_lines" + } + ], + "record_refs": [ + { + "record_id": "R6049443374", + "locator": "### B10 — P lines333" + } + ], + "unknown_refs": [] + }, + "uses": [ + { + "id": "U10.1", + "kind": "premise", + "binding": { + "consumer_statement_id": "UNIFORM-MATRIX-CAP-LIFETIME-20260924-v1::Theorem-C", + "consumer_unit_id": "B10", + "consumer_source": { + "source_id": "P", + "lines": [ + 333, + 333 + ], + "locator": "P lines333", + "precision": "exact_lines" + }, + "supplier_ids": [ + "S-U10.1-UNITS" + ], + "claimed_interface": { + "text": "B08–B09: compact-target uniform convergence/bound.", + "source_refs": [], + "record_refs": [ + { + "record_id": "R6049443374", + "locator": "B10/U10.1" + } + ], + "unknown_refs": [] + }, + "parameter_mapping": { + "text": "Recorded occurrence: B08–B09: compact-target uniform convergence/bound.\n\nLiteral consuming expression at P lines333:\nuniformly and with a uniform finite upper bound. Although frames were used in the proof, (10.2) is invariant under a rotation of the transverse frame: the original zero-gradient law and determinant weight are unchanged by that orthogonal coordinate change. Thus it is a function of u alone. Uniformity was proved on the compact orthogonal group and descends to the sphere; no nonexistent global continuous transverse frame on the sphere is assumed.\n\nAdditional supplier-to-consumer substitutions beyond this retained wording/expression are unexpanded in this companion; no extra map is inferred.", + "source_refs": [ + { + "source_id": "P", + "lines": [ + 333, + 333 + ], + "locator": "P lines333", + "precision": "exact_lines" + } + ], + "record_refs": [ + { + "record_id": "R6049443374", + "locator": "B10/U10.1" + } + ], + "unknown_refs": [] + }, + "context": { + "text": "Recorded owning-block description: Unnamed descent to u/sphere; does not posit a global continuous transverse frame.", + "source_refs": [ + { + "source_id": "P", + "lines": [ + 333, + 333 + ], + "locator": "P lines333", + "precision": "exact_lines" + } + ], + "record_refs": [ + { + "record_id": "R6049443374", + "locator": "### B10 — P lines333" + } + ], + "unknown_refs": [] + }, + "source_reading": [] + }, + "provenance": [ + { + "record_id": "R6049443374", + "locator": "B10/U10.1" + } + ], + "applicability_reviews": [], + "unknown_refs": [] + }, + { + "id": "U10.2", + "kind": "premise", + "binding": { + "consumer_statement_id": "UNIFORM-MATRIX-CAP-LIFETIME-20260924-v1::Theorem-C", + "consumer_unit_id": "B10", + "consumer_source": { + "source_id": "P", + "lines": [ + 333, + 333 + ], + "locator": "P lines333", + "precision": "exact_lines" + }, + "supplier_ids": [ + "S-U10.2-UNNAMED" + ], + "claimed_interface": { + "text": "orthogonal transverse-frame invariance of zero-gradient law and determinant weight.", + "source_refs": [], + "record_refs": [ + { + "record_id": "R6049443374", + "locator": "B10/U10.2" + } + ], + "unknown_refs": [] + }, + "parameter_mapping": { + "text": "Recorded occurrence: orthogonal transverse-frame invariance of zero-gradient law and determinant weight.\n\nLiteral consuming expression at P lines333:\nuniformly and with a uniform finite upper bound. Although frames were used in the proof, (10.2) is invariant under a rotation of the transverse frame: the original zero-gradient law and determinant weight are unchanged by that orthogonal coordinate change. Thus it is a function of u alone. Uniformity was proved on the compact orthogonal group and descends to the sphere; no nonexistent global continuous transverse frame on the sphere is assumed.\n\nAdditional supplier-to-consumer substitutions beyond this retained wording/expression are unexpanded in this companion; no extra map is inferred.", + "source_refs": [ + { + "source_id": "P", + "lines": [ + 333, + 333 + ], + "locator": "P lines333", + "precision": "exact_lines" + } + ], + "record_refs": [ + { + "record_id": "R6049443374", + "locator": "B10/U10.2" + } + ], + "unknown_refs": [] + }, + "context": { + "text": "Recorded owning-block description: Unnamed descent to u/sphere; does not posit a global continuous transverse frame.", + "source_refs": [ + { + "source_id": "P", + "lines": [ + 333, + 333 + ], + "locator": "P lines333", + "precision": "exact_lines" + } + ], + "record_refs": [ + { + "record_id": "R6049443374", + "locator": "### B10 — P lines333" + } + ], + "unknown_refs": [] + }, + "source_reading": [] + }, + "provenance": [ + { + "record_id": "R6049443374", + "locator": "B10/U10.2" + } + ], + "applicability_reviews": [], + "unknown_refs": [] + }, + { + "id": "U10.3", + "kind": "premise", + "binding": { + "consumer_statement_id": "UNIFORM-MATRIX-CAP-LIFETIME-20260924-v1::Theorem-C", + "consumer_unit_id": "B10", + "consumer_source": { + "source_id": "P", + "lines": [ + 333, + 333 + ], + "locator": "P lines333", + "precision": "exact_lines" + }, + "supplier_ids": [ + "S-U10.3-P" + ], + "claimed_interface": { + "text": "P §3: compact O(d) uniformity.", + "source_refs": [], + "record_refs": [ + { + "record_id": "R6049443374", + "locator": "B10/U10.3" + } + ], + "unknown_refs": [] + }, + "parameter_mapping": { + "text": "Recorded occurrence: P §3: compact O(d) uniformity.\n\nLiteral consuming expression at P lines333:\nuniformly and with a uniform finite upper bound. Although frames were used in the proof, (10.2) is invariant under a rotation of the transverse frame: the original zero-gradient law and determinant weight are unchanged by that orthogonal coordinate change. Thus it is a function of u alone. Uniformity was proved on the compact orthogonal group and descends to the sphere; no nonexistent global continuous transverse frame on the sphere is assumed.\n\nAdditional supplier-to-consumer substitutions beyond this retained wording/expression are unexpanded in this companion; no extra map is inferred.", + "source_refs": [ + { + "source_id": "P", + "lines": [ + 333, + 333 + ], + "locator": "P lines333", + "precision": "exact_lines" + } + ], + "record_refs": [ + { + "record_id": "R6049443374", + "locator": "B10/U10.3" + } + ], + "unknown_refs": [] + }, + "context": { + "text": "Recorded owning-block description: Unnamed descent to u/sphere; does not posit a global continuous transverse frame.", + "source_refs": [ + { + "source_id": "P", + "lines": [ + 333, + 333 + ], + "locator": "P lines333", + "precision": "exact_lines" + } + ], + "record_refs": [ + { + "record_id": "R6049443374", + "locator": "### B10 — P lines333" + } + ], + "unknown_refs": [] + }, + "source_reading": [] + }, + "provenance": [ + { + "record_id": "R6049443374", + "locator": "B10/U10.3" + } + ], + "applicability_reviews": [], + "unknown_refs": [] + } + ], + "premise_groups": [ + { + "id": "G-B10", + "combination": "ALL", + "conclusion": "B10", + "premise_use_ids": [ + "U10.1", + "U10.2", + "U10.3" + ], + "basis": [ + { + "record_id": "R6049443374", + "locator": "### B10 — P lines333" + }, + { + "record_id": "R6054305355", + "locator": "## COMPLETE / own RELEASE — P-C candidate kinds and group table" + } + ] + } + ], + "related_unit_ids": [] + }, + { + "id": "B11", + "source": { + "source_id": "P", + "lines": [ + 335, + 335 + ], + "locator": "P lines335", + "precision": "exact_lines" + }, + "section": 10, + "description": { + "text": "r A_r p_r and domination; independent of a merely fixed-axis assertion.", + "source_refs": [ + { + "source_id": "P", + "lines": [ + 335, + 335 + ], + "locator": "P lines335", + "precision": "exact_lines" + } + ], + "record_refs": [ + { + "record_id": "R6049443374", + "locator": "### B11 — P lines335" + } + ], + "unknown_refs": [] + }, + "uses": [ + { + "id": "U11.1", + "kind": "premise", + "binding": { + "consumer_statement_id": "UNIFORM-MATRIX-CAP-LIFETIME-20260924-v1::Theorem-C", + "consumer_unit_id": "B11", + "consumer_source": { + "source_id": "P", + "lines": [ + 335, + 335 + ], + "locator": "P lines335", + "precision": "exact_lines" + }, + "supplier_ids": [ + "S-U11.1-E2" + ], + "claimed_interface": { + "text": "E2 §9.4: selected intensity uses actual global elder indicator/p_r.", + "source_refs": [], + "record_refs": [ + { + "record_id": "R6049443374", + "locator": "B11/U11.1" + } + ], + "unknown_refs": [ + "UNKNOWN-U2" + ] + }, + "parameter_mapping": { + "text": "Recorded occurrence: E2 §9.4: selected intensity uses actual global elder indicator/p_r.\n\nLiteral consuming expression at P lines335:\nThe selected intensity is r A_r p_r with the same measures. This supplies the domination needed below, rather than assuming a fixed-axis statement can be integrated.\n\nAdditional supplier-to-consumer substitutions beyond this retained wording/expression are unexpanded in this companion; no extra map is inferred.", + "source_refs": [ + { + "source_id": "P", + "lines": [ + 335, + 335 + ], + "locator": "P lines335", + "precision": "exact_lines" + } + ], + "record_refs": [ + { + "record_id": "R6049443374", + "locator": "B11/U11.1" + } + ], + "unknown_refs": [ + "UNKNOWN-U2" + ] + }, + "context": { + "text": "Recorded owning-block description: r A_r p_r and domination; independent of a merely fixed-axis assertion.\n\nSource-attributed reading/scope qualifications:\nE2 §9.4 uses the actual global elder/type Borel mark, the full-pin density and one determinant product weight W_r; there is no second determinant factor or local-cap substitution for the global mark. Its external Armentano–Azaïs–León base remains imported/unexpanded. The near-diagonal exhaustion at E2:110 imports P §§3/5/10 estimates rather than reproving them; the remaining off-diagonal/unbounded-mark/coefficient obligations are separate.\n\nThe historical N2 observation records both the E2 §9.4 consumption and its import of P §§3/5/10. The source asserts the P10 bound from P3/5; those earlier sections are unexpanded here. No noncircularity or present applicability verdict is added.\n\nReferenced UNKNOWN annotations retain their historical observation/response scope; they are not current failure or acceptance verdicts.", + "source_refs": [ + { + "source_id": "P", + "lines": [ + 335, + 335 + ], + "locator": "P lines335", + "precision": "exact_lines" + }, + { + "source_id": "E2", + "lines": [ + 94, + 110 + ], + "locator": "§9.4 global elder/type mark and imported diagonal exhaustion", + "precision": "exact_lines" + }, + { + "source_id": "E2", + "lines": [ + 121, + 131 + ], + "locator": "Separate obligations retained by E2", + "precision": "exact_lines" + }, + { + "source_id": "E2", + "lines": [ + 110, + 110 + ], + "locator": "Imported parent estimates in near-diagonal exhaustion", + "precision": "exact_lines" + } + ], + "record_refs": [ + { + "record_id": "R6049443374", + "locator": "### B11 — P lines335" + }, + { + "record_id": "R6049548422", + "locator": "4. Consumption boundaries / E2" + }, + { + "record_id": "R6057972030", + "locator": "Exact arrays for the existing ReadingBoundary fields / E2 row; Source reasons and limits / E2" + }, + { + "record_id": "R6049548422", + "locator": "4. Consumption boundaries / E2 / (b) N2" + }, + { + "record_id": "R6049640627", + "locator": "U2" + } + ], + "unknown_refs": [ + "UNKNOWN-U2", + "UNKNOWN-U4" + ] + }, + "source_reading": [ + { + "boundary_id": "READ-E2", + "supplier_ids": [ + "S-U11.1-E2" + ], + "applies_to": [ + { + "source_id": "E2", + "lines": [ + 94, + 110 + ], + "locator": "§9.4 global elder/type mark and imported diagonal exhaustion", + "precision": "exact_lines" + }, + { + "source_id": "E2", + "lines": [ + 121, + 131 + ], + "locator": "Separate obligations retained by E2", + "precision": "exact_lines" + } + ], + "explanation": { + "text": "E2 §9.4 uses the actual global elder/type Borel mark, the full-pin density and one determinant product weight W_r; there is no second determinant factor or local-cap substitution for the global mark. Its external Armentano–Azaïs–León base remains imported/unexpanded. The near-diagonal exhaustion at E2:110 imports P §§3/5/10 estimates rather than reproving them; the remaining off-diagonal/unbounded-mark/coefficient obligations are separate.", + "source_refs": [ + { + "source_id": "E2", + "lines": [ + 94, + 110 + ], + "locator": "§9.4 global elder/type mark and imported diagonal exhaustion", + "precision": "exact_lines" + }, + { + "source_id": "E2", + "lines": [ + 121, + 131 + ], + "locator": "Separate obligations retained by E2", + "precision": "exact_lines" + } + ], + "record_refs": [ + { + "record_id": "R6049548422", + "locator": "4. Consumption boundaries / E2" + }, + { + "record_id": "R6057972030", + "locator": "Exact arrays for the existing ReadingBoundary fields / E2 row; Source reasons and limits / E2" + } + ], + "unknown_refs": [ + "UNKNOWN-U4" + ] + } + }, + { + "boundary_id": "READ-E2", + "supplier_ids": [ + "S-U11.1-E2" + ], + "applies_to": [ + { + "source_id": "E2", + "lines": [ + 110, + 110 + ], + "locator": "Imported parent estimates in near-diagonal exhaustion", + "precision": "exact_lines" + } + ], + "explanation": { + "text": "The historical N2 observation records both the E2 §9.4 consumption and its import of P §§3/5/10. The source asserts the P10 bound from P3/5; those earlier sections are unexpanded here. No noncircularity or present applicability verdict is added.", + "source_refs": [ + { + "source_id": "E2", + "lines": [ + 110, + 110 + ], + "locator": "Imported parent estimates in near-diagonal exhaustion", + "precision": "exact_lines" + } + ], + "record_refs": [ + { + "record_id": "R6049548422", + "locator": "4. Consumption boundaries / E2 / (b) N2" + }, + { + "record_id": "R6049640627", + "locator": "U2" + } + ], + "unknown_refs": [ + "UNKNOWN-U2" + ] + } + } + ] + }, + "provenance": [ + { + "record_id": "R6049443374", + "locator": "B11/U11.1" + } + ], + "applicability_reviews": [], + "unknown_refs": [ + "UNKNOWN-U2", + "UNKNOWN-U4" + ] + }, + { + "id": "U11.2", + "kind": "premise", + "binding": { + "consumer_statement_id": "UNIFORM-MATRIX-CAP-LIFETIME-20260924-v1::Theorem-C", + "consumer_unit_id": "B11", + "consumer_source": { + "source_id": "P", + "lines": [ + 335, + 335 + ], + "locator": "P lines335", + "precision": "exact_lines" + }, + "supplier_ids": [ + "S-U11.2-UNITS" + ], + "claimed_interface": { + "text": "B10: uniform upper bound.", + "source_refs": [], + "record_refs": [ + { + "record_id": "R6049443374", + "locator": "B11/U11.2" + } + ], + "unknown_refs": [] + }, + "parameter_mapping": { + "text": "Recorded occurrence: B10: uniform upper bound.\n\nLiteral consuming expression at P lines335:\nThe selected intensity is r A_r p_r with the same measures. This supplies the domination needed below, rather than assuming a fixed-axis statement can be integrated.\n\nAdditional supplier-to-consumer substitutions beyond this retained wording/expression are unexpanded in this companion; no extra map is inferred.", + "source_refs": [ + { + "source_id": "P", + "lines": [ + 335, + 335 + ], + "locator": "P lines335", + "precision": "exact_lines" + } + ], + "record_refs": [ + { + "record_id": "R6049443374", + "locator": "B11/U11.2" + } + ], + "unknown_refs": [] + }, + "context": { + "text": "Recorded owning-block description: r A_r p_r and domination; independent of a merely fixed-axis assertion.", + "source_refs": [ + { + "source_id": "P", + "lines": [ + 335, + 335 + ], + "locator": "P lines335", + "precision": "exact_lines" + } + ], + "record_refs": [ + { + "record_id": "R6049443374", + "locator": "### B11 — P lines335" + } + ], + "unknown_refs": [] + }, + "source_reading": [] + }, + "provenance": [ + { + "record_id": "R6049443374", + "locator": "B11/U11.2" + } + ], + "applicability_reviews": [], + "unknown_refs": [] + } + ], + "premise_groups": [ + { + "id": "G-B11", + "combination": "ALL", + "conclusion": "B11", + "premise_use_ids": [ + "U11.1", + "U11.2" + ], + "basis": [ + { + "record_id": "R6049443374", + "locator": "### B11 — P lines335" + }, + { + "record_id": "R6054305355", + "locator": "## COMPLETE / own RELEASE — P-C candidate kinds and group table" + } + ] + } + ], + "related_unit_ids": [] + }, + { + "id": "B12", + "source": { + "source_id": "P", + "lines": [ + 339, + 339 + ], + "locator": "P lines339", + "precision": "exact_lines" + }, + "section": 11, + "description": { + "text": "Quantifier use ell0.", + "source_refs": [], + "record_refs": [ + { + "record_id": "R6049443374", + "locator": "B12/U12.1" + } + ], + "unknown_refs": [] + }, + "parameter_mapping": { + "text": "Recorded occurrence: P §1: compact K with k_->0.\n\nLiteral consuming expression at P lines339:\nFor ell0.", + "source_refs": [], + "record_refs": [ + { + "record_id": "R6049443374", + "locator": "B21/U21.1" + } + ], + "unknown_refs": [] + }, + "parameter_mapping": { + "text": "Recorded occurrence: K compact and k_->0.\n\nLiteral consuming expression at P lines363:\nwhich is finite because k>=k_->0. This proves (1.2). It is an O(ell^(2/3)) difference, not a claim that either density separately has a second-order expansion with that remainder. Convergence of A_r to A_0 was not assigned a numerical rate.\n\nAdditional supplier-to-consumer substitutions beyond this retained wording/expression are unexpanded in this companion; no extra map is inferred.", + "source_refs": [ + { + "source_id": "P", + "lines": [ + 363, + 363 + ], + "locator": "P lines363", + "precision": "exact_lines" + } + ], + "record_refs": [ + { + "record_id": "R6049443374", + "locator": "B21/U21.1" + } + ], + "unknown_refs": [] + }, + "context": { + "text": "Recorded owning-block description: Finiteness and Theorem B (1.2). Separate densities receive no second-order rate here.", + "source_refs": [ + { + "source_id": "P", + "lines": [ + 363, + 363 + ], + "locator": "P lines363", + "precision": "exact_lines" + } + ], + "record_refs": [ + { + "record_id": "R6049443374", + "locator": "### B21 — P lines363" + } + ], + "unknown_refs": [] + }, + "source_reading": [] + }, + "provenance": [ + { + "record_id": "R6049443374", + "locator": "B21/U21.1" + } + ], + "applicability_reviews": [], + "unknown_refs": [] + }, + { + "id": "U21.2", + "kind": "premise", + "binding": { + "consumer_statement_id": "UNIFORM-MATRIX-CAP-LIFETIME-20260924-v1::Theorem-C", + "consumer_unit_id": "B21", + "consumer_source": { + "source_id": "P", + "lines": [ + 363, + 363 + ], + "locator": "P lines363", + "precision": "exact_lines" + }, + "supplier_ids": [ + "S-U21.2-UNITS" + ], + "claimed_interface": { + "text": "B20: resulting difference estimate.", + "source_refs": [], + "record_refs": [ + { + "record_id": "R6049443374", + "locator": "B21/U21.2" + } + ], + "unknown_refs": [] + }, + "parameter_mapping": { + "text": "Recorded occurrence: B20: resulting difference estimate.\n\nLiteral consuming expression at P lines363:\nwhich is finite because k>=k_->0. This proves (1.2). It is an O(ell^(2/3)) difference, not a claim that either density separately has a second-order expansion with that remainder. Convergence of A_r to A_0 was not assigned a numerical rate.\n\nAdditional supplier-to-consumer substitutions beyond this retained wording/expression are unexpanded in this companion; no extra map is inferred.", + "source_refs": [ + { + "source_id": "P", + "lines": [ + 363, + 363 + ], + "locator": "P lines363", + "precision": "exact_lines" + } + ], + "record_refs": [ + { + "record_id": "R6049443374", + "locator": "B21/U21.2" + } + ], + "unknown_refs": [] + }, + "context": { + "text": "Recorded owning-block description: Finiteness and Theorem B (1.2). Separate densities receive no second-order rate here.", + "source_refs": [ + { + "source_id": "P", + "lines": [ + 363, + 363 + ], + "locator": "P lines363", + "precision": "exact_lines" + } + ], + "record_refs": [ + { + "record_id": "R6049443374", + "locator": "### B21 — P lines363" + } + ], + "unknown_refs": [] + }, + "source_reading": [] + }, + "provenance": [ + { + "record_id": "R6049443374", + "locator": "B21/U21.2" + } + ], + "applicability_reviews": [], + "unknown_refs": [] + } + ], + "premise_groups": [ + { + "id": "G-B21", + "combination": "ALL", + "conclusion": "B21", + "premise_use_ids": [ + "U21.1", + "U21.2" + ], + "basis": [ + { + "record_id": "R6049443374", + "locator": "### B21 — P lines363" + }, + { + "record_id": "R6054305355", + "locator": "## COMPLETE / own RELEASE — P-C candidate kinds and group table" + } + ] + } + ], + "related_unit_ids": [] + }, + { + "id": "B22", + "source": { + "source_id": "P", + "lines": [ + 367, + 367 + ], + "locator": "P lines367", + "precision": "exact_lines" + }, + "section": 12, + "description": { + "text": "Unexpanded counting-measure integration step to cumulative quantities.", + "source_refs": [ + { + "source_id": "P", + "lines": [ + 367, + 367 + ], + "locator": "P lines367", + "precision": "exact_lines" + } + ], + "record_refs": [ + { + "record_id": "R6049443374", + "locator": "### B22 — P lines367" + } + ], + "unknown_refs": [] + }, + "uses": [ + { + "id": "U22.1", + "kind": "premise", + "binding": { + "consumer_statement_id": "UNIFORM-MATRIX-CAP-LIFETIME-20260924-v1::Theorem-C", + "consumer_unit_id": "B22", + "consumer_source": { + "source_id": "P", + "lines": [ + 367, + 367 + ], + "locator": "P lines367", + "precision": "exact_lines" + }, + "supplier_ids": [ + "S-U22.1-P" + ], + "claimed_interface": { + "text": "P §11: nonnegative density versions for restricted populations.", + "source_refs": [], + "record_refs": [ + { + "record_id": "R6049443374", + "locator": "B22/U22.1" + } + ], + "unknown_refs": [] + }, + "parameter_mapping": { + "text": "Recorded occurrence: P §11: nonnegative density versions for restricted populations.\n\nLiteral consuming expression at P lines367:\nIntegrating the density versions gives the following expected per-unit-volume results for the same spatial/mark-restricted populations:\n\nAdditional supplier-to-consumer substitutions beyond this retained wording/expression are unexpanded in this companion; no extra map is inferred.", + "source_refs": [ + { + "source_id": "P", + "lines": [ + 367, + 367 + ], + "locator": "P lines367", + "precision": "exact_lines" + } + ], + "record_refs": [ + { + "record_id": "R6049443374", + "locator": "B22/U22.1" + } + ], + "unknown_refs": [] + }, + "context": { + "text": "Recorded owning-block description: Unexpanded counting-measure integration step to cumulative quantities.\n\nSource-attributed reading/scope qualifications:\nThe compact cumulative and moment formulas are read for sufficiently small t, inheriting the compact-window lifetime range ell−2/3; retained as a hypothesis, not a proof step.", + "source_refs": [ + { + "source_id": "P", + "lines": [ + 372, + 372 + ], + "locator": "P lines372", + "precision": "exact_lines" + } + ], + "record_refs": [ + { + "record_id": "R6049443374", + "locator": "### B24 — P lines372" + } + ], + "unknown_refs": [] + }, + "uses": [], + "premise_groups": [], + "related_unit_ids": [] + }, + { + "id": "B25", + "source": { + "source_id": "P", + "lines": [ + 374, + 375 + ], + "locator": "P lines374–375", + "precision": "exact_lines" + }, + "section": 12, + "description": { + "text": "(12.2) selected moment conclusion for q>−2/3.", + "source_refs": [ + { + "source_id": "P", + "lines": [ + 374, + 375 + ], + "locator": "P lines374–375", + "precision": "exact_lines" + } + ], + "record_refs": [ + { + "record_id": "R6049443374", + "locator": "### B25 — P lines374–375" + } + ], + "unknown_refs": [] + }, + "uses": [ + { + "id": "U25.1", + "kind": "premise", + "binding": { + "consumer_statement_id": "UNIFORM-MATRIX-CAP-LIFETIME-20260924-v1::Theorem-C", + "consumer_unit_id": "B25", + "consumer_source": { + "source_id": "P", + "lines": [ + 374, + 375 + ], + "locator": "P lines374–375", + "precision": "exact_lines" + }, + "supplier_ids": [ + "S-U25.1-P" + ], + "claimed_interface": { + "text": "P §11: positive compact leading density.", + "source_refs": [], + "record_refs": [ + { + "record_id": "R6049443374", + "locator": "B25/U25.1" + } + ], + "unknown_refs": [] + }, + "parameter_mapping": { + "text": "Recorded occurrence: P §11: positive compact leading density.\n\nLiteral consuming expression at P lines374–375:\n E sum_{selected, ell<=t} ell^q\n ~ c_{B,K} t^(q+2/3)/(q+2/3). (12.2)\n\nAdditional supplier-to-consumer substitutions beyond this retained wording/expression are unexpanded in this companion; no extra map is inferred.", + "source_refs": [ + { + "source_id": "P", + "lines": [ + 374, + 375 + ], + "locator": "P lines374–375", + "precision": "exact_lines" + } + ], + "record_refs": [ + { + "record_id": "R6049443374", + "locator": "B25/U25.1" + } + ], + "unknown_refs": [] + }, + "context": { + "text": "Recorded owning-block description: (12.2) selected moment conclusion for q>−2/3.\n\nSource-attributed reading/scope qualifications:\nThe compact cumulative and moment formulas are read for sufficiently small t, inheriting the compact-window lifetime range ell−2/3.\n\nSource-attributed reading/scope qualifications:\nThe compact cumulative and moment formulas are read for sufficiently small t, inheriting the compact-window lifetime range ell−5/3 domain for the defect measure.", + "source_refs": [ + { + "source_id": "P", + "lines": [ + 377, + 377 + ], + "locator": "P lines377", + "precision": "exact_lines" + } + ], + "record_refs": [ + { + "record_id": "R6049443374", + "locator": "### B26 — P lines377" + } + ], + "unknown_refs": [] + }, + "uses": [ + { + "id": "U26.1", + "kind": "premise", + "binding": { + "consumer_statement_id": "UNIFORM-MATRIX-CAP-LIFETIME-20260924-v1::Theorem-C", + "consumer_unit_id": "B26", + "consumer_source": { + "source_id": "P", + "lines": [ + 377, + 377 + ], + "locator": "P lines377", + "precision": "exact_lines" + }, + "supplier_ids": [ + "S-U26.1-P" + ], + "claimed_interface": { + "text": "P §11: common candidate leading density.", + "source_refs": [], + "record_refs": [ + { + "record_id": "R6049443374", + "locator": "B26/U26.1" + } + ], + "unknown_refs": [] + }, + "parameter_mapping": { + "text": "Recorded occurrence: P §11: common candidate leading density.\n\nLiteral consuming expression at P lines377:\nThe same leading expression holds for candidates. For q>-5/3 the nonselected difference alone satisfies\n\nAdditional supplier-to-consumer substitutions beyond this retained wording/expression are unexpanded in this companion; no extra map is inferred.", + "source_refs": [ + { + "source_id": "P", + "lines": [ + 377, + 377 + ], + "locator": "P lines377", + "precision": "exact_lines" + } + ], + "record_refs": [ + { + "record_id": "R6049443374", + "locator": "B26/U26.1" + } + ], + "unknown_refs": [] + }, + "context": { + "text": "Recorded owning-block description: Candidate leading expression; declares separate q>−5/3 domain for the defect measure.\n\nSource-attributed reading/scope qualifications:\nThe compact cumulative and moment formulas are read for sufficiently small t, inheriting the compact-window lifetime range ell-5/3 the nonselected difference alone satisfies\n\nAdditional supplier-to-consumer substitutions beyond this retained wording/expression are unexpanded in this companion; no extra map is inferred.", + "source_refs": [ + { + "source_id": "P", + "lines": [ + 377, + 377 + ], + "locator": "P lines377", + "precision": "exact_lines" + } + ], + "record_refs": [ + { + "record_id": "R6049443374", + "locator": "B26/U26.2" + } + ], + "unknown_refs": [] + }, + "context": { + "text": "Recorded owning-block description: Candidate leading expression; declares separate q>−5/3 domain for the defect measure.\n\nSource-attributed reading/scope qualifications:\nThe compact cumulative and moment formulas are read for sufficiently small t, inheriting the compact-window lifetime range ell−5/3.", + "source_refs": [], + "record_refs": [ + { + "record_id": "R6049443374", + "locator": "B27/U27.2" + } + ], + "unknown_refs": [] + }, + "parameter_mapping": { + "text": "Recorded occurrence: unnamed integrable-power integral with q>−5/3.\n\nLiteral consuming expression at P lines379–380:\n E sum_{candidate but not selected, ell<=t} ell^q\n <= C_q t^(q+5/3). (12.3)\n\nAdditional supplier-to-consumer substitutions beyond this retained wording/expression are unexpanded in this companion; no extra map is inferred.", + "source_refs": [ + { + "source_id": "P", + "lines": [ + 379, + 380 + ], + "locator": "P lines379–380", + "precision": "exact_lines" + } + ], + "record_refs": [ + { + "record_id": "R6049443374", + "locator": "B27/U27.2" + } + ], + "unknown_refs": [] + }, + "context": { + "text": "Recorded owning-block description: (12.3) direct measure; no subtraction of divergent expectations.\n\nSource-attributed reading/scope qualifications:\nThe compact cumulative and moment formulas are read for sufficiently small t, inheriting the compact-window lifetime range ell0, independent of b and k, on which its eigenvalues are bounded above and away from zero. Reduce r_0 below the torus injectivity scale and below one. Do NOT require a globally uniform lower bound for Z_r or a globally uniform constant in (1.1).\n\nAdditional supplier-to-consumer substitutions beyond this retained wording/expression are unexpanded in this companion; no extra map is inferred.", + "source_refs": [ + { + "source_id": "P", + "lines": [ + 388, + 388 + ], + "locator": "P lines388", + "precision": "exact_lines" + } + ], + "record_refs": [ + { + "record_id": "R6049443374", + "locator": "B30/U30.1" + } + ], + "unknown_refs": [] + }, + "context": { + "text": "Recorded owning-block description: All b,k,r/frame scope; no all-mark lower floor for Z or global probability constant.\n\nSource-attributed reading/scope qualifications:\nREC144 is the recorded A2 uniform-Gramian-gap reading for [0,r_0]×O(d), distinct from the cap-cylinder radius paragraph. REC is a reading/review record, not an independent replacement proof.", + "source_refs": [ + { + "source_id": "P", + "lines": [ + 388, + 388 + ], + "locator": "P lines388", + "precision": "exact_lines" + }, + { + "source_id": "REC", + "lines": [ + 144, + 144 + ], + "locator": "A2 uniform Gramian gap row", + "precision": "exact_lines" + } + ], + "record_refs": [ + { + "record_id": "R6049443374", + "locator": "### B30 — P lines388" + }, + { + "record_id": "R6049548422", + "locator": "4. Consumption boundaries / REC (N1)" + } + ], + "unknown_refs": [] + }, + "source_reading": [ + { + "boundary_id": "READ-REC", + "supplier_ids": [ + "S-U30.1-P" + ], + "applies_to": [ + { + "source_id": "REC", + "lines": [ + 144, + 144 + ], + "locator": "A2 uniform Gramian gap row", + "precision": "exact_lines" + } + ], + "explanation": { + "text": "REC144 is the recorded A2 uniform-Gramian-gap reading for [0,r_0]×O(d), distinct from the cap-cylinder radius paragraph. REC is a reading/review record, not an independent replacement proof.", + "source_refs": [ + { + "source_id": "REC", + "lines": [ + 144, + 144 + ], + "locator": "A2 uniform Gramian gap row", + "precision": "exact_lines" + } + ], + "record_refs": [ + { + "record_id": "R6049548422", + "locator": "4. Consumption boundaries / REC (N1)" + } + ], + "unknown_refs": [] + } + } + ] + }, + "provenance": [ + { + "record_id": "R6049443374", + "locator": "B30/U30.1" + } + ], + "applicability_reviews": [], + "unknown_refs": [] + }, + { + "id": "U30.2", + "kind": "premise", + "binding": { + "consumer_statement_id": "UNIFORM-MATRIX-CAP-LIFETIME-20260924-v1::Theorem-C", + "consumer_unit_id": "B30", + "consumer_source": { + "source_id": "P", + "lines": [ + 388, + 388 + ], + "locator": "P lines388", + "precision": "exact_lines" + }, + "supplier_ids": [ + "S-U30.2-UNNAMED" + ], + "claimed_interface": { + "text": "unnamed reduction of fixed r0 below embedding/injectivity and 1 (REC radius).", + "source_refs": [], + "record_refs": [ + { + "record_id": "R6049443374", + "locator": "B30/U30.2" + } + ], + "unknown_refs": [ + "UNKNOWN-U6" + ] + }, + "parameter_mapping": { + "text": "Recorded occurrence: unnamed reduction of fixed r0 below embedding/injectivity and 1 (REC radius).\n\nLiteral consuming expression at P lines388:\nThe covariance Sigma_r of U_r depends on radius and frame, NOT on the imposed target. Section 3 therefore supplies a fixed r_0>0, independent of b and k, on which its eigenvalues are bounded above and away from zero. Reduce r_0 below the torus injectivity scale and below one. Do NOT require a globally uniform lower bound for Z_r or a globally uniform constant in (1.1).\n\nAdditional supplier-to-consumer substitutions beyond this retained wording/expression are unexpanded in this companion; no extra map is inferred.", + "source_refs": [ + { + "source_id": "P", + "lines": [ + 388, + 388 + ], + "locator": "P lines388", + "precision": "exact_lines" + } + ], + "record_refs": [ + { + "record_id": "R6049443374", + "locator": "B30/U30.2" + } + ], + "unknown_refs": [ + "UNKNOWN-U6" + ] + }, + "context": { + "text": "Recorded owning-block description: All b,k,r/frame scope; no all-mark lower floor for Z or global probability constant.\n\nSource-attributed reading/scope qualifications:\nThe inherited label “REC radius” is qualified: P388 reduces its own covariance r_0 below the torus injectivity scale and1. REC163–166 bounds cap/Theorem-A r_*; the stronger quantitative R12 reading remains separate and is not a P-C premise. Whether the extra cylinder restriction belongs to this r_0 was a historical observation, not a current mathematical disposition.\n\nReferenced UNKNOWN annotations retain their historical observation/response scope; they are not current failure or acceptance verdicts.", + "source_refs": [ + { + "source_id": "P", + "lines": [ + 388, + 388 + ], + "locator": "P lines388", + "precision": "exact_lines" + }, + { + "source_id": "REC", + "lines": [ + 163, + 166 + ], + "locator": "Radius distinction: Theorem-A cylinder versus covariance radius", + "precision": "exact_lines" + } + ], + "record_refs": [ + { + "record_id": "R6049443374", + "locator": "### B30 — P lines388" + }, + { + "record_id": "R6049548422", + "locator": "4. Consumption boundaries / REC (N1)" + }, + { + "record_id": "R6049640627", + "locator": "N1–N7 are retained" + } + ], + "unknown_refs": [ + "UNKNOWN-U6" + ] + }, + "source_reading": [ + { + "boundary_id": "READ-REC", + "supplier_ids": [ + "S-U30.2-UNNAMED" + ], + "applies_to": [ + { + "source_id": "REC", + "lines": [ + 163, + 166 + ], + "locator": "Radius distinction: Theorem-A cylinder versus covariance radius", + "precision": "exact_lines" + } + ], + "explanation": { + "text": "The inherited label “REC radius” is qualified: P388 reduces its own covariance r_0 below the torus injectivity scale and1. REC163–166 bounds cap/Theorem-A r_*; the stronger quantitative R12 reading remains separate and is not a P-C premise. Whether the extra cylinder restriction belongs to this r_0 was a historical observation, not a current mathematical disposition.", + "source_refs": [ + { + "source_id": "REC", + "lines": [ + 163, + 166 + ], + "locator": "Radius distinction: Theorem-A cylinder versus covariance radius", + "precision": "exact_lines" + } + ], + "record_refs": [ + { + "record_id": "R6049548422", + "locator": "4. 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For the second inequality it suffices to use its two coordinates b-k r^3/2 and 12k: if r<=1, then b^2<=2(b-k r^3/2)^2+k^2/2. Thus the invertible covariance bound yields\n\nAdditional supplier-to-consumer substitutions beyond this retained wording/expression are unexpanded in this companion; no extra map is inferred.", + "source_refs": [ + { + "source_id": "P", + "lines": [ + 395, + 395 + ], + "locator": "P lines395", + "precision": "exact_lines" + } + ], + "record_refs": [ + { + "record_id": "R6049443374", + "locator": "B33/U33.1" + } + ], + "unknown_refs": [] + }, + "context": { + "text": "Recorded owning-block description: Unnamed coercivity-to-tail chain, not a compact-mark estimate extrapolated globally.", + "source_refs": [ + { + "source_id": "P", + "lines": [ + 395, + 395 + ], + "locator": "P lines395", + "precision": "exact_lines" + } + ], + "record_refs": [ + { + "record_id": "R6049443374", + "locator": "### B33 — P lines395" + } + ], + "unknown_refs": [] + }, + "source_reading": [] + }, + "provenance": [ + { + "record_id": "R6049443374", + "locator": "B33/U33.1" + } + ], + "applicability_reviews": [], + "unknown_refs": [] + }, + { + "id": "U33.2", + "kind": "premise", + "binding": { + "consumer_statement_id": "UNIFORM-MATRIX-CAP-LIFETIME-20260924-v1::Theorem-C", + "consumer_unit_id": "B33", + "consumer_source": { + "source_id": "P", + "lines": [ + 395, + 395 + ], + "locator": "P lines395", + "precision": "exact_lines" + }, + "supplier_ids": [ + "S-U33.2-UNITS" + ], + "claimed_interface": { + "text": "B30: bounded invertible covariance.", + "source_refs": [], + "record_refs": [ + { + "record_id": "R6049443374", + "locator": "B33/U33.2" + } + ], + "unknown_refs": [] + }, + "parameter_mapping": { + "text": "Recorded occurrence: B30: bounded invertible covariance.\n\nLiteral consuming expression at P lines395:\nwith fixed c,C>0. For the second inequality it suffices to use its two coordinates b-k r^3/2 and 12k: if r<=1, then b^2<=2(b-k r^3/2)^2+k^2/2. Thus the invertible covariance bound yields\n\nAdditional supplier-to-consumer substitutions beyond this retained wording/expression are unexpanded in this companion; no extra map is inferred.", + "source_refs": [ + { + "source_id": "P", + "lines": [ + 395, + 395 + ], + "locator": "P lines395", + "precision": "exact_lines" + } + ], + "record_refs": [ + { + "record_id": "R6049443374", + "locator": "B33/U33.2" + } + ], + "unknown_refs": [] + }, + "context": { + "text": "Recorded owning-block description: Unnamed coercivity-to-tail chain, not a compact-mark estimate extrapolated globally.", + "source_refs": [ + { + "source_id": "P", + "lines": [ + 395, + 395 + ], + "locator": "P lines395", + "precision": "exact_lines" + } + ], + "record_refs": [ + { + "record_id": "R6049443374", + "locator": "### B33 — P lines395" + } + ], + "unknown_refs": [] + }, + "source_reading": [] + }, + "provenance": [ + { + "record_id": "R6049443374", + "locator": "B33/U33.2" + } + ], + "applicability_reviews": [], + "unknown_refs": [] + }, + { + "id": "U33.3", + "kind": "premise", + "binding": { + "consumer_statement_id": "UNIFORM-MATRIX-CAP-LIFETIME-20260924-v1::Theorem-C", + "consumer_unit_id": "B33", + "consumer_source": { + "source_id": "P", + "lines": [ + 395, + 395 + ], + "locator": "P lines395", + "precision": "exact_lines" + }, + "supplier_ids": [ + "S-U33.3-UNNAMED" + ], + "claimed_interface": { + "text": "unnamed multivariate Gaussian density estimate.", + "source_refs": [], + "record_refs": [ + { + "record_id": "R6049443374", + "locator": "B33/U33.3" + } + ], + "unknown_refs": [] + }, + "parameter_mapping": { + "text": "Recorded occurrence: unnamed multivariate Gaussian density estimate.\n\nLiteral consuming expression at P lines395:\nwith fixed c,C>0. For the second inequality it suffices to use its two coordinates b-k r^3/2 and 12k: if r<=1, then b^2<=2(b-k r^3/2)^2+k^2/2. Thus the invertible covariance bound yields\n\nAdditional supplier-to-consumer substitutions beyond this retained wording/expression are unexpanded in this companion; no extra map is inferred.", + "source_refs": [ + { + "source_id": "P", + "lines": [ + 395, + 395 + ], + "locator": "P lines395", + "precision": "exact_lines" + } + ], + "record_refs": [ + { + "record_id": "R6049443374", + "locator": "B33/U33.3" + } + ], + "unknown_refs": [] + }, + "context": { + "text": "Recorded owning-block description: Unnamed coercivity-to-tail chain, not a compact-mark estimate extrapolated globally.", + "source_refs": [ + { + "source_id": "P", + "lines": [ + 395, + 395 + ], + "locator": "P lines395", + "precision": "exact_lines" + } + ], + "record_refs": [ + { + "record_id": "R6049443374", + "locator": "### B33 — P lines395" + } + ], + "unknown_refs": [] + }, + "source_reading": [] + }, + "provenance": [ + { + "record_id": "R6049443374", + "locator": "B33/U33.3" + } + ], + "applicability_reviews": [], + "unknown_refs": [] + } + ], + "premise_groups": [ + { + "id": "G-B33", + "combination": "ALL", + "conclusion": "B34", + "premise_use_ids": [ + "U33.1", + "U33.2", + "U33.3" + ], + "basis": [ + { + "record_id": "R6049443374", + "locator": "### B33 — P lines395" + }, + { + "record_id": "R6054305355", + "locator": "## COMPLETE / own RELEASE — P-C candidate kinds and group table" + } + ] + } + ], + "related_unit_ids": [] + }, + { + "id": "B34", + "source": { + "source_id": "P", + "lines": [ + 397, + 397 + ], + "locator": "P lines397", + "precision": "exact_lines" + }, + "section": 13, + "description": { + "text": "(13.2) Gaussian pin-density bound, paired with B33.", + "source_refs": [ + { + "source_id": "P", + "lines": [ + 397, + 397 + ], + "locator": "P lines397", + "precision": "exact_lines" + } + ], + "record_refs": [ + { + "record_id": "R6049443374", + "locator": "### B34 — P lines397" + } + ], + "unknown_refs": [] + }, + "uses": [], + "premise_groups": [], + "related_unit_ids": [] + }, + { + "id": "B35", + "source": { + "source_id": "P", + "lines": [ + 399, + 399 + ], + "locator": "P lines399", + "precision": "exact_lines" + }, + "section": 13, + "description": { + "text": "Target-growth extension is explicitly asserted here; original compact bound alone is insufficient.", + "source_refs": [ + { + "source_id": "P", + "lines": [ + 399, + 399 + ], + "locator": "P lines399", + "precision": "exact_lines" + } + ], + "record_refs": [ + { + "record_id": "R6049443374", + "locator": "### B35 — P lines399" + } + ], + "unknown_refs": [] + }, + "uses": [ + { + "id": "U35.1", + "kind": "premise", + "binding": { + "consumer_statement_id": "UNIFORM-MATRIX-CAP-LIFETIME-20260924-v1::Theorem-C", + "consumer_unit_id": "B35", + "consumer_source": { + "source_id": "P", + "lines": [ + 399, + 399 + ], + "locator": "P lines399", + "precision": "exact_lines" + }, + "supplier_ids": [ + "S-U35.1-UNNAMED" + ], + "claimed_interface": { + "text": "unnamed conditional Fourier Gaussian mean/variance regression.", + "source_refs": [], + "record_refs": [ + { + "record_id": "R6049443374", + "locator": "B35/U35.1" + } + ], + "unknown_refs": [ + "UNKNOWN-U7" + ] + }, + "parameter_mapping": { + "text": "Recorded occurrence: unnamed conditional Fourier Gaussian mean/variance regression.\n\nLiteral consuming expression at P lines399:\nConditional Fourier-coefficient means are bounded by C|v_r| and their centered variances by one. The same summability/Minkowski proof as Section 4 now gives the TARGET-GROWTH bound\n\nAdditional supplier-to-consumer substitutions beyond this retained wording/expression are unexpanded in this companion; no extra map is inferred.", + "source_refs": [ + { + "source_id": "P", + "lines": [ + 399, + 399 + ], + "locator": "P lines399", + "precision": "exact_lines" + } + ], + "record_refs": [ + { + "record_id": "R6049443374", + "locator": "B35/U35.1" + } + ], + "unknown_refs": [ + "UNKNOWN-U7" + ] + }, + "context": { + "text": "Recorded owning-block description: Target-growth extension is explicitly asserted here; original compact bound alone is insufficient.\n\nReferenced UNKNOWN annotations retain their historical observation/response scope; they are not current failure or acceptance verdicts.", + "source_refs": [ + { + "source_id": "P", + "lines": [ + 399, + 399 + ], + "locator": "P lines399", + "precision": "exact_lines" + } + ], + "record_refs": [ + { + "record_id": "R6049443374", + "locator": "### B35 — P lines399" + } + ], + "unknown_refs": [ + "UNKNOWN-U7" + ] + }, + "source_reading": [] + }, + "provenance": [ + { + "record_id": "R6049443374", + "locator": "B35/U35.1" + } + ], + "applicability_reviews": [], + "unknown_refs": [ + "UNKNOWN-U7" + ] + }, + { + "id": "U35.2", + "kind": "premise", + "binding": { + "consumer_statement_id": "UNIFORM-MATRIX-CAP-LIFETIME-20260924-v1::Theorem-C", + "consumer_unit_id": "B35", + "consumer_source": { + "source_id": "P", + "lines": [ + 399, + 399 + ], + "locator": "P lines399", + "precision": "exact_lines" + }, + "supplier_ids": [ + "S-U35.2-P" + ], + "claimed_interface": { + "text": "P §4 summability/Minkowski mechanism.", + "source_refs": [], + "record_refs": [ + { + "record_id": "R6049443374", + "locator": "B35/U35.2" + } + ], + "unknown_refs": [] + }, + "parameter_mapping": { + "text": "Recorded occurrence: P §4 summability/Minkowski mechanism.\n\nLiteral consuming expression at P lines399:\nConditional Fourier-coefficient means are bounded by C|v_r| and their centered variances by one. The same summability/Minkowski proof as Section 4 now gives the TARGET-GROWTH bound\n\nAdditional supplier-to-consumer substitutions beyond this retained wording/expression are unexpanded in this companion; no extra map is inferred.", + "source_refs": [ + { + "source_id": "P", + "lines": [ + 399, + 399 + ], + "locator": "P lines399", + "precision": "exact_lines" + } + ], + "record_refs": [ + { + "record_id": "R6049443374", + "locator": "B35/U35.2" + } + ], + "unknown_refs": [] + }, + "context": { + "text": "Recorded owning-block description: Target-growth extension is explicitly asserted here; original compact bound alone is insufficient.", + "source_refs": [ + { + "source_id": "P", + "lines": [ + 399, + 399 + ], + "locator": "P lines399", + "precision": "exact_lines" + } + ], + "record_refs": [ + { + "record_id": "R6049443374", + "locator": "### B35 — P lines399" + } + ], + "unknown_refs": [] + }, + "source_reading": [] + }, + "provenance": [ + { + "record_id": "R6049443374", + "locator": "B35/U35.2" + } + ], + "applicability_reviews": [], + "unknown_refs": [] + }, + { + "id": "U35.3", + "kind": "premise", + "binding": { + "consumer_statement_id": "UNIFORM-MATRIX-CAP-LIFETIME-20260924-v1::Theorem-C", + "consumer_unit_id": "B35", + "consumer_source": { + "source_id": "P", + "lines": [ + 399, + 399 + ], + "locator": "P lines399", + "precision": "exact_lines" + }, + "supplier_ids": [ + "S-U35.3-UNITS" + ], + "claimed_interface": { + "text": "B30 inverse covariance for regression coefficients", + "source_refs": [], + "record_refs": [ + { + "record_id": "R6049640627", + "locator": "paragraph beginning \"I accept A1–A6 as proposed additive uses\" / U35.3" + } + ], + "unknown_refs": [] + }, + "parameter_mapping": { + "text": "Recorded occurrence: B30 inverse covariance for regression coefficients\n\nLiteral consuming expression at P lines399:\nConditional Fourier-coefficient means are bounded by C|v_r| and their centered variances by one. The same summability/Minkowski proof as Section 4 now gives the TARGET-GROWTH bound\n\nAdditional supplier-to-consumer substitutions beyond this retained wording/expression are unexpanded in this companion; no extra map is inferred.", + "source_refs": [ + { + "source_id": "P", + "lines": [ + 399, + 399 + ], + "locator": "P lines399", + "precision": "exact_lines" + } + ], + "record_refs": [ + { + "record_id": "R6049640627", + "locator": "paragraph beginning \"I accept A1–A6 as proposed additive uses\" / U35.3" + } + ], + "unknown_refs": [] + }, + "context": { + "text": "Recorded owning-block description: Target-growth extension is explicitly asserted here; original compact bound alone is insufficient.", + "source_refs": [ + { + "source_id": "P", + "lines": [ + 399, + 399 + ], + "locator": "P lines399", + "precision": "exact_lines" + } + ], + "record_refs": [ + { + "record_id": "R6049443374", + "locator": "### B35 — P lines399" + } + ], + "unknown_refs": [] + }, + "source_reading": [] + }, + "provenance": [ + { + "record_id": "R6049640627", + "locator": "paragraph beginning \"I accept A1–A6 as proposed additive uses\" / U35.3" + }, + { + "record_id": "R6049548422", + "locator": "2. Input-use challenges (instruction 2): additive amendments / A3" + } + ], + "applicability_reviews": [], + "unknown_refs": [] + } + ], + "premise_groups": [ + { + "id": "G-B35", + "combination": "ALL", + "conclusion": "B36", + "premise_use_ids": [ + "U35.1", + "U35.2", + "U35.3" + ], + "basis": [ + { + "record_id": "R6049443374", + "locator": "### B35 — P lines399" + }, + { + "record_id": "R6054305355", + "locator": "## COMPLETE / own RELEASE — P-C candidate kinds and group table" + } + ] + } + ], + "related_unit_ids": [] + }, + { + "id": "B36", + "source": { + "source_id": "P", + "lines": [ + 401, + 401 + ], + "locator": "P lines401", + "precision": "exact_lines" + }, + "section": 13, + "description": { + "text": "(13.3) target-polynomial C³ moments; paired with B35.", + "source_refs": [ + { + "source_id": "P", + "lines": [ + 401, + 401 + ], + "locator": "P lines401", + "precision": "exact_lines" + } + ], + "record_refs": [ + { + "record_id": "R6049443374", + "locator": "### B36 — P lines401" + } + ], + "unknown_refs": [] + }, + "uses": [], + "premise_groups": [], + "related_unit_ids": [] + }, + { + "id": "B37", + "source": { + "source_id": "P", + "lines": [ + 403, + 403 + ], + "locator": "P lines403", + "precision": "exact_lines" + }, + "section": 13, + "description": { + "text": "Every finite p and uniform r/frame scope; one repeated applicability use, not an extra bound.", + "source_refs": [ + { + "source_id": "P", + "lines": [ + 403, + 403 + ], + "locator": "P lines403", + "precision": "exact_lines" + } + ], + "record_refs": [ + { + "record_id": "R6049443374", + "locator": "### B37 — P lines403" + } + ], + "unknown_refs": [] + }, + "uses": [ + { + "id": "U37.1", + "kind": "premise", + "binding": { + "consumer_statement_id": "UNIFORM-MATRIX-CAP-LIFETIME-20260924-v1::Theorem-C", + "consumer_unit_id": "B37", + "consumer_source": { + "source_id": "P", + "lines": [ + 403, + 403 + ], + "locator": "P lines403", + "precision": "exact_lines" + }, + "supplier_ids": [ + "S-U37.1-UNITS" + ], + "claimed_interface": { + "text": "B35–B36: target-polynomial extension.", + "source_refs": [], + "record_refs": [ + { + "record_id": "R6049443374", + "locator": "B37/U37.1" + } + ], + "unknown_refs": [] + }, + "parameter_mapping": { + "text": "Recorded occurrence: B35–B36: target-polynomial extension.\n\nLiteral consuming expression at P lines403:\nfor every fixed finite p, uniformly over r and frames on this r_0 band. This is not the compact-target bound (4.1) applied outside its scope; it is its explicit polynomial-growth version.\n\nAdditional supplier-to-consumer substitutions beyond this retained wording/expression are unexpanded in this companion; no extra map is inferred.", + "source_refs": [ + { + "source_id": "P", + "lines": [ + 403, + 403 + ], + "locator": "P lines403", + "precision": "exact_lines" + } + ], + "record_refs": [ + { + "record_id": "R6049443374", + "locator": "B37/U37.1" + } + ], + "unknown_refs": [] + }, + "context": { + "text": "Recorded owning-block description: Every finite p and uniform r/frame scope; one repeated applicability use, not an extra bound.", + "source_refs": [ + { + "source_id": "P", + "lines": [ + 403, + 403 + ], + "locator": "P lines403", + "precision": "exact_lines" + } + ], + "record_refs": [ + { + "record_id": "R6049443374", + "locator": "### B37 — P lines403" + } + ], + "unknown_refs": [] + }, + "source_reading": [] + }, + "provenance": [ + { + "record_id": "R6049443374", + "locator": "B37/U37.1" + } + ], + "applicability_reviews": [], + "unknown_refs": [] + } + ], + "premise_groups": [ + { + "id": "G-B37", + "combination": "ALL", + "conclusion": "B37", + "premise_use_ids": [ + "U37.1" + ], + "basis": [ + { + "record_id": "R6049443374", + "locator": "### B37 — P lines403" + }, + { + "record_id": "R6054305355", + "locator": "## COMPLETE / own RELEASE — P-C candidate kinds and group table" + } + ] + } + ], + "related_unit_ids": [] + }, + { + "id": "B38", + "source": { + "source_id": "P", + "lines": [ + 405, + 405 + ], + "locator": "P lines405", + "precision": "exact_lines" + }, + "section": 13, + "description": { + "text": "Earlier P §5 imported; supporting type limit reads E1+W1 where consumed.", + "source_refs": [ + { + "source_id": "P", + "lines": [ + 405, + 405 + ], + "locator": "P lines405", + "precision": "exact_lines" + } + ], + "record_refs": [ + { + "record_id": "R6049443374", + "locator": "### B38 — P lines405" + } + ], + "unknown_refs": [] + }, + "uses": [ + { + "id": "U38.1", + "kind": "premise", + "binding": { + "consumer_statement_id": "UNIFORM-MATRIX-CAP-LIFETIME-20260924-v1::Theorem-C", + "consumer_unit_id": "B38", + "consumer_source": { + "source_id": "P", + "lines": [ + 405, + 405 + ], + "locator": "P lines405", + "precision": "exact_lines" + }, + "supplier_ids": [ + "S-U38.1-UNNAMED" + ], + "claimed_interface": { + "text": "P (5.1): endpoint identities.", + "source_refs": [], + "record_refs": [ + { + "record_id": "R6049443374", + "locator": "B38/U38.1" + } + ], + "unknown_refs": [] + }, + "parameter_mapping": { + "text": "Recorded occurrence: P (5.1): endpoint identities.\n\nLiteral consuming expression at P lines405:\nBy (5.1),(5.3), for r<=1,\n\nAdditional supplier-to-consumer substitutions beyond this retained wording/expression are unexpanded in this companion; no extra map is inferred.", + "source_refs": [ + { + "source_id": "P", + "lines": [ + 405, + 405 + ], + "locator": "P lines405", + "precision": "exact_lines" + } + ], + "record_refs": [ + { + "record_id": "R6049443374", + "locator": "B38/U38.1" + } + ], + "unknown_refs": [] + }, + "context": { + "text": "Recorded owning-block description: Earlier P §5 imported; supporting type limit reads E1+W1 where consumed.\n\nSource-attributed reading/scope qualifications:\nE1 is a reading correction to P §5, not an additional probability result or counted premise. Read the Hessian congruence as D_r=diag(r^(-1/2),I), with det(D_r H_i D_r)=det(H_i)/r.", + "source_refs": [ + { + "source_id": "P", + "lines": [ + 405, + 405 + ], + "locator": "P lines405", + "precision": "exact_lines" + }, + { + "source_id": "E1", + "lines": [ + 21, + 40 + ], + "locator": "Corrected congruence and normalization", + "precision": "exact_lines" + } + ], + "record_refs": [ + { + "record_id": "R6049443374", + "locator": "### B38 — P lines405" + }, + { + "record_id": "R6049548422", + "locator": "4. Consumption boundaries / E1" + }, + { + "record_id": "R6053473777", + "locator": "Source-bound decision table / 4. Reading boundary" + } + ], + "unknown_refs": [] + }, + "source_reading": [ + { + "boundary_id": "READ-E1", + "supplier_ids": [ + "S-U38.1-UNNAMED" + ], + "applies_to": [ + { + "source_id": "E1", + "lines": [ + 21, + 40 + ], + "locator": "Corrected congruence and normalization", + "precision": "exact_lines" + } + ], + "explanation": { + "text": "E1 is a reading correction to P §5, not an additional probability result or counted premise. Read the Hessian congruence as D_r=diag(r^(-1/2),I), with det(D_r H_i D_r)=det(H_i)/r.", + "source_refs": [ + { + "source_id": "E1", + "lines": [ + 21, + 40 + ], + "locator": "Corrected congruence and normalization", + "precision": "exact_lines" + } + ], + "record_refs": [ + { + "record_id": "R6049548422", + "locator": "4. Consumption boundaries / E1" + }, + { + "record_id": "R6053473777", + "locator": "Source-bound decision table / 4. Reading boundary" + } + ], + "unknown_refs": [] + } + } + ] + }, + "provenance": [ + { + "record_id": "R6049443374", + "locator": "B38/U38.1" + } + ], + "applicability_reviews": [], + "unknown_refs": [] + }, + { + "id": "U38.2", + "kind": "premise", + "binding": { + "consumer_statement_id": "UNIFORM-MATRIX-CAP-LIFETIME-20260924-v1::Theorem-C", + "consumer_unit_id": "B38", + "consumer_source": { + "source_id": "P", + "lines": [ + 405, + 405 + ], + "locator": "P lines405", + "precision": "exact_lines" + }, + "supplier_ids": [ + "S-U38.2-UNNAMED" + ], + "claimed_interface": { + "text": "P (5.3): determinant product envelope.", + "source_refs": [], + "record_refs": [ + { + "record_id": "R6049443374", + "locator": "B38/U38.2" + } + ], + "unknown_refs": [] + }, + "parameter_mapping": { + "text": "Recorded occurrence: P (5.3): determinant product envelope.\n\nLiteral consuming expression at P lines405:\nBy (5.1),(5.3), for r<=1,\n\nAdditional supplier-to-consumer substitutions beyond this retained wording/expression are unexpanded in this companion; no extra map is inferred.", + "source_refs": [ + { + "source_id": "P", + "lines": [ + 405, + 405 + ], + "locator": "P lines405", + "precision": "exact_lines" + } + ], + "record_refs": [ + { + "record_id": "R6049443374", + "locator": "B38/U38.2" + } + ], + "unknown_refs": [] + }, + "context": { + "text": "Recorded owning-block description: Earlier P §5 imported; supporting type limit reads E1+W1 where consumed.\n\nSource-attributed reading/scope qualifications:\nE1 is a reading correction to P §5, not an additional probability result or counted premise. Read the Hessian congruence as D_r=diag(r^(-1/2),I), with det(D_r H_i D_r)=det(H_i)/r.", + "source_refs": [ + { + "source_id": "P", + "lines": [ + 405, + 405 + ], + "locator": "P lines405", + "precision": "exact_lines" + }, + { + "source_id": "E1", + "lines": [ + 21, + 40 + ], + "locator": "Corrected congruence and normalization", + "precision": "exact_lines" + } + ], + "record_refs": [ + { + "record_id": "R6049443374", + "locator": "### B38 — P lines405" + }, + { + "record_id": "R6049548422", + "locator": "4. Consumption boundaries / E1" + }, + { + "record_id": "R6053473777", + "locator": "Source-bound decision table / 4. Reading boundary" + } + ], + "unknown_refs": [] + }, + "source_reading": [ + { + "boundary_id": "READ-E1", + "supplier_ids": [ + "S-U38.2-UNNAMED" + ], + "applies_to": [ + { + "source_id": "E1", + "lines": [ + 21, + 40 + ], + "locator": "Corrected congruence and normalization", + "precision": "exact_lines" + } + ], + "explanation": { + "text": "E1 is a reading correction to P §5, not an additional probability result or counted premise. Read the Hessian congruence as D_r=diag(r^(-1/2),I), with det(D_r H_i D_r)=det(H_i)/r.", + "source_refs": [ + { + "source_id": "E1", + "lines": [ + 21, + 40 + ], + "locator": "Corrected congruence and normalization", + "precision": "exact_lines" + } + ], + "record_refs": [ + { + "record_id": "R6049548422", + "locator": "4. Consumption boundaries / E1" + }, + { + "record_id": "R6053473777", + "locator": "Source-bound decision table / 4. Reading boundary" + } + ], + "unknown_refs": [] + } + } + ] + }, + "provenance": [ + { + "record_id": "R6049443374", + "locator": "B38/U38.2" + } + ], + "applicability_reviews": [], + "unknown_refs": [] + } + ], + "premise_groups": [ + { + "id": "G-B38", + "combination": "ALL", + "conclusion": "B39", + "premise_use_ids": [ + "U38.1", + "U38.2" + ], + "basis": [ + { + "record_id": "R6049443374", + "locator": "### B38 — P lines405" + }, + { + "record_id": "R6054305355", + "locator": "## COMPLETE / own RELEASE — P-C candidate kinds and group table" + } + ] + } + ], + "related_unit_ids": [] + }, + { + "id": "B39", + "source": { + "source_id": "P", + "lines": [ + 407, + 408 + ], + "locator": "P lines407–408", + "precision": "exact_lines" + }, + "section": 13, + "description": { + "text": "Two displayed determinant/typed-weight inequalities from B38.", + "source_refs": [ + { + "source_id": "P", + "lines": [ + 407, + 408 + ], + "locator": "P lines407–408", + "precision": "exact_lines" + } + ], + "record_refs": [ + { + "record_id": "R6049443374", + "locator": "### B39 — P lines407–408" + } + ], + "unknown_refs": [] + }, + "uses": [], + "premise_groups": [], + "related_unit_ids": [] + }, + { + "id": "B40", + "source": { + "source_id": "P", + "lines": [ + 410, + 410 + ], + "locator": "P lines410", + "precision": "exact_lines" + }, + "section": 13, + "description": { + "text": "Combines into unnormalized intensity majorant; remains valid at shrinking k.", + "source_refs": [ + { + "source_id": "P", + "lines": [ + 410, + 410 + ], + "locator": "P lines410", + "precision": "exact_lines" + } + ], + "record_refs": [ + { + "record_id": "R6049443374", + "locator": "### B40 — P lines410" + } + ], + "unknown_refs": [] + }, + "uses": [ + { + "id": "U40.1", + "kind": "premise", + "binding": { + "consumer_statement_id": "UNIFORM-MATRIX-CAP-LIFETIME-20260924-v1::Theorem-C", + "consumer_unit_id": "B40", + "consumer_source": { + "source_id": "P", + "lines": [ + 410, + 410 + ], + "locator": "P lines410", + "precision": "exact_lines" + }, + "supplier_ids": [ + "S-U40.1-UNITS" + ], + "claimed_interface": { + "text": "B39: determinant inequalities without k or Z division.", + "source_refs": [], + "record_refs": [ + { + "record_id": "R6049443374", + "locator": "B40/U40.1" + } + ], + "unknown_refs": [] + }, + "parameter_mapping": { + "text": "Recorded occurrence: B39: determinant inequalities without k or Z division.\n\nLiteral consuming expression at P lines410:\nThese inequalities remain true when k is arbitrarily small; no division by k or by Z_r has occurred. Combining with (13.2),(13.3) gives the full unnormalized-intensity majorant\n\nAdditional supplier-to-consumer substitutions beyond this retained wording/expression are unexpanded in this companion; no extra map is inferred.", + "source_refs": [ + { + "source_id": "P", + "lines": [ + 410, + 410 + ], + "locator": "P lines410", + "precision": "exact_lines" + } + ], + "record_refs": [ + { + "record_id": "R6049443374", + "locator": "B40/U40.1" + } + ], + "unknown_refs": [] + }, + "context": { + "text": "Recorded owning-block description: Combines into unnormalized intensity majorant; remains valid at shrinking k.", + "source_refs": [ + { + "source_id": "P", + "lines": [ + 410, + 410 + ], + "locator": "P lines410", + "precision": "exact_lines" + } + ], + "record_refs": [ + { + "record_id": "R6049443374", + "locator": "### B40 — P lines410" + } + ], + "unknown_refs": [] + }, + "source_reading": [] + }, + "provenance": [ + { + "record_id": "R6049443374", + "locator": "B40/U40.1" + } + ], + "applicability_reviews": [], + "unknown_refs": [] + }, + { + "id": "U40.2", + "kind": "premise", + "binding": { + "consumer_statement_id": "UNIFORM-MATRIX-CAP-LIFETIME-20260924-v1::Theorem-C", + "consumer_unit_id": "B40", + "consumer_source": { + "source_id": "P", + "lines": [ + 410, + 410 + ], + "locator": "P lines410", + "precision": "exact_lines" + }, + "supplier_ids": [ + "S-U40.2-UNITS" + ], + "claimed_interface": { + "text": "B34: Gaussian pin tail.", + "source_refs": [], + "record_refs": [ + { + "record_id": "R6049443374", + "locator": "B40/U40.2" + } + ], + "unknown_refs": [] + }, + "parameter_mapping": { + "text": "Recorded occurrence: B34: Gaussian pin tail.\n\nLiteral consuming expression at P lines410:\nThese inequalities remain true when k is arbitrarily small; no division by k or by Z_r has occurred. Combining with (13.2),(13.3) gives the full unnormalized-intensity majorant\n\nAdditional supplier-to-consumer substitutions beyond this retained wording/expression are unexpanded in this companion; no extra map is inferred.", + "source_refs": [ + { + "source_id": "P", + "lines": [ + 410, + 410 + ], + "locator": "P lines410", + "precision": "exact_lines" + } + ], + "record_refs": [ + { + "record_id": "R6049443374", + "locator": "B40/U40.2" + } + ], + "unknown_refs": [] + }, + "context": { + "text": "Recorded owning-block description: Combines into unnormalized intensity majorant; remains valid at shrinking k.", + "source_refs": [ + { + "source_id": "P", + "lines": [ + 410, + 410 + ], + "locator": "P lines410", + "precision": "exact_lines" + } + ], + "record_refs": [ + { + "record_id": "R6049443374", + "locator": "### B40 — P lines410" + } + ], + "unknown_refs": [] + }, + "source_reading": [] + }, + "provenance": [ + { + "record_id": "R6049443374", + "locator": "B40/U40.2" + } + ], + "applicability_reviews": [], + "unknown_refs": [] + }, + { + "id": "U40.3", + "kind": "premise", + "binding": { + "consumer_statement_id": "UNIFORM-MATRIX-CAP-LIFETIME-20260924-v1::Theorem-C", + "consumer_unit_id": "B40", + "consumer_source": { + "source_id": "P", + "lines": [ + 410, + 410 + ], + "locator": "P lines410", + "precision": "exact_lines" + }, + "supplier_ids": [ + "S-U40.3-UNITS" + ], + "claimed_interface": { + "text": "B36: all-mark moments.", + "source_refs": [], + "record_refs": [ + { + "record_id": "R6049443374", + "locator": "B40/U40.3" + } + ], + "unknown_refs": [] + }, + "parameter_mapping": { + "text": "Recorded occurrence: B36: all-mark moments.\n\nLiteral consuming expression at P lines410:\nThese inequalities remain true when k is arbitrarily small; no division by k or by Z_r has occurred. Combining with (13.2),(13.3) gives the full unnormalized-intensity majorant\n\nAdditional supplier-to-consumer substitutions beyond this retained wording/expression are unexpanded in this companion; no extra map is inferred.", + "source_refs": [ + { + "source_id": "P", + "lines": [ + 410, + 410 + ], + "locator": "P lines410", + "precision": "exact_lines" + } + ], + "record_refs": [ + { + "record_id": "R6049443374", + "locator": "B40/U40.3" + } + ], + "unknown_refs": [] + }, + "context": { + "text": "Recorded owning-block description: Combines into unnormalized intensity majorant; remains valid at shrinking k.", + "source_refs": [ + { + "source_id": "P", + "lines": [ + 410, + 410 + ], + "locator": "P lines410", + "precision": "exact_lines" + } + ], + "record_refs": [ + { + "record_id": "R6049443374", + "locator": "### B40 — P lines410" + } + ], + "unknown_refs": [] + }, + "source_reading": [] + }, + "provenance": [ + { + "record_id": "R6049443374", + "locator": "B40/U40.3" + } + ], + "applicability_reviews": [], + "unknown_refs": [] + } + ], + "premise_groups": [ + { + "id": "G-B40", + "combination": "ALL", + "conclusion": "B41", + "premise_use_ids": [ + "U40.1", + "U40.2", + "U40.3" + ], + "basis": [ + { + "record_id": "R6049443374", + "locator": "### B40 — P lines410" + }, + { + "record_id": "R6054305355", + "locator": "## COMPLETE / own RELEASE — P-C candidate kinds and group table" + } + ] + } + ], + "related_unit_ids": [] + }, + { + "id": "B41", + "source": { + "source_id": "P", + "lines": [ + 412, + 413 + ], + "locator": "P lines412–413", + "precision": "exact_lines" + }, + "section": 13, + "description": { + "text": "(13.4) H(b,k) conclusion; no probability normalization.", + "source_refs": [ + { + "source_id": "P", + "lines": [ + 412, + 413 + ], + "locator": "P lines412–413", + "precision": "exact_lines" + } + ], + "record_refs": [ + { + "record_id": "R6049443374", + "locator": "### B41 — P lines412–413" + } + ], + "unknown_refs": [] + }, + "uses": [], + "premise_groups": [], + "related_unit_ids": [] + }, + { + "id": "B42", + "source": { + "source_id": "P", + "lines": [ + 415, + 415 + ], + "locator": "P lines415", + "precision": "exact_lines" + }, + "section": 13, + "description": { + "text": "Z_r>0 finite and p_r→1 pointwise; no globally uniform normalizer or selection rate.", + "source_refs": [ + { + "source_id": "P", + "lines": [ + 415, + 415 + ], + "locator": "P lines415", + "precision": "exact_lines" + } + ], + "record_refs": [ + { + "record_id": "R6049443374", + "locator": "### B42 — P lines415" + } + ], + "unknown_refs": [] + }, + "uses": [ + { + "id": "U42.1", + "kind": "premise", + "binding": { + "consumer_statement_id": "UNIFORM-MATRIX-CAP-LIFETIME-20260924-v1::Theorem-C", + "consumer_unit_id": "B42", + "consumer_source": { + "source_id": "P", + "lines": [ + 415, + 415 + ], + "locator": "P lines415", + "precision": "exact_lines" + }, + "supplier_ids": [ + "S-U42.1-P" + ], + "claimed_interface": { + "text": "P §2: append both distinct-site endpoint Hessians, full jet rank.", + "source_refs": [], + "record_refs": [ + { + "record_id": "R6049443374", + "locator": "B42/U42.1" + } + ], + "unknown_refs": [] + }, + "parameter_mapping": { + "text": "Recorded occurrence: P §2: append both distinct-site endpoint Hessians, full jet rank.\n\nLiteral consuming expression at P lines415:\nFor every fixed positive r and every b,k>0, Z_r is positive and finite: append BOTH endpoint Hessians to the distinct-site pins; the full residual Gaussian density is positive on a product of an open maximum cone and an open index-(d-1) cone. Thus p_r is defined, even though no globally uniform lower floor has been used. For every fixed b,k>0, Theorem A on a compact neighborhood implies p_r->1 as r->0.\n\nAdditional supplier-to-consumer substitutions beyond this retained wording/expression are unexpanded in this companion; no extra map is inferred.", + "source_refs": [ + { + "source_id": "P", + "lines": [ + 415, + 415 + ], + "locator": "P lines415", + "precision": "exact_lines" + } + ], + "record_refs": [ + { + "record_id": "R6049443374", + "locator": "B42/U42.1" + } + ], + "unknown_refs": [] + }, + "context": { + "text": "Recorded owning-block description: Z_r>0 finite and p_r→1 pointwise; no globally uniform normalizer or selection rate.", + "source_refs": [ + { + "source_id": "P", + "lines": [ + 415, + 415 + ], + "locator": "P lines415", + "precision": "exact_lines" + } + ], + "record_refs": [ + { + "record_id": "R6049443374", + "locator": "### B42 — P lines415" + } + ], + "unknown_refs": [] + }, + "source_reading": [] + }, + "provenance": [ + { + "record_id": "R6049443374", + "locator": "B42/U42.1" + } + ], + "applicability_reviews": [], + "unknown_refs": [] + }, + { + "id": "U42.2", + "kind": "premise", + "binding": { + "consumer_statement_id": "UNIFORM-MATRIX-CAP-LIFETIME-20260924-v1::Theorem-C", + "consumer_unit_id": "B42", + "consumer_source": { + "source_id": "P", + "lines": [ + 415, + 415 + ], + "locator": "P lines415", + "precision": "exact_lines" + }, + "supplier_ids": [ + "S-U42.2-UNNAMED" + ], + "claimed_interface": { + "text": "unnamed Gaussian positive density on product of open typed cones.", + "source_refs": [], + "record_refs": [ + { + "record_id": "R6049443374", + "locator": "B42/U42.2" + } + ], + "unknown_refs": [] + }, + "parameter_mapping": { + "text": "Recorded occurrence: unnamed Gaussian positive density on product of open typed cones.\n\nLiteral consuming expression at P lines415:\nFor every fixed positive r and every b,k>0, Z_r is positive and finite: append BOTH endpoint Hessians to the distinct-site pins; the full residual Gaussian density is positive on a product of an open maximum cone and an open index-(d-1) cone. Thus p_r is defined, even though no globally uniform lower floor has been used. For every fixed b,k>0, Theorem A on a compact neighborhood implies p_r->1 as r->0.\n\nAdditional supplier-to-consumer substitutions beyond this retained wording/expression are unexpanded in this companion; no extra map is inferred.", + "source_refs": [ + { + "source_id": "P", + "lines": [ + 415, + 415 + ], + "locator": "P lines415", + "precision": "exact_lines" + } + ], + "record_refs": [ + { + "record_id": "R6049443374", + "locator": "B42/U42.2" + } + ], + "unknown_refs": [] + }, + "context": { + "text": "Recorded owning-block description: Z_r>0 finite and p_r→1 pointwise; no globally uniform normalizer or selection rate.", + "source_refs": [ + { + "source_id": "P", + "lines": [ + 415, + 415 + ], + "locator": "P lines415", + "precision": "exact_lines" + } + ], + "record_refs": [ + { + "record_id": "R6049443374", + "locator": "### B42 — P lines415" + } + ], + "unknown_refs": [] + }, + "source_reading": [] + }, + "provenance": [ + { + "record_id": "R6049443374", + "locator": "B42/U42.2" + } + ], + "applicability_reviews": [], + "unknown_refs": [] + }, + { + "id": "U42.3", + "kind": "premise", + "binding": { + "consumer_statement_id": "UNIFORM-MATRIX-CAP-LIFETIME-20260924-v1::Theorem-C", + "consumer_unit_id": "B42", + "consumer_source": { + "source_id": "P", + "lines": [ + 415, + 415 + ], + "locator": "P lines415", + "precision": "exact_lines" + }, + "supplier_ids": [ + "S-U42.3-UNITS" + ], + "claimed_interface": { + "text": "B34–B39: finite determinant moments.", + "source_refs": [], + "record_refs": [ + { + "record_id": "R6049443374", + "locator": "B42/U42.3" + } + ], + "unknown_refs": [] + }, + "parameter_mapping": { + "text": "Recorded occurrence: B34–B39: finite determinant moments.\n\nLiteral consuming expression at P lines415:\nFor every fixed positive r and every b,k>0, Z_r is positive and finite: append BOTH endpoint Hessians to the distinct-site pins; the full residual Gaussian density is positive on a product of an open maximum cone and an open index-(d-1) cone. Thus p_r is defined, even though no globally uniform lower floor has been used. For every fixed b,k>0, Theorem A on a compact neighborhood implies p_r->1 as r->0.\n\nAdditional supplier-to-consumer substitutions beyond this retained wording/expression are unexpanded in this companion; no extra map is inferred.", + "source_refs": [ + { + "source_id": "P", + "lines": [ + 415, + 415 + ], + "locator": "P lines415", + "precision": "exact_lines" + } + ], + "record_refs": [ + { + "record_id": "R6049443374", + "locator": "B42/U42.3" + } + ], + "unknown_refs": [] + }, + "context": { + "text": "Recorded owning-block description: Z_r>0 finite and p_r→1 pointwise; no globally uniform normalizer or selection rate.", + "source_refs": [ + { + "source_id": "P", + "lines": [ + 415, + 415 + ], + "locator": "P lines415", + "precision": "exact_lines" + } + ], + "record_refs": [ + { + "record_id": "R6049443374", + "locator": "### B42 — P lines415" + } + ], + "unknown_refs": [] + }, + "source_reading": [] + }, + "provenance": [ + { + "record_id": "R6049443374", + "locator": "B42/U42.3" + } + ], + "applicability_reviews": [], + "unknown_refs": [] + }, + { + "id": "U42.4", + "kind": "premise", + "binding": { + "consumer_statement_id": "UNIFORM-MATRIX-CAP-LIFETIME-20260924-v1::Theorem-C", + "consumer_unit_id": "B42", + "consumer_source": { + "source_id": "P", + "lines": [ + 415, + 415 + ], + "locator": "P lines415", + "precision": "exact_lines" + }, + "supplier_ids": [ + "S-U42.4-P" + ], + "claimed_interface": { + "text": "P Theorem A on each fixed compact mark neighbourhood.", + "source_refs": [], + "record_refs": [ + { + "record_id": "R6049443374", + "locator": "B42/U42.4" + } + ], + "unknown_refs": [] + }, + "parameter_mapping": { + "text": "Recorded occurrence: P Theorem A on each fixed compact mark neighbourhood.\n\nLiteral consuming expression at P lines415:\nFor every fixed positive r and every b,k>0, Z_r is positive and finite: append BOTH endpoint Hessians to the distinct-site pins; the full residual Gaussian density is positive on a product of an open maximum cone and an open index-(d-1) cone. Thus p_r is defined, even though no globally uniform lower floor has been used. For every fixed b,k>0, Theorem A on a compact neighborhood implies p_r->1 as r->0.\n\nAdditional supplier-to-consumer substitutions beyond this retained wording/expression are unexpanded in this companion; no extra map is inferred.", + "source_refs": [ + { + "source_id": "P", + "lines": [ + 415, + 415 + ], + "locator": "P lines415", + "precision": "exact_lines" + } + ], + "record_refs": [ + { + "record_id": "R6049443374", + "locator": "B42/U42.4" + } + ], + "unknown_refs": [] + }, + "context": { + "text": "Recorded owning-block description: Z_r>0 finite and p_r→1 pointwise; no globally uniform normalizer or selection rate.\n\nSource-attributed reading/scope qualifications:\nCAP enters through the recorded Theorem A / P §8 reading. Only its deterministic theorem and §§2–5 are consumed. CAP30–47 is the excluded 2D fixed-axis, fixed-mark probabilistic corollary; its numerical window/constants are not transferred to arbitrary d, marks or frames. The cap-local maximin identification is not a global finite-bar once-counting proof.\n\nREC163–166 bounds the cap/Theorem-A existential r_* by the embedding condition r=ell/r_0^3. 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After the exact change (11.1),\n\nAdditional supplier-to-consumer substitutions beyond this retained wording/expression are unexpanded in this companion; no extra map is inferred.", + "source_refs": [ + { + "source_id": "P", + "lines": [ + 417, + 417 + ], + "locator": "P lines417", + "precision": "exact_lines" + } + ], + "record_refs": [ + { + "record_id": "R6049443374", + "locator": "B43/U43.2" + } + ], + "unknown_refs": [] + }, + "context": { + "text": "Recorded owning-block description: Produces the exact lower cutoff k≥ell/r0³; retained in B44.", + "source_refs": [ + { + "source_id": "P", + "lines": [ + 417, + 417 + ], + "locator": "P lines417", + "precision": "exact_lines" + } + ], + "record_refs": [ + { + "record_id": "R6049443374", + "locator": "### B43 — P lines417" + } + ], + "unknown_refs": [] + }, + "source_reading": [] + }, + "provenance": [ + { + "record_id": "R6049443374", + "locator": "B43/U43.2" + } + ], + "applicability_reviews": [], + "unknown_refs": [] + } + ], + "premise_groups": [ + { + "id": "G-B43", + "combination": "ALL", + "conclusion": "B44", + "premise_use_ids": [ + "U43.1", + "U43.2" + ], + "basis": [ + { + "record_id": "R6049443374", + "locator": "### B43 — P lines417" + }, + { + "record_id": "R6054305355", + "locator": "## COMPLETE / own RELEASE — P-C candidate kinds and group table" + } + ] + } + ], + "related_unit_ids": [] + }, + { + "id": "B44", + "source": { + "source_id": "P", + "lines": [ + 419, + 422 + ], + "locator": "P lines419–422", + "precision": "exact_lines" + }, + "section": 13, + "description": { + "text": "(13.5) unrestricted mark integral with indicator/zero extension; parent B43.", + "source_refs": [ + { + "source_id": "P", + "lines": [ + 419, + 422 + ], + "locator": "P lines419–422", + "precision": "exact_lines" + } + ], + "record_refs": [ + { + "record_id": "R6049443374", + "locator": "### B44 — P lines419–422" + } + ], + "unknown_refs": [] + }, + "uses": [], + "premise_groups": [], + "related_unit_ids": [] + }, + { + "id": "B45", + "source": { + "source_id": "P", + "lines": [ + 424, + 424 + ], + "locator": "P lines424", + "precision": "exact_lines" + }, + "section": 13, + "description": { + "text": "Includes shrinking-k boundary without a global Q^W probability constant.", + "source_refs": [ + { + "source_id": "P", + "lines": [ + 424, + 424 + ], + "locator": "P lines424", + "precision": "exact_lines" + } + ], + "record_refs": [ + { + "record_id": "R6049443374", + "locator": "### B45 — P lines424" + } + ], + "unknown_refs": [] + }, + "uses": [ + { + "id": "U45.1", + "kind": "premise", + "binding": { + "consumer_statement_id": "UNIFORM-MATRIX-CAP-LIFETIME-20260924-v1::Theorem-C", + "consumer_unit_id": "B45", + "consumer_source": { + "source_id": "P", + "lines": [ + 424, + 424 + ], + "locator": "P lines424", + "precision": "exact_lines" + }, + "supplier_ids": [ + "S-U45.1-E2" + ], + "claimed_interface": { + "text": "E2 §9.4: selected global mark.", + "source_refs": [], + "record_refs": [ + { + "record_id": "R6049443374", + "locator": "B45/U45.1" + } + ], + "unknown_refs": [] + }, + "parameter_mapping": { + "text": "Recorded occurrence: E2 §9.4: selected global mark.\n\nLiteral consuming expression at P lines424:\nwith the integrand defined to be zero where the indicator is zero. The selected near density has the additional factor p_r. Both integrands are dominated by H(b,k)/(3 k^(2/3)). This majorant is integrable: the k exponent -2/3 is strictly greater than -1 at zero, and Gaussian tails absorb the polynomial at infinity and in b. 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The near-diagonal exhaustion at E2:110 imports P §§3/5/10 estimates rather than reproving them; the remaining off-diagonal/unbounded-mark/coefficient obligations are separate.\n\nReferenced UNKNOWN annotations retain their historical observation/response scope; they are not current failure or acceptance verdicts.", + "source_refs": [ + { + "source_id": "P", + "lines": [ + 424, + 424 + ], + "locator": "P lines424", + "precision": "exact_lines" + }, + { + "source_id": "E2", + "lines": [ + 94, + 110 + ], + "locator": "§9.4 global elder/type mark and imported diagonal exhaustion", + "precision": "exact_lines" + }, + { + "source_id": "E2", + "lines": [ + 121, + 131 + ], + "locator": "Separate obligations retained by E2", + "precision": "exact_lines" + } + ], + "record_refs": [ + { + "record_id": "R6049443374", + "locator": "### B45 — P lines424" + }, + { + "record_id": "R6049548422", + "locator": "4. 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The near-diagonal exhaustion at E2:110 imports P §§3/5/10 estimates rather than reproving them; the remaining off-diagonal/unbounded-mark/coefficient obligations are separate.", + "source_refs": [ + { + "source_id": "E2", + "lines": [ + 94, + 110 + ], + "locator": "§9.4 global elder/type mark and imported diagonal exhaustion", + "precision": "exact_lines" + }, + { + "source_id": "E2", + "lines": [ + 121, + 131 + ], + "locator": "Separate obligations retained by E2", + "precision": "exact_lines" + } + ], + "record_refs": [ + { + "record_id": "R6049548422", + "locator": "4. 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The selected near density has the additional factor p_r. Both integrands are dominated by H(b,k)/(3 k^(2/3)). This majorant is integrable: the k exponent -2/3 is strictly greater than -1 at zero, and Gaussian tails absorb the polynomial at infinity and in b. 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The selected near density has the additional factor p_r. Both integrands are dominated by H(b,k)/(3 k^(2/3)). This majorant is integrable: the k exponent -2/3 is strictly greater than -1 at zero, and Gaussian tails absorb the polynomial at infinity and in b. 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Dominated convergence therefore gives the same limit for the two near densities:\n\nAdditional supplier-to-consumer substitutions beyond this retained wording/expression are unexpanded in this companion; no extra map is inferred.", + "source_refs": [ + { + "source_id": "P", + "lines": [ + 426, + 426 + ], + "locator": "P lines426", + "precision": "exact_lines" + } + ], + "record_refs": [ + { + "record_id": "R6049443374", + "locator": "B46/U46.1" + } + ], + "unknown_refs": [] + }, + "context": { + "text": "Recorded owning-block description: All births/positive gaps leading limit; no quantitative rate supplied by DCT.", + "source_refs": [ + { + "source_id": "P", + "lines": [ + 426, + 426 + ], + "locator": "P lines426", + "precision": "exact_lines" + } + ], + "record_refs": [ + { + "record_id": "R6049443374", + "locator": "### B46 — P lines426" + } + ], + "unknown_refs": [] + }, + "source_reading": [] + }, + "provenance": [ + { + "record_id": "R6049443374", + "locator": "B46/U46.1" + } + ], + "applicability_reviews": [], + "unknown_refs": [] + }, + { + "id": "U46.2", + "kind": "premise", + "binding": { + "consumer_statement_id": "UNIFORM-MATRIX-CAP-LIFETIME-20260924-v1::Theorem-C", + "consumer_unit_id": "B46", + "consumer_source": { + "source_id": "P", + "lines": [ + 426, + 426 + ], + "locator": "P lines426", + "precision": "exact_lines" + }, + "supplier_ids": [ + "S-U46.2-UNITS" + ], + "claimed_interface": { + "text": "B09: contact A_r→A_0.", + "source_refs": [], + "record_refs": [ + { + "record_id": "R6049443374", + "locator": "B46/U46.2" + } + ], + "unknown_refs": [] + }, + "parameter_mapping": { + "text": "Recorded occurrence: B09: contact A_r→A_0.\n\nLiteral consuming expression at P lines426:\nFor each fixed b,k>0,u, the indicator tends to one, A_r->A_0 and p_r->1. Dominated convergence therefore gives the same limit for the two near densities:\n\nAdditional supplier-to-consumer substitutions beyond this retained wording/expression are unexpanded in this companion; no extra map is inferred.", + "source_refs": [ + { + "source_id": "P", + "lines": [ + 426, + 426 + ], + "locator": "P lines426", + "precision": "exact_lines" + } + ], + "record_refs": [ + { + "record_id": "R6049443374", + "locator": "B46/U46.2" + } + ], + "unknown_refs": [] + }, + "context": { + "text": "Recorded owning-block description: All births/positive gaps leading limit; no quantitative rate supplied by DCT.", + "source_refs": [ + { + "source_id": "P", + "lines": [ + 426, + 426 + ], + "locator": "P lines426", + "precision": "exact_lines" + } + ], + "record_refs": [ + { + "record_id": "R6049443374", + "locator": "### B46 — P lines426" + } + ], + "unknown_refs": [] + }, + "source_reading": [] + }, + "provenance": [ + { + "record_id": "R6049443374", + "locator": "B46/U46.2" + } + ], + "applicability_reviews": [], + "unknown_refs": [] + }, + { + "id": "U46.3", + "kind": "premise", + "binding": { + "consumer_statement_id": "UNIFORM-MATRIX-CAP-LIFETIME-20260924-v1::Theorem-C", + "consumer_unit_id": "B46", + "consumer_source": { + "source_id": "P", + "lines": [ + 426, + 426 + ], + "locator": "P lines426", + "precision": "exact_lines" + }, + "supplier_ids": [ + "S-U46.3-UNITS" + ], + "claimed_interface": { + "text": "B42: p_r→1 pointwise.", + "source_refs": [], + "record_refs": [ + { + "record_id": "R6049443374", + "locator": "B46/U46.3" + } + ], + "unknown_refs": [] + }, + "parameter_mapping": { + "text": "Recorded occurrence: B42: p_r→1 pointwise.\n\nLiteral consuming expression at P lines426:\nFor each fixed b,k>0,u, the indicator tends to one, A_r->A_0 and p_r->1. Dominated convergence therefore gives the same limit for the two near densities:\n\nAdditional supplier-to-consumer substitutions beyond this retained wording/expression are unexpanded in this companion; no extra map is inferred.", + "source_refs": [ + { + "source_id": "P", + "lines": [ + 426, + 426 + ], + "locator": "P lines426", + "precision": "exact_lines" + } + ], + "record_refs": [ + { + "record_id": "R6049443374", + "locator": "B46/U46.3" + } + ], + "unknown_refs": [] + }, + "context": { + "text": "Recorded owning-block description: All births/positive gaps leading limit; no quantitative rate supplied by DCT.", + "source_refs": [ + { + "source_id": "P", + "lines": [ + 426, + 426 + ], + "locator": "P lines426", + "precision": "exact_lines" + } + ], + "record_refs": [ + { + "record_id": "R6049443374", + "locator": "### B46 — P lines426" + } + ], + "unknown_refs": [] + }, + "source_reading": [] + }, + "provenance": [ + { + "record_id": "R6049443374", + "locator": "B46/U46.3" + } + ], + "applicability_reviews": [], + "unknown_refs": [] + }, + { + "id": "U46.4", + "kind": "premise", + "binding": { + "consumer_statement_id": "UNIFORM-MATRIX-CAP-LIFETIME-20260924-v1::Theorem-C", + "consumer_unit_id": "B46", + "consumer_source": { + "source_id": "P", + "lines": [ + 426, + 426 + ], + "locator": "P lines426", + "precision": "exact_lines" + }, + "supplier_ids": [ + "S-U46.4-UNITS" + ], + "claimed_interface": { + "text": "B45: integrable domination / dominated convergence.", + "source_refs": [], + "record_refs": [ + { + "record_id": "R6049443374", + "locator": "B46/U46.4" + } + ], + "unknown_refs": [] + }, + "parameter_mapping": { + "text": "Recorded occurrence: B45: integrable domination / dominated convergence.\n\nLiteral consuming expression at P lines426:\nFor each fixed b,k>0,u, the indicator tends to one, A_r->A_0 and p_r->1. Dominated convergence therefore gives the same limit for the two near densities:\n\nAdditional supplier-to-consumer substitutions beyond this retained wording/expression are unexpanded in this companion; no extra map is inferred.", + "source_refs": [ + { + "source_id": "P", + "lines": [ + 426, + 426 + ], + "locator": "P lines426", + "precision": "exact_lines" + } + ], + "record_refs": [ + { + "record_id": "R6049443374", + "locator": "B46/U46.4" + } + ], + "unknown_refs": [] + }, + "context": { + "text": "Recorded owning-block description: All births/positive gaps leading limit; no quantitative rate supplied by DCT.", + "source_refs": [ + { + "source_id": "P", + "lines": [ + 426, + 426 + ], + "locator": "P lines426", + "precision": "exact_lines" + } + ], + "record_refs": [ + { + "record_id": "R6049443374", + "locator": "### B46 — P lines426" + } + ], + "unknown_refs": [] + }, + "source_reading": [] + }, + "provenance": [ + { + "record_id": "R6049443374", + "locator": "B46/U46.4" + } + ], + "applicability_reviews": [], + "unknown_refs": [] + }, + { + "id": "U46.5", + "kind": "premise", + "binding": { + "consumer_statement_id": "UNIFORM-MATRIX-CAP-LIFETIME-20260924-v1::Theorem-C", + "consumer_unit_id": "B46", + "consumer_source": { + "source_id": "P", + "lines": [ + 426, + 426 + ], + "locator": "P lines426", + "precision": "exact_lines" + }, + "supplier_ids": [ + "S-U46.5-P" + ], + "claimed_interface": { + "text": "apply P3/5 on a compact neighborhood of each fixed b∈R,k>0", + "source_refs": [], + "record_refs": [ + { + "record_id": "R6049640627", + "locator": "paragraph beginning \"I accept A1–A6 as proposed additive uses\" / U46.5" + } + ], + "unknown_refs": [] + }, + "parameter_mapping": { + "text": "Recorded occurrence: apply P3/5 on a compact neighborhood of each fixed b∈R,k>0\n\nLiteral consuming expression at P lines426:\nFor each fixed b,k>0,u, the indicator tends to one, A_r->A_0 and p_r->1. Dominated convergence therefore gives the same limit for the two near densities:\n\nAdditional supplier-to-consumer substitutions beyond this retained wording/expression are unexpanded in this companion; no extra map is inferred.", + "source_refs": [ + { + "source_id": "P", + "lines": [ + 426, + 426 + ], + "locator": "P lines426", + "precision": "exact_lines" + } + ], + "record_refs": [ + { + "record_id": "R6049640627", + "locator": "paragraph beginning \"I accept A1–A6 as proposed additive uses\" / U46.5" + } + ], + "unknown_refs": [] + }, + "context": { + "text": "Recorded owning-block description: All births/positive gaps leading limit; no quantitative rate supplied by DCT.\n\nSource-attributed reading/scope qualifications:\nP §§3/5 are applied on a compact neighborhood of each fixed b∈R,k>0. This is a pointwise local application inside the later dominated-convergence argument, not an all-mark uniform convergence assertion.", + "source_refs": [ + { + "source_id": "P", + "lines": [ + 426, + 426 + ], + "locator": "P lines426", + "precision": "exact_lines" + }, + { + "source_id": "P", + "lines": [ + 426, + 426 + ], + "locator": "P lines426", + "precision": "exact_lines" + } + ], + "record_refs": [ + { + "record_id": "R6049443374", + "locator": "### B46 — P lines426" + }, + { + "record_id": "R6049548422", + "locator": "2. Input-use challenges / A6" + }, + { + "record_id": "R6049640627", + "locator": "U46.5" + } + ], + "unknown_refs": [] + }, + "source_reading": [] + }, + "provenance": [ + { + "record_id": "R6049640627", + "locator": "paragraph beginning \"I accept A1–A6 as proposed additive uses\" / U46.5" + }, + { + "record_id": "R6049548422", + "locator": "2. Input-use challenges (instruction 2): additive amendments / A6" + } + ], + "applicability_reviews": [], + "unknown_refs": [] + } + ], + "premise_groups": [ + { + "id": "G-B46", + "combination": "ALL", + "conclusion": "B47", + "premise_use_ids": [ + "U46.1", + "U46.2", + "U46.3", + "U46.4", + "U46.5" + ], + "basis": [ + { + "record_id": "R6049443374", + "locator": "### B46 — P lines426" + }, + { + "record_id": "R6054305355", + "locator": "## COMPLETE / own RELEASE — P-C candidate kinds and group table" + } + ] + } + ], + "related_unit_ids": [] + }, + { + "id": "B47", + "source": { + "source_id": "P", + "lines": [ + 428, + 431 + ], + "locator": "P lines428–431", + "precision": "exact_lines" + }, + "section": 13, + "description": { + "text": "(13.6) finite positive unrestricted contact integral, paired with B46.", + "source_refs": [ + { + "source_id": "P", + "lines": [ + 428, + 431 + ], + "locator": "P lines428–431", + "precision": "exact_lines" + } + ], + "record_refs": [ + { + "record_id": "R6049443374", + "locator": "### B47 — P lines428–431" + } + ], + "unknown_refs": [] + }, + "uses": [], + "premise_groups": [], + "related_unit_ids": [] + }, + { + "id": "B48", + "source": { + "source_id": "P", + "lines": [ + 433, + 433 + ], + "locator": "P lines433", + "precision": "exact_lines" + }, + "section": 13, + "description": { + "text": "Unnormalized intensity route; explicit boundary: leading limit only.", + "source_refs": [ + { + "source_id": "P", + "lines": [ + 433, + 433 + ], + "locator": "P lines433", + "precision": "exact_lines" + } + ], + "record_refs": [ + { + "record_id": "R6049443374", + "locator": "### B48 — P lines433" + } + ], + "unknown_refs": [] + }, + "uses": [ + { + "id": "U48.1", + "kind": "premise", + "binding": { + "consumer_statement_id": "UNIFORM-MATRIX-CAP-LIFETIME-20260924-v1::Theorem-C", + "consumer_unit_id": "B48", + "consumer_source": { + "source_id": "P", + "lines": [ + 433, + 433 + ], + "locator": "P lines433", + "precision": "exact_lines" + }, + "supplier_ids": [ + "S-U48.1-UNITS" + ], + "claimed_interface": { + "text": "B17/B47: common nonnegative coefficient integrand.", + "source_refs": [], + "record_refs": [ + { + "record_id": "R6049443374", + "locator": "B48/U48.1" + } + ], + "unknown_refs": [] + }, + "parameter_mapping": { + "text": "Recorded occurrence: B17/B47: common nonnegative coefficient integrand.\n\nLiteral consuming expression at P lines433:\nIn particular c_{B,K} increases to c_{d,L} along an exhausting sequence of mark rectangles. This step uses the unnormalized product pi_r Z_r, not an unjustified globally uniform Q^W probability bound. It proves an unrestricted leading limit; it does not invent a quantitative unrestricted remainder from dominated convergence.\n\nAdditional supplier-to-consumer substitutions beyond this retained wording/expression are unexpanded in this companion; no extra map is inferred.", + "source_refs": [ + { + "source_id": "P", + "lines": [ + 433, + 433 + ], + "locator": "P lines433", + "precision": "exact_lines" + } + ], + "record_refs": [ + { + "record_id": "R6049443374", + "locator": "B48/U48.1" + } + ], + "unknown_refs": [] + }, + "context": { + "text": "Recorded owning-block description: Unnormalized intensity route; explicit boundary: leading limit only.", + "source_refs": [ + { + "source_id": "P", + "lines": [ + 433, + 433 + ], + "locator": "P lines433", + "precision": "exact_lines" + } + ], + "record_refs": [ + { + "record_id": "R6049443374", + "locator": "### B48 — P lines433" + } + ], + "unknown_refs": [] + }, + "source_reading": [] + }, + "provenance": [ + { + "record_id": "R6049443374", + "locator": "B48/U48.1" + } + ], + "applicability_reviews": [], + "unknown_refs": [] + }, + { + "id": "U48.2", + "kind": "premise", + "binding": { + "consumer_statement_id": "UNIFORM-MATRIX-CAP-LIFETIME-20260924-v1::Theorem-C", + "consumer_unit_id": "B48", + "consumer_source": { + "source_id": "P", + "lines": [ + 433, + 433 + ], + "locator": "P lines433", + "precision": "exact_lines" + }, + "supplier_ids": [ + "S-U48.2-UNNAMED" + ], + "claimed_interface": { + "text": "unnamed monotone mark-rectangle exhaustion.", + "source_refs": [], + "record_refs": [ + { + "record_id": "R6049443374", + "locator": "B48/U48.2" + } + ], + "unknown_refs": [] + }, + "parameter_mapping": { + "text": "Recorded occurrence: unnamed monotone mark-rectangle exhaustion.\n\nLiteral consuming expression at P lines433:\nIn particular c_{B,K} increases to c_{d,L} along an exhausting sequence of mark rectangles. This step uses the unnormalized product pi_r Z_r, not an unjustified globally uniform Q^W probability bound. It proves an unrestricted leading limit; it does not invent a quantitative unrestricted remainder from dominated convergence.\n\nAdditional supplier-to-consumer substitutions beyond this retained wording/expression are unexpanded in this companion; no extra map is inferred.", + "source_refs": [ + { + "source_id": "P", + "lines": [ + 433, + 433 + ], + "locator": "P lines433", + "precision": "exact_lines" + } + ], + "record_refs": [ + { + "record_id": "R6049443374", + "locator": "B48/U48.2" + } + ], + "unknown_refs": [] + }, + "context": { + "text": "Recorded owning-block description: Unnormalized intensity route; explicit boundary: leading limit only.", + "source_refs": [ + { + "source_id": "P", + "lines": [ + 433, + 433 + ], + "locator": "P lines433", + "precision": "exact_lines" + } + ], + "record_refs": [ + { + "record_id": "R6049443374", + "locator": "### B48 — P lines433" + } + ], + "unknown_refs": [] + }, + "source_reading": [] + }, + "provenance": [ + { + "record_id": "R6049443374", + "locator": "B48/U48.2" + } + ], + "applicability_reviews": [], + "unknown_refs": [] + } + ], + "premise_groups": [ + { + "id": "G-B48", + "combination": "ALL", + "conclusion": "B48", + "premise_use_ids": [ + "U48.1", + "U48.2" + ], + "basis": [ + { + "record_id": "R6049443374", + "locator": "### B48 — P lines433" + }, + { + "record_id": "R6054305355", + "locator": "## COMPLETE / own RELEASE — P-C candidate kinds and group table" + } + ] + } + ], + "related_unit_ids": [] + }, + { + "id": "B49", + "source": { + "source_id": "P", + "lines": [ + 437, + 437 + ], + "locator": "P lines437", + "precision": "exact_lines" + }, + "section": 14, + "description": { + "text": "Far domain uses original pins, not singular contact transformation.", + "source_refs": [ + { + "source_id": "P", + "lines": [ + 437, + 437 + ], + "locator": "P lines437", + "precision": "exact_lines" + } + ], + "record_refs": [ + { + "record_id": "R6049443374", + "locator": "### B49 — P lines437" + } + ], + "unknown_refs": [] + }, + "uses": [ + { + "id": "U49.1", + "kind": "premise", + "binding": { + "consumer_statement_id": "UNIFORM-MATRIX-CAP-LIFETIME-20260924-v1::Theorem-C", + "consumer_unit_id": "B49", + "consumer_source": { + "source_id": "P", + "lines": [ + 437, + 437 + ], + "locator": "P lines437", + "precision": "exact_lines" + }, + "supplier_ids": [ + "S-U49.1-P" + ], + "claimed_interface": { + "text": "P §2: full rank of every distinct-site jet list.", + "source_refs": [], + "record_refs": [ + { + "record_id": "R6049443374", + "locator": "B49/U49.1" + } + ], + "unknown_refs": [] + }, + "parameter_mapping": { + "text": "Recorded occurrence: P §2: full rank of every distinct-site jet list.\n\nLiteral consuming expression at P lines437:\nOn the compact set of spatial pairs with torus distance at least r_0, the ORIGINAL full-pin covariance is uniformly positive definite. Every distinct-site jet list has full rank by Section 2, and compactness applies without a diagonal singularity. Its inverse is uniformly bounded. For 00, positive densities p_G(0),p_Vu(0), and D_u>0. All are continuous in the frame and invariant under transverse-frame changes.\n\nAdditional supplier-to-consumer substitutions beyond this retained wording/expression are unexpanded in this companion; no extra map is inferred.", + "source_refs": [ + { + "source_id": "P", + "lines": [ + 456, + 456 + ], + "locator": "P lines456", + "precision": "exact_lines" + } + ], + "record_refs": [ + { + "record_id": "R6049443374", + "locator": "B57/U57.1" + } + ], + "unknown_refs": [] + }, + "context": { + "text": "Recorded owning-block description: Actual conditional Gaussian on Sym_(d−1), no GOE claim.", + "source_refs": [ + { + "source_id": "P", + "lines": [ + 456, + 456 + ], + "locator": "P lines456", + "precision": "exact_lines" + } + ], + "record_refs": [ + { + "record_id": "R6049443374", + "locator": "### B57 — P lines456" + } + ], + "unknown_refs": [] + }, + "source_reading": [] + }, + "provenance": [ + { + "record_id": "R6049443374", + "locator": "B57/U57.1" + } + ], + "applicability_reviews": [], + "unknown_refs": [] + }, + { + "id": "U57.2", + "kind": "premise", + "binding": { + "consumer_statement_id": "UNIFORM-MATRIX-CAP-LIFETIME-20260924-v1::Theorem-C", + "consumer_unit_id": "B57", + "consumer_source": { + "source_id": "P", + "lines": [ + 456, + 456 + ], + "locator": "P lines456", + "precision": "exact_lines" + }, + "supplier_ids": [ + "S-U57.2-UNNAMED" + ], + "claimed_interface": { + "text": "unnamed Gaussian conditional density/open-negative-cone positivity.", + "source_refs": [], + "record_refs": [ + { + "record_id": "R6049443374", + "locator": "B57/U57.2" + } + ], + "unknown_refs": [] + }, + "parameter_mapping": { + "text": "Recorded occurrence: unnamed Gaussian conditional density/open-negative-cone positivity.\n\nLiteral consuming expression at P lines456:\nHere A_u conditional on V_u=0 is an actual centered nondegenerate Gaussian symmetric matrix, not automatically GOE. Finite-jet rank proves tau_u>0, positive densities p_G(0),p_Vu(0), and D_u>0. All are continuous in the frame and invariant under transverse-frame changes.\n\nAdditional supplier-to-consumer substitutions beyond this retained wording/expression are unexpanded in this companion; no extra map is inferred.", + "source_refs": [ + { + "source_id": "P", + "lines": [ + 456, + 456 + ], + "locator": "P lines456", + "precision": "exact_lines" + } + ], + "record_refs": [ + { + "record_id": "R6049443374", + "locator": "B57/U57.2" + } + ], + "unknown_refs": [] + }, + "context": { + "text": "Recorded owning-block description: Actual conditional Gaussian on Sym_(d−1), no GOE claim.", + "source_refs": [ + { + "source_id": "P", + "lines": [ + 456, + 456 + ], + "locator": "P lines456", + "precision": "exact_lines" + } + ], + "record_refs": [ + { + "record_id": "R6049443374", + "locator": "### B57 — P lines456" + } + ], + "unknown_refs": [] + }, + "source_reading": [] + }, + "provenance": [ + { + "record_id": "R6049443374", + "locator": "B57/U57.2" + } + ], + "applicability_reviews": [], + "unknown_refs": [] + }, + { + "id": "U57.3", + "kind": "premise", + "binding": { + "consumer_statement_id": "UNIFORM-MATRIX-CAP-LIFETIME-20260924-v1::Theorem-C", + "consumer_unit_id": "B57", + "consumer_source": { + "source_id": "P", + "lines": [ + 456, + 456 + ], + "locator": "P lines456", + "precision": "exact_lines" + }, + "supplier_ids": [ + "S-U57.3-UNITS", + "S-U57.3-P" + ], + "claimed_interface": { + "text": "P §3 / B10: frame continuity and transverse invariance.", + "source_refs": [], + "record_refs": [ + { + "record_id": "R6049443374", + "locator": "B57/U57.3" + } + ], + "unknown_refs": [] + }, + "parameter_mapping": { + "text": "Recorded occurrence: P §3 / B10: frame continuity and transverse invariance.\n\nLiteral consuming expression at P lines456:\nHere A_u conditional on V_u=0 is an actual centered nondegenerate Gaussian symmetric matrix, not automatically GOE. Finite-jet rank proves tau_u>0, positive densities p_G(0),p_Vu(0), and D_u>0. All are continuous in the frame and invariant under transverse-frame changes.\n\nAdditional supplier-to-consumer substitutions beyond this retained wording/expression are unexpanded in this companion; no extra map is inferred.", + "source_refs": [ + { + "source_id": "P", + "lines": [ + 456, + 456 + ], + "locator": "P lines456", + "precision": "exact_lines" + } + ], + "record_refs": [ + { + "record_id": "R6049443374", + "locator": "B57/U57.3" + } + ], + "unknown_refs": [] + }, + "context": { + "text": "Recorded owning-block description: Actual conditional Gaussian on Sym_(d−1), no GOE claim.", + "source_refs": [ + { + "source_id": "P", + "lines": [ + 456, + 456 + ], + "locator": "P lines456", + "precision": "exact_lines" + } + ], + "record_refs": [ + { + "record_id": "R6049443374", + "locator": "### B57 — P lines456" + } + ], + "unknown_refs": [] + }, + "source_reading": [] + }, + "provenance": [ + { + "record_id": "R6049443374", + "locator": "B57/U57.3" + } + ], + "applicability_reviews": [], + "unknown_refs": [] + } + ], + "premise_groups": [ + { + "id": "G-B57", + "combination": "ALL", + "conclusion": "B56", + "premise_use_ids": [ + "U57.1", + "U57.2", + "U57.3" + ], + "basis": [ + { + "record_id": "R6049443374", + "locator": "### B57 — P lines456" + }, + { + "record_id": "R6054305355", + "locator": "## COMPLETE / own RELEASE — P-C candidate kinds and group table" + } + ] + } + ], + "related_unit_ids": [] + }, + { + "id": "B58", + "source": { + "source_id": "P", + "lines": [ + 458, + 458 + ], + "locator": "P lines458", + "precision": "exact_lines" + }, + "section": 15, + "description": { + "text": "Supplies density/cone factorization; display B59.", + "source_refs": [ + { + "source_id": "P", + "lines": [ + 458, + 458 + ], + "locator": "P lines458", + "precision": "exact_lines" + } + ], + "record_refs": [ + { + "record_id": "R6049443374", + "locator": "### B58 — P lines458" + } + ], + "unknown_refs": [] + }, + "uses": [ + { + "id": "U58.1", + "kind": "premise", + "binding": { + "consumer_statement_id": "UNIFORM-MATRIX-CAP-LIFETIME-20260924-v1::Theorem-C", + "consumer_unit_id": "B58", + "consumer_source": { + "source_id": "P", + "lines": [ + 458, + 458 + ], + "locator": "P lines458", + "precision": "exact_lines" + }, + "supplier_ids": [ + "S-U58.1-UNITS" + ], + "claimed_interface": { + "text": "B55: odd/even block independence.", + "source_refs": [], + "record_refs": [ + { + "record_id": "R6049443374", + "locator": "B58/U58.1" + } + ], + "unknown_refs": [] + }, + "parameter_mapping": { + "text": "Recorded occurrence: B55: odd/even block independence.\n\nLiteral consuming expression at P lines458:\nThe contact density and cone moment factor as\n\nAdditional supplier-to-consumer substitutions beyond this retained wording/expression are unexpanded in this companion; no extra map is inferred.", + "source_refs": [ + { + "source_id": "P", + "lines": [ + 458, + 458 + ], + "locator": "P lines458", + "precision": "exact_lines" + } + ], + "record_refs": [ + { + "record_id": "R6049443374", + "locator": "B58/U58.1" + } + ], + "unknown_refs": [] + }, + "context": { + "text": "Recorded owning-block description: Supplies density/cone factorization; display B59.", + "source_refs": [ + { + "source_id": "P", + "lines": [ + 458, + 458 + ], + "locator": "P lines458", + "precision": "exact_lines" + } + ], + "record_refs": [ + { + "record_id": "R6049443374", + "locator": "### B58 — P lines458" + } + ], + "unknown_refs": [] + }, + "source_reading": [] + }, + "provenance": [ + { + "record_id": "R6049443374", + "locator": "B58/U58.1" + } + ], + "applicability_reviews": [], + "unknown_refs": [] + }, + { + "id": "U58.2", + "kind": "premise", + "binding": { + "consumer_statement_id": "UNIFORM-MATRIX-CAP-LIFETIME-20260924-v1::Theorem-C", + "consumer_unit_id": "B58", + "consumer_source": { + "source_id": "P", + "lines": [ + 458, + 458 + ], + "locator": "P lines458", + "precision": "exact_lines" + }, + "supplier_ids": [ + "S-U58.2-P" + ], + "claimed_interface": { + "text": "P §3: contact target (f,G,V_u,t_u)=(b,0,0,12k).", + "source_refs": [], + "record_refs": [ + { + "record_id": "R6049443374", + "locator": "B58/U58.2" + } + ], + "unknown_refs": [] + }, + "parameter_mapping": { + "text": "Recorded occurrence: P §3: contact target (f,G,V_u,t_u)=(b,0,0,12k).\n\nLiteral consuming expression at P lines458:\nThe contact density and cone moment factor as\n\nAdditional supplier-to-consumer substitutions beyond this retained wording/expression are unexpanded in this companion; no extra map is inferred.", + "source_refs": [ + { + "source_id": "P", + "lines": [ + 458, + 458 + ], + "locator": "P lines458", + "precision": "exact_lines" + } + ], + "record_refs": [ + { + "record_id": "R6049443374", + "locator": "B58/U58.2" + } + ], + "unknown_refs": [] + }, + "context": { + "text": "Recorded owning-block description: Supplies density/cone factorization; display B59.", + "source_refs": [ + { + "source_id": "P", + "lines": [ + 458, + 458 + ], + "locator": "P lines458", + "precision": "exact_lines" + } + ], + "record_refs": [ + { + "record_id": "R6049443374", + "locator": "### B58 — P lines458" + } + ], + "unknown_refs": [] + }, + "source_reading": [] + }, + "provenance": [ + { + "record_id": "R6049443374", + "locator": "B58/U58.2" + } + ], + "applicability_reviews": [], + "unknown_refs": [] + }, + { + "id": "U58.3", + "kind": "premise", + "binding": { + "consumer_statement_id": "UNIFORM-MATRIX-CAP-LIFETIME-20260924-v1::Theorem-C", + "consumer_unit_id": "B58", + "consumer_source": { + "source_id": "P", + "lines": [ + 458, + 458 + ], + "locator": "P lines458", + "precision": "exact_lines" + }, + "supplier_ids": [ + "S-U58.3-P" + ], + "claimed_interface": { + "text": "P §5: contact z_0 cone moment.", + "source_refs": [], + "record_refs": [ + { + "record_id": "R6049443374", + "locator": "B58/U58.3" + } + ], + "unknown_refs": [] + }, + "parameter_mapping": { + "text": "Recorded occurrence: P §5: contact z_0 cone moment.\n\nLiteral consuming expression at P lines458:\nThe contact density and cone moment factor as\n\nAdditional supplier-to-consumer substitutions beyond this retained wording/expression are unexpanded in this companion; no extra map is inferred.", + "source_refs": [ + { + "source_id": "P", + "lines": [ + 458, + 458 + ], + "locator": "P lines458", + "precision": "exact_lines" + } + ], + "record_refs": [ + { + "record_id": "R6049443374", + "locator": "B58/U58.3" + } + ], + "unknown_refs": [] + }, + "context": { + "text": "Recorded owning-block description: Supplies density/cone factorization; display B59.", + "source_refs": [ + { + "source_id": "P", + "lines": [ + 458, + 458 + ], + "locator": "P lines458", + "precision": "exact_lines" + } + ], + "record_refs": [ + { + "record_id": "R6049443374", + "locator": "### B58 — P lines458" + } + ], + "unknown_refs": [] + }, + "source_reading": [] + }, + "provenance": [ + { + "record_id": "R6049443374", + "locator": "B58/U58.3" + } + ], + "applicability_reviews": [], + "unknown_refs": [] + }, + { + "id": "U58.4", + "kind": "premise", + "binding": { + "consumer_statement_id": "UNIFORM-MATRIX-CAP-LIFETIME-20260924-v1::Theorem-C", + "consumer_unit_id": "B58", + "consumer_source": { + "source_id": "P", + "lines": [ + 458, + 458 + ], + "locator": "P lines458", + "precision": "exact_lines" + }, + "supplier_ids": [ + "S-U58.4-UNNAMED" + ], + "claimed_interface": { + "text": "centered Gaussian conditional density of t_u at G=0, separately from odd/even independence", + "source_refs": [], + "record_refs": [ + { + "record_id": "R6049640627", + "locator": "paragraph beginning \"I accept A1–A6 as proposed additive uses\" / U58.4" + } + ], + "unknown_refs": [] + }, + "parameter_mapping": { + "text": "Recorded occurrence: centered Gaussian conditional density of t_u at G=0, separately from odd/even independence\n\nLiteral consuming expression at P lines458:\nThe contact density and cone moment factor as\n\nAdditional supplier-to-consumer substitutions beyond this retained wording/expression are unexpanded in this companion; no extra map is inferred.", + "source_refs": [ + { + "source_id": "P", + "lines": [ + 458, + 458 + ], + "locator": "P lines458", + "precision": "exact_lines" + } + ], + "record_refs": [ + { + "record_id": "R6049640627", + "locator": "paragraph beginning \"I accept A1–A6 as proposed additive uses\" / U58.4" + } + ], + "unknown_refs": [] + }, + "context": { + "text": "Recorded owning-block description: Supplies density/cone factorization; display B59.\n\nSource-attributed reading/scope qualifications:\nThe centered one-dimensional conditional Gaussian density factor is separately recorded from odd/even block independence; neither this factor nor parity authorizes an isotropic-GOE substitution.", + "source_refs": [ + { + "source_id": "P", + "lines": [ + 458, + 458 + ], + "locator": "P lines458", + "precision": "exact_lines" + }, + { + "source_id": "P", + "lines": [ + 458, + 458 + ], + "locator": "P lines458", + "precision": "exact_lines" + }, + { + "source_id": "P", + "lines": [ + 460, + 461 + ], + "locator": "P lines460–461", + "precision": "exact_lines" + } + ], + "record_refs": [ + { + "record_id": "R6049443374", + "locator": "### B58 — P lines458" + }, + { + "record_id": "R6049548422", + "locator": "2. Input-use challenges / A5" + }, + { + "record_id": "R6049640627", + "locator": "U58.4" + } + ], + "unknown_refs": [] + }, + "source_reading": [] + }, + "provenance": [ + { + "record_id": "R6049640627", + "locator": "paragraph beginning \"I accept A1–A6 as proposed additive uses\" / U58.4" + }, + { + "record_id": "R6049548422", + "locator": "2. Input-use challenges (instruction 2): additive amendments / A5" + } + ], + "applicability_reviews": [], + "unknown_refs": [] + } + ], + "premise_groups": [ + { + "id": "G-B58", + "combination": "ALL", + "conclusion": "B59", + "premise_use_ids": [ + "U58.1", + "U58.2", + "U58.3", + "U58.4" + ], + "basis": [ + { + "record_id": "R6049443374", + "locator": "### B58 — P lines458" + }, + { + "record_id": "R6054305355", + "locator": "## COMPLETE / own RELEASE — P-C candidate kinds and group table" + } + ] + } + ], + "related_unit_ids": [] + }, + { + "id": "B59", + "source": { + "source_id": "P", + "lines": [ + 460, + 461 + ], + "locator": "P lines460–461", + "precision": "exact_lines" + }, + "section": 15, + "description": { + "text": "Two factored formulas from B58; retains (6k)² and conditional f=b,V_u=0.", + "source_refs": [ + { + "source_id": "P", + "lines": [ + 460, + 461 + ], + "locator": "P lines460–461", + "precision": "exact_lines" + } + ], + "record_refs": [ + { + "record_id": "R6049443374", + "locator": "### B59 — P lines460–461" + } + ], + "unknown_refs": [] + }, + "uses": [], + "premise_groups": [], + "related_unit_ids": [] + }, + { + "id": "B60", + "source": { + "source_id": "P", + "lines": [ + 463, + 463 + ], + "locator": "P lines463", + "precision": "exact_lines" + }, + "section": 15, + "description": { + "text": "Eliminates birth mark; density normalizer p_Vu(0) retained.", + "source_refs": [ + { + "source_id": "P", + "lines": [ + 463, + 463 + ], + "locator": "P lines463", + "precision": "exact_lines" + } + ], + "record_refs": [ + { + "record_id": "R6049443374", + "locator": "### B60 — P lines463" + } + ], + "unknown_refs": [] + }, + "uses": [ + { + "id": "U60.1", + "kind": "premise", + "binding": { + "consumer_statement_id": "UNIFORM-MATRIX-CAP-LIFETIME-20260924-v1::Theorem-C", + "consumer_unit_id": "B60", + "consumer_source": { + "source_id": "P", + "lines": [ + 463, + 463 + ], + "locator": "P lines463", + "precision": "exact_lines" + }, + "supplier_ids": [ + "S-U60.1-UNNAMED" + ], + "claimed_interface": { + "text": "unnamed ordinary Gaussian disintegration over b.", + "source_refs": [], + "record_refs": [ + { + "record_id": "R6049443374", + "locator": "B60/U60.1" + } + ], + "unknown_refs": [] + }, + "parameter_mapping": { + "text": "Recorded occurrence: unnamed ordinary Gaussian disintegration over b.\n\nLiteral consuming expression at P lines463:\nwhere phi_tau is the centered scalar Gaussian density of standard deviation tau. Integrating b by ordinary Gaussian disintegration gives p_Vu(0) D_u. Thus (13.6) becomes\n\nAdditional supplier-to-consumer substitutions beyond this retained wording/expression are unexpanded in this companion; no extra map is inferred.", + "source_refs": [ + { + "source_id": "P", + "lines": [ + 463, + 463 + ], + "locator": "P lines463", + "precision": "exact_lines" + } + ], + "record_refs": [ + { + "record_id": "R6049443374", + "locator": "B60/U60.1" + } + ], + "unknown_refs": [] + }, + "context": { + "text": "Recorded owning-block description: Eliminates birth mark; density normalizer p_Vu(0) retained.", + "source_refs": [ + { + "source_id": "P", + "lines": [ + 463, + 463 + ], + "locator": "P lines463", + "precision": "exact_lines" + } + ], + "record_refs": [ + { + "record_id": "R6049443374", + "locator": "### B60 — P lines463" + } + ], + "unknown_refs": [] + }, + "source_reading": [] + }, + "provenance": [ + { + "record_id": "R6049443374", + "locator": "B60/U60.1" + } + ], + "applicability_reviews": [], + "unknown_refs": [] + }, + { + "id": "U60.2", + "kind": "premise", + "binding": { + "consumer_statement_id": "UNIFORM-MATRIX-CAP-LIFETIME-20260924-v1::Theorem-C", + "consumer_unit_id": "B60", + "consumer_source": { + "source_id": "P", + "lines": [ + 463, + 463 + ], + "locator": "P lines463", + "precision": "exact_lines" + }, + "supplier_ids": [ + "S-U60.2-UNITS" + ], + "claimed_interface": { + "text": "B47 (13.6): unrestricted coefficient.", + "source_refs": [], + "record_refs": [ + { + "record_id": "R6049443374", + "locator": "B60/U60.2" + } + ], + "unknown_refs": [] + }, + "parameter_mapping": { + "text": "Recorded occurrence: B47 (13.6): unrestricted coefficient.\n\nLiteral consuming expression at P lines463:\nwhere phi_tau is the centered scalar Gaussian density of standard deviation tau. Integrating b by ordinary Gaussian disintegration gives p_Vu(0) D_u. Thus (13.6) becomes\n\nAdditional supplier-to-consumer substitutions beyond this retained wording/expression are unexpanded in this companion; no extra map is inferred.", + "source_refs": [ + { + "source_id": "P", + "lines": [ + 463, + 463 + ], + "locator": "P lines463", + "precision": "exact_lines" + } + ], + "record_refs": [ + { + "record_id": "R6049443374", + "locator": "B60/U60.2" + } + ], + "unknown_refs": [] + }, + "context": { + "text": "Recorded owning-block description: Eliminates birth mark; density normalizer p_Vu(0) retained.", + "source_refs": [ + { + "source_id": "P", + "lines": [ + 463, + 463 + ], + "locator": "P lines463", + "precision": "exact_lines" + } + ], + "record_refs": [ + { + "record_id": "R6049443374", + "locator": "### B60 — P lines463" + } + ], + "unknown_refs": [] + }, + "source_reading": [] + }, + "provenance": [ + { + "record_id": "R6049443374", + "locator": "B60/U60.2" + } + ], + "applicability_reviews": [], + "unknown_refs": [] + }, + { + "id": "U60.3", + "kind": "premise", + "binding": { + "consumer_statement_id": "UNIFORM-MATRIX-CAP-LIFETIME-20260924-v1::Theorem-C", + "consumer_unit_id": "B60", + "consumer_source": { + "source_id": "P", + "lines": [ + 463, + 463 + ], + "locator": "P lines463", + "precision": "exact_lines" + }, + "supplier_ids": [ + "S-U60.3-UNITS" + ], + "claimed_interface": { + "text": "B59: factorization.", + "source_refs": [], + "record_refs": [ + { + "record_id": "R6049443374", + "locator": "B60/U60.3" + } + ], + "unknown_refs": [] + }, + "parameter_mapping": { + "text": "Recorded occurrence: B59: factorization.\n\nLiteral consuming expression at P lines463:\nwhere phi_tau is the centered scalar Gaussian density of standard deviation tau. Integrating b by ordinary Gaussian disintegration gives p_Vu(0) D_u. Thus (13.6) becomes\n\nAdditional supplier-to-consumer substitutions beyond this retained wording/expression are unexpanded in this companion; no extra map is inferred.", + "source_refs": [ + { + "source_id": "P", + "lines": [ + 463, + 463 + ], + "locator": "P lines463", + "precision": "exact_lines" + } + ], + "record_refs": [ + { + "record_id": "R6049443374", + "locator": "B60/U60.3" + } + ], + "unknown_refs": [] + }, + "context": { + "text": "Recorded owning-block description: Eliminates birth mark; density normalizer p_Vu(0) retained.", + "source_refs": [ + { + "source_id": "P", + "lines": [ + 463, + 463 + ], + "locator": "P lines463", + "precision": "exact_lines" + } + ], + "record_refs": [ + { + "record_id": "R6049443374", + "locator": "### B60 — P lines463" + } + ], + "unknown_refs": [] + }, + "source_reading": [] + }, + "provenance": [ + { + "record_id": "R6049443374", + "locator": "B60/U60.3" + } + ], + "applicability_reviews": [], + "unknown_refs": [] + } + ], + "premise_groups": [ + { + "id": "G-B60", + "combination": "ALL", + "conclusion": "B61", + "premise_use_ids": [ + "U60.1", + "U60.2", + "U60.3" + ], + "basis": [ + { + "record_id": "R6049443374", + "locator": "### B60 — P lines463" + }, + { + "record_id": "R6054305355", + "locator": "## COMPLETE / own RELEASE — P-C candidate kinds and group table" + } + ] + } + ], + "related_unit_ids": [] + }, + { + "id": "B61", + "source": { + "source_id": "P", + "lines": [ + 465, + 467 + ], + "locator": "P lines465–467", + "precision": "exact_lines" + }, + "section": 15, + "description": { + "text": "Intermediate coefficient formula with 144 and k^(4/3), paired with B60.", + "source_refs": [ + { + "source_id": "P", + "lines": [ + 465, + 467 + ], + "locator": "P lines465–467", + "precision": "exact_lines" + } + ], + "record_refs": [ + { + "record_id": "R6049443374", + "locator": "### B61 — P lines465–467" + } + ], + "unknown_refs": [] + }, + "uses": [], + "premise_groups": [], + "related_unit_ids": [] + }, + { + "id": "B62", + "source": { + "source_id": "P", + "lines": [ + 469, + 469 + ], + "locator": "P lines469", + "precision": "exact_lines" + }, + "section": 15, + "description": { + "text": "Evaluates the scalar mark integral; no evaluated decimal coefficient.", + "source_refs": [ + { + "source_id": "P", + "lines": [ + 469, + 469 + ], + "locator": "P lines469", + "precision": "exact_lines" + } + ], + "record_refs": [ + { + "record_id": "R6049443374", + "locator": "### B62 — P lines469" + } + ], + "unknown_refs": [] + }, + "uses": [ + { + "id": "U62.1", + "kind": "premise", + "binding": { + "consumer_statement_id": "UNIFORM-MATRIX-CAP-LIFETIME-20260924-v1::Theorem-C", + "consumer_unit_id": "B62", + "consumer_source": { + "source_id": "P", + "lines": [ + 469, + 469 + ], + "locator": "P lines469", + "precision": "exact_lines" + }, + "supplier_ids": [ + "S-U62.1-UNNAMED" + ], + "claimed_interface": { + "text": "scalar substitution t=12k.", + "source_refs": [], + "record_refs": [ + { + "record_id": "R6049443374", + "locator": "B62/U62.1" + } + ], + "unknown_refs": [] + }, + "parameter_mapping": { + "text": "Recorded occurrence: scalar substitution t=12k.\n\nLiteral consuming expression at P lines469:\nThe scalar integral can be evaluated exactly. With t=12k and the elementary gamma integral,\n\nAdditional supplier-to-consumer substitutions beyond this retained wording/expression are unexpanded in this companion; no extra map is inferred.", + "source_refs": [ + { + "source_id": "P", + "lines": [ + 469, + 469 + ], + "locator": "P lines469", + "precision": "exact_lines" + } + ], + "record_refs": [ + { + "record_id": "R6049443374", + "locator": "B62/U62.1" + } + ], + "unknown_refs": [] + }, + "context": { + "text": "Recorded owning-block description: Evaluates the scalar mark integral; no evaluated decimal coefficient.", + "source_refs": [ + { + "source_id": "P", + "lines": [ + 469, + 469 + ], + "locator": "P lines469", + "precision": "exact_lines" + } + ], + "record_refs": [ + { + "record_id": "R6049443374", + "locator": "### B62 — P lines469" + } + ], + "unknown_refs": [] + }, + "source_reading": [] + }, + "provenance": [ + { + "record_id": "R6049443374", + "locator": "B62/U62.1" + } + ], + "applicability_reviews": [], + "unknown_refs": [] + }, + { + "id": "U62.2", + "kind": "premise", + "binding": { + "consumer_statement_id": "UNIFORM-MATRIX-CAP-LIFETIME-20260924-v1::Theorem-C", + "consumer_unit_id": "B62", + "consumer_source": { + "source_id": "P", + "lines": [ + 469, + 469 + ], + "locator": "P lines469", + "precision": "exact_lines" + }, + "supplier_ids": [ + "S-U62.2-UNNAMED" + ], + "claimed_interface": { + "text": "unnamed elementary gamma integral.", + "source_refs": [], + "record_refs": [ + { + "record_id": "R6049443374", + "locator": "B62/U62.2" + } + ], + "unknown_refs": [] + }, + "parameter_mapping": { + "text": "Recorded occurrence: unnamed elementary gamma integral.\n\nLiteral consuming expression at P lines469:\nThe scalar integral can be evaluated exactly. 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+ 419, + 422 + ], + "locator": "P lines419–422", + "precision": "exact_lines" + }, + { + "source_id": "P", + "lines": [ + 428, + 431 + ], + "locator": "P lines428–431", + "precision": "exact_lines" + }, + { + "source_id": "P", + "lines": [ + 441, + 441 + ], + "locator": "P lines441", + "precision": "exact_lines" + } + ], + "record_refs": [ + { + "record_id": "R6049443374", + "locator": "B53/U53.3" + } + ], + "unknown_refs": [] + }, + "expansion": "in_slice", + "unknown_refs": [] + }, + { + "id": "S-U53.4-P", + "kind": "source_section", + "unit_ids": [], + "source_refs": [ + { + "source_id": "P", + "lines": null, + "locator": "Recorded earlier-source pointer: P §8: almost-sure Morse/distinct-value locus and actual global elder mark.", + "precision": "named_locator_unexpanded" + } + ], + "external_ref": null, + "interface": { + "text": "Recorded input designation (inventory/correction transcription): P §8: almost-sure Morse/distinct-value locus and actual global elder mark.", + "source_refs": [ + { + "source_id": "P", + "lines": null, + "locator": "Recorded earlier-source pointer: P §8: almost-sure Morse/distinct-value locus and actual global elder mark.", + "precision": "named_locator_unexpanded" + } + ], + "record_refs": [ + { + "record_id": "R6049443374", + "locator": "B53/U53.4" + } + ], + "unknown_refs": [ + "UNKNOWN-U1" + ] + }, + "expansion": "unexpanded", + "unknown_refs": [ + "UNKNOWN-U1" + ] + }, + { + "id": "S-U53.5-UNNAMED", + "kind": "unnamed", + "unit_ids": [], + "source_refs": [], + "external_ref": null, + "interface": { + "text": "Recorded input designation (inventory/correction transcription): ordinary superlevel H0 maximum-birth/merging-saddle-death once-counting assertion.", + "source_refs": [], + "record_refs": [ + { + "record_id": "R6049443374", + "locator": "B53/U53.5" + } + ], + "unknown_refs": [ + "UNKNOWN-U3" + ] + }, + "expansion": "unexpanded", + "unknown_refs": [ + "UNKNOWN-U3" + ] + }, + { + "id": "S-U54.1-UNNAMED", + "kind": "unnamed", + "unit_ids": [], + "source_refs": [], + "external_ref": null, + "interface": { + "text": "Recorded input designation (inventory/correction transcription): stationary real covariance inversion symmetry.", + "source_refs": [], + "record_refs": [ + { + "record_id": "R6049443374", + "locator": "B54/U54.1" + } + ], + "unknown_refs": [] + }, + "expansion": "unexpanded", + "unknown_refs": [] + }, + { + "id": "S-U55.1-UNITS", + "kind": "inventory_unit", + "unit_ids": [ + "B54" + ], + "source_refs": [ + { + "source_id": "P", + "lines": [ + 449, + 449 + ], + "locator": "P lines449", + "precision": "exact_lines" + } + ], + "external_ref": null, + "interface": { + "text": "Recorded input designation (inventory/correction transcription): B54: odd derivatives of even covariance vanish.", + "source_refs": [ + { + "source_id": "P", + "lines": [ + 449, + 449 + ], + "locator": "P lines449", + "precision": "exact_lines" + } + ], + "record_refs": [ + { + "record_id": "R6049443374", + "locator": "B55/U55.1" + } + ], + "unknown_refs": [] + }, + "expansion": "in_slice", + "unknown_refs": [] + }, + { + "id": "S-U55.2-UNNAMED", + "kind": "unnamed", + "unit_ids": [], + "source_refs": [], + "external_ref": null, + "interface": { + "text": "Recorded input designation (inventory/correction transcription): unnamed joint-Gaussian zero-cross-covariance independence.", + "source_refs": [], + "record_refs": [ + { + "record_id": "R6049443374", + "locator": "B55/U55.2" + } + ], + "unknown_refs": [] + }, + "expansion": "unexpanded", + "unknown_refs": [] + }, + { + "id": "S-U57.1-P", + "kind": "source_section", + "unit_ids": [], + "source_refs": [ + { + "source_id": "P", + "lines": null, + "locator": "Recorded earlier-source pointer: P §2: contact finite-jet nondegeneracy.", + "precision": "named_locator_unexpanded" + } + ], + "external_ref": null, + "interface": { + "text": "Recorded input designation (inventory/correction transcription): P §2: contact finite-jet nondegeneracy.", + "source_refs": [ + { + "source_id": "P", + "lines": null, + "locator": "Recorded earlier-source pointer: P §2: contact finite-jet nondegeneracy.", + "precision": "named_locator_unexpanded" + } + ], + "record_refs": [ + { + "record_id": "R6049443374", + "locator": "B57/U57.1" + } + ], + "unknown_refs": [ + "UNKNOWN-U1" + ] + }, + "expansion": "unexpanded", + "unknown_refs": [ + "UNKNOWN-U1" + ] + }, + { + "id": "S-U57.2-UNNAMED", + "kind": "unnamed", + "unit_ids": [], + "source_refs": [], + "external_ref": null, + "interface": { + "text": "Recorded input designation (inventory/correction transcription): unnamed Gaussian conditional density/open-negative-cone positivity.", + "source_refs": [], + "record_refs": [ + { + "record_id": "R6049443374", + "locator": "B57/U57.2" + } + ], + "unknown_refs": [] + }, + "expansion": "unexpanded", + "unknown_refs": [] + }, + { + "id": "S-U57.3-UNITS", + "kind": "inventory_unit", + "unit_ids": [ + "B10" + ], + "source_refs": [ + { + "source_id": "P", + "lines": [ + 333, + 333 + ], + "locator": "P lines333", + "precision": "exact_lines" + } + ], + "external_ref": null, + "interface": { + "text": "Recorded input designation (inventory/correction transcription): P §3 / B10: frame continuity and transverse invariance.", + "source_refs": [ + { + "source_id": "P", + "lines": [ + 333, + 333 + ], + "locator": "P lines333", + "precision": "exact_lines" + } + ], + "record_refs": [ + { + "record_id": "R6049443374", + "locator": "B57/U57.3" + } + ], + "unknown_refs": [] + }, + "expansion": "in_slice", + "unknown_refs": [] + }, + { + "id": "S-U57.3-P", + "kind": "source_section", + "unit_ids": [], + "source_refs": [ + { + "source_id": "P", + "lines": null, + "locator": "Recorded earlier-source pointer: P §3 / B10: frame continuity and transverse invariance.", + "precision": "named_locator_unexpanded" + } + ], + "external_ref": null, + "interface": { + "text": "Recorded input designation (inventory/correction transcription): P §3 / B10: frame continuity and transverse invariance.", + "source_refs": [ + { + "source_id": "P", + "lines": null, + "locator": "Recorded earlier-source pointer: P §3 / B10: frame continuity and transverse invariance.", + "precision": "named_locator_unexpanded" + } + ], + "record_refs": [ + { + "record_id": "R6049443374", + "locator": "B57/U57.3" + } + ], + "unknown_refs": [ + "UNKNOWN-U1" + ] + }, + "expansion": "unexpanded", + "unknown_refs": [ + "UNKNOWN-U1" + ] + }, + { + "id": "S-U58.1-UNITS", + "kind": "inventory_unit", + "unit_ids": [ + "B55" + ], + "source_refs": [ + { + "source_id": "P", + "lines": [ + 451, + 451 + ], + "locator": "P lines451", + "precision": "exact_lines" + } + ], + "external_ref": null, + "interface": { + "text": "Recorded input designation (inventory/correction transcription): B55: odd/even block independence.", + "source_refs": [ + { + "source_id": "P", + "lines": [ + 451, + 451 + ], + "locator": "P lines451", + "precision": "exact_lines" + } + ], + "record_refs": [ + { + "record_id": "R6049443374", + "locator": "B58/U58.1" + } + ], + "unknown_refs": [] + }, + "expansion": "in_slice", + "unknown_refs": [] + }, + { + "id": "S-U58.2-P", + "kind": "source_section", + "unit_ids": [], + "source_refs": [ + { + "source_id": "P", + "lines": null, + "locator": "Recorded earlier-source pointer: P §3: contact target (f,G,V_u,t_u)=(b,0,0,12k).", + "precision": "named_locator_unexpanded" + } + ], + "external_ref": null, + "interface": { + "text": "Recorded input designation (inventory/correction transcription): P §3: contact target (f,G,V_u,t_u)=(b,0,0,12k).", + "source_refs": [ + { + "source_id": "P", + "lines": null, + "locator": "Recorded earlier-source pointer: P §3: contact target (f,G,V_u,t_u)=(b,0,0,12k).", + "precision": "named_locator_unexpanded" + } + ], + "record_refs": [ + { + "record_id": "R6049443374", + "locator": "B58/U58.2" + } + ], + "unknown_refs": [ + "UNKNOWN-U1" + ] + }, + "expansion": "unexpanded", + "unknown_refs": [ + "UNKNOWN-U1" + ] + }, + { + "id": "S-U58.3-P", + "kind": "source_section", + "unit_ids": [], + "source_refs": [ + { + "source_id": "P", + "lines": null, + "locator": "Recorded earlier-source pointer: P §5: contact z_0 cone moment.", + "precision": "named_locator_unexpanded" + } + ], + "external_ref": null, + "interface": { + "text": "Recorded input designation (inventory/correction transcription): P §5: contact z_0 cone moment.", + "source_refs": [ + { + "source_id": "P", + "lines": null, + "locator": "Recorded earlier-source pointer: P §5: contact z_0 cone moment.", + "precision": "named_locator_unexpanded" + } + ], + "record_refs": [ + { + "record_id": "R6049443374", + "locator": "B58/U58.3" + } + ], + "unknown_refs": [ + "UNKNOWN-U1" + ] + }, + "expansion": "unexpanded", + "unknown_refs": [ + "UNKNOWN-U1" + ] + }, + { + "id": "S-U58.4-UNNAMED", + "kind": "unnamed", + "unit_ids": [], + "source_refs": [], + "external_ref": null, + "interface": { + "text": "Recorded input designation (inventory/correction transcription): centered Gaussian conditional density of t_u at G=0, separately from odd/even independence", + "source_refs": [], + "record_refs": [ + { + "record_id": "R6049640627", + "locator": "paragraph beginning \"I accept A1–A6 as proposed additive uses\" / U58.4" + } + ], + "unknown_refs": [] + }, + "expansion": "unexpanded", + "unknown_refs": [] + }, + { + "id": "S-U60.1-UNNAMED", + "kind": "unnamed", + "unit_ids": [], + "source_refs": [], + "external_ref": null, + "interface": { + "text": "Recorded input designation (inventory/correction transcription): unnamed ordinary Gaussian disintegration over b.", + "source_refs": [], + "record_refs": [ + { + "record_id": "R6049443374", + "locator": "B60/U60.1" + } + ], + "unknown_refs": [] + }, + "expansion": "unexpanded", + "unknown_refs": [] + }, + { + "id": "S-U60.2-UNITS", + "kind": "inventory_unit", + "unit_ids": [ + "B47" + ], + "source_refs": [ + { + "source_id": "P", + "lines": [ + 428, + 431 + ], + "locator": "P lines428–431", + "precision": "exact_lines" + } + ], + "external_ref": null, + "interface": { + "text": "Recorded input designation (inventory/correction transcription): B47 (13.6): unrestricted coefficient.", + "source_refs": [ + { + "source_id": "P", + "lines": [ + 428, + 431 + ], + "locator": "P lines428–431", + "precision": "exact_lines" + } + ], + "record_refs": [ + { + "record_id": "R6049443374", + "locator": "B60/U60.2" + } + ], + "unknown_refs": [] + }, + "expansion": "in_slice", + "unknown_refs": [] + }, + { + "id": "S-U60.3-UNITS", + "kind": "inventory_unit", + "unit_ids": [ + "B59" + ], + "source_refs": [ + { + "source_id": "P", + "lines": [ + 460, + 461 + ], + "locator": "P lines460–461", + "precision": "exact_lines" + } + ], + "external_ref": null, + "interface": { + "text": "Recorded input designation (inventory/correction transcription): B59: factorization.", + "source_refs": [ + { + "source_id": "P", + "lines": [ + 460, + 461 + ], + "locator": "P lines460–461", + "precision": "exact_lines" + } + ], + "record_refs": [ + { + "record_id": "R6049443374", + "locator": "B60/U60.3" + } + ], + "unknown_refs": [] + }, + "expansion": "in_slice", + "unknown_refs": [] + }, + { + "id": "S-U62.1-UNNAMED", + "kind": "unnamed", + "unit_ids": [], + "source_refs": [], + "external_ref": null, + "interface": { + "text": "Recorded input designation (inventory/correction transcription): scalar substitution t=12k.", + "source_refs": [], + "record_refs": [ + { + "record_id": "R6049443374", + "locator": "B62/U62.1" + } + ], + "unknown_refs": [] + }, + "expansion": "unexpanded", + "unknown_refs": [] + }, + { + "id": "S-U62.2-UNNAMED", + "kind": "unnamed", + "unit_ids": [], + "source_refs": [], + "external_ref": null, + "interface": { + "text": "Recorded input designation (inventory/correction transcription): unnamed elementary gamma integral.", + "source_refs": [], + "record_refs": [ + { + "record_id": "R6049443374", + "locator": "B62/U62.2" + } + ], + "unknown_refs": [] + }, + "expansion": "unexpanded", + "unknown_refs": [] + }, + { + "id": "S-U64.1-UNITS", + "kind": "inventory_unit", + "unit_ids": [ + "B61" + ], + "source_refs": [ + { + "source_id": "P", + "lines": [ + 465, + 467 + ], + "locator": "P lines465–467", + "precision": "exact_lines" + } + ], + "external_ref": null, + "interface": { + "text": "Recorded input designation (inventory/correction transcription): B61: b-integrated coefficient.", + "source_refs": [ + { + "source_id": "P", + "lines": [ + 465, + 467 + ], + "locator": "P lines465–467", + "precision": "exact_lines" + } + ], + "record_refs": [ + { + "record_id": "R6049443374", + "locator": "B64/U64.1" + } + ], + "unknown_refs": [] + }, + "expansion": "in_slice", + "unknown_refs": [] + }, + { + "id": "S-U64.2-UNITS", + "kind": "inventory_unit", + "unit_ids": [ + "B63" + ], + "source_refs": [ + { + "source_id": "P", + "lines": [ + 471, + 472 + ], + "locator": "P lines471–472", + "precision": "exact_lines" + } + ], + "external_ref": null, + "interface": { + "text": "Recorded input designation (inventory/correction transcription): B63: evaluated scalar integral.", + "source_refs": [ + { + "source_id": "P", + "lines": [ + 471, + 472 + ], + "locator": "P lines471–472", + "precision": "exact_lines" + } + ], + "record_refs": [ + { + "record_id": "R6049443374", + "locator": "B64/U64.2" + } + ], + "unknown_refs": [] + }, + "expansion": "in_slice", + "unknown_refs": [] + }, + { + "id": "S-U66.1-UNITS", + "kind": "inventory_unit", + "unit_ids": [ + "B57", + "B65" + ], + "source_refs": [ + { + "source_id": "P", + "lines": [ + 456, + 456 + ], + "locator": "P lines456", + "precision": "exact_lines" + }, + { + "source_id": "P", + "lines": [ + 476, + 478 + ], + "locator": "P lines476–478", + "precision": "exact_lines" + } + ], + "external_ref": null, + "interface": { + "text": "Recorded input designation (inventory/correction transcription): B57/B65: positive finite angular/cone representation.", + "source_refs": [ + { + "source_id": "P", + "lines": [ + 456, + 456 + ], + "locator": "P lines456", + "precision": "exact_lines" + }, + { + "source_id": "P", + "lines": [ + 476, + 478 + ], + "locator": "P lines476–478", + "precision": "exact_lines" + } + ], + "record_refs": [ + { + "record_id": "R6049443374", + "locator": "B66/U66.1" + } + ], + "unknown_refs": [] + }, + "expansion": "in_slice", + "unknown_refs": [] + }, + { + "id": "S-U66.2-UNNAMED", + "kind": "unnamed", + "unit_ids": [], + "source_refs": [], + "external_ref": null, + "interface": { + "text": "Recorded input designation (inventory/correction transcription): exact periodized covariance derivatives.", + "source_refs": [], + "record_refs": [ + { + "record_id": "R6049443374", + "locator": "B66/U66.2" + } + ], + "unknown_refs": [] + }, + "expansion": "unexpanded", + "unknown_refs": [] + }, + { + "id": "S-U66.3-UNNAMED", + "kind": "unnamed", + "unit_ids": [], + "source_refs": [], + "external_ref": null, + "interface": { + "text": "Recorded input designation (inventory/correction transcription): unnamed positive field-amplitude/lifetime scaling of the bar measure.", + "source_refs": [], + "record_refs": [ + { + "record_id": "R6049443374", + "locator": "B66/U66.3" + } + ], + "unknown_refs": [] + }, + "expansion": "unexpanded", + "unknown_refs": [] + } + ], + "unknowns": [ + { + "id": "UNKNOWN-U1", + "description": { + "text": "Historical omission observation at 2026-10-08T00:22:13Z, U1: derivations in P §§1–9. This includes (3.2), the Section-4 mechanism, and the target/k-independence of the (5.1)/(5.3) constants asserted at l410. The original author response retains U1/U7 as imported/unexpanded earlier Gaussian-regression/moment mechanisms. No present mathematical disposition is inferred; the original records retain their dates and scopes.", + "source_refs": [], + "record_refs": [ + { + "record_id": "R6049548422", + "locator": "UNKNOWN / U1" + }, + { + "record_id": "R6049640627", + "locator": "U1/U7 remain imported/unexpanded earlier Gaussian-regression/moment mechanisms in this inventory." + } + ], + "unknown_refs": [] + }, + "affects_use_ids": [], + "provenance": [ + { + "record_id": "R6049548422", + "locator": "UNKNOWN / U1" + }, + { + "record_id": "R6049640627", + "locator": "U1/U7 remain imported/unexpanded earlier Gaussian-regression/moment mechanisms in this inventory." + } + ] + }, + { + "id": "UNKNOWN-U2", + "description": { + "text": "Historical omission observation at 2026-10-08T00:22:13Z, U2: non-circularity of the E2 §9.4 ↔ P §10 edge (N2). The original author response records a later local application note for nonauthor attack; it does not supply a current use-bound assessment here. No present mathematical disposition is inferred; the original records retain their dates and scopes.", + "source_refs": [], + "record_refs": [ + { + "record_id": "R6049548422", + "locator": "UNKNOWN / U2" + }, + { + "record_id": "R6049640627", + "locator": "paragraph beginning \"U1/U7 remain imported/unexpanded earlier Gaussian-regression/moment mechanisms in this inventory.\" / U2" + } + ], + "unknown_refs": [] + }, + "affects_use_ids": [ + "U04.1", + "U11.1" + ], + "provenance": [ + { + "record_id": "R6049548422", + "locator": "UNKNOWN / U2" + }, + { + "record_id": "R6049640627", + "locator": "paragraph beginning \"U1/U7 remain imported/unexpanded earlier Gaussian-regression/moment mechanisms in this inventory.\" / U2" + } + ] + }, + { + "id": "UNKNOWN-U3", + "description": { + "text": "Historical omission observation at 2026-10-08T00:22:13Z, U3: the global finite-bar once-counting bijection. The original author response reports a separate interval-decomposition derivation awaiting a distinct attack at that date; later proof/formal work is outside this inventory. No present mathematical disposition is inferred; the original records retain their dates and scopes.", + "source_refs": [], + "record_refs": [ + { + "record_id": "R6049548422", + "locator": "UNKNOWN / U3" + }, + { + "record_id": "R6049640627", + "locator": "paragraph beginning \"The active U3 task6049585299\"" + } + ], + "unknown_refs": [] + }, + "affects_use_ids": [ + "U53.5" + ], + "provenance": [ + { + "record_id": "R6049548422", + "locator": "UNKNOWN / U3" + }, + { + "record_id": "R6049640627", + "locator": "paragraph beginning \"The active U3 task6049585299\"" + } + ] + }, + { + "id": "UNKNOWN-U4", + "description": { + "text": "Historical omission observation at 2026-10-08T00:22:13Z, U4: the external Armentano–Azaïs–León KR base behind E2. The original author response reports inspecting the external v3 base and preserves E2’s separate full-Borel extension; no external derivation is expanded here. No present mathematical disposition is inferred; the original records retain their dates and scopes.", + "source_refs": [], + "record_refs": [ + { + "record_id": "R6049548422", + "locator": "UNKNOWN / U4" + }, + { + "record_id": "R6049640627", + "locator": "paragraph beginning \"U1/U7 remain imported/unexpanded earlier Gaussian-regression/moment mechanisms in this inventory.\" / U4" + } + ], + "unknown_refs": [] + }, + "affects_use_ids": [], + "provenance": [ + { + "record_id": "R6049548422", + "locator": "UNKNOWN / U4" + }, + { + "record_id": "R6049640627", + "locator": "paragraph beginning \"U1/U7 remain imported/unexpanded earlier Gaussian-regression/moment mechanisms in this inventory.\" / U4" + } + ] + }, + { + "id": "UNKNOWN-U5", + "description": { + "text": "Historical omission observation at 2026-10-08T00:22:13Z, U5: the definition of `A^*`. The original author interprets A* as the B09/B10 uniform upper bound while retaining its missing definition in P. No present mathematical disposition is inferred; the original records retain their dates and scopes.", + "source_refs": [], + "record_refs": [ + { + "record_id": "R6049548422", + "locator": "UNKNOWN / U5" + }, + { + "record_id": "R6049640627", + "locator": "paragraph beginning \"U1/U7 remain imported/unexpanded earlier Gaussian-regression/moment mechanisms in this inventory.\" / U5" + } + ], + "unknown_refs": [] + }, + "affects_use_ids": [ + "U20.4" + ], + "provenance": [ + { + "record_id": "R6049548422", + "locator": "UNKNOWN / U5" + }, + { + "record_id": "R6049640627", + "locator": "paragraph beginning \"U1/U7 remain imported/unexpanded earlier Gaussian-regression/moment mechanisms in this inventory.\" / U5" + } + ] + }, + { + "id": "UNKNOWN-U6", + "description": { + "text": "Historical omission observation at 2026-10-08T00:22:13Z, U6: whether r_0 must also be below L/(4√2). The original author distinguishes P13 covariance r0 from the Theorem-A cylinder radius and records a separate stronger quantitative R12 reading; R12 is not a P-C premise. No present mathematical disposition is inferred; the original records retain their dates and scopes.", + "source_refs": [], + "record_refs": [ + { + "record_id": "R6049548422", + "locator": "UNKNOWN / U6" + }, + { + "record_id": "R6049640627", + "locator": "paragraph beginning \"U1/U7 remain imported/unexpanded earlier Gaussian-regression/moment mechanisms in this inventory.\" / U6" + } + ], + "unknown_refs": [] + }, + "affects_use_ids": [ + "U30.2" + ], + "provenance": [ + { + "record_id": "R6049548422", + "locator": "UNKNOWN / U6" + }, + { + "record_id": "R6049640627", + "locator": "paragraph beginning \"U1/U7 remain imported/unexpanded earlier Gaussian-regression/moment mechanisms in this inventory.\" / U6" + } + ] + }, + { + "id": "UNKNOWN-U7", + "description": { + "text": "Historical omission observation at 2026-10-08T00:22:13Z, U7: the unnamed regression and moment mechanisms in U35.1 and U50.1, which can't be derived inside this slice. The original author response retains U1/U7 as imported/unexpanded earlier Gaussian-regression/moment mechanisms. No present mathematical disposition is inferred; the original records retain their dates and scopes.", + "source_refs": [], + "record_refs": [ + { + "record_id": "R6049548422", + "locator": "UNKNOWN / U7" + }, + { + "record_id": "R6049640627", + "locator": "U1/U7 remain imported/unexpanded earlier Gaussian-regression/moment mechanisms in this inventory." + } + ], + "unknown_refs": [] + }, + "affects_use_ids": [ + "U35.1", + "U50.1" + ], + "provenance": [ + { + "record_id": "R6049548422", + "locator": "UNKNOWN / U7" + }, + { + "record_id": "R6049640627", + "locator": "U1/U7 remain imported/unexpanded earlier Gaussian-regression/moment mechanisms in this inventory." + } + ] + } + ], + "history": [ + { + "id": "H-INVENTORY", + "kind": "inventory_statement", + "record": { + "record_id": "R6049443374", + "locator": "## Frozen source and extraction convention" + }, + "affects_unit_ids": [], + "affects_use_ids": [], + "text": "Original descriptive inventory and syntactic extraction boundary, retained at its source cut; historical 109-use statement is not the amended denominator." + }, + { + "id": "H-OMISSION", + "kind": "omission_observation", + "record": { + "record_id": "R6049548422", + "locator": "### 1. Block syntax (instruction 1): reproduced, no extraction omission" + }, + "affects_unit_ids": [], + "affects_use_ids": [], + "text": "Historical omission/application observations, additive suggestions and U1–U7/N-note qualifications retain their dates/scopes. Historical PASS words are not current applicability ReviewBindings." + }, + { + "id": "H-CORRECTION", + "kind": "author_inventory_amendment", + "record": { + "record_id": "R6049640627", + "locator": "I accept A1–A6 as proposed additive uses" + }, + "affects_unit_ids": [], + "affects_use_ids": [ + "U01.3", + "U20.4", + "U35.3", + "U50.4", + "U58.4", + "U46.5" + ], + "text": "Original author additive uses and reading corrections are retained; the historical 114 inferential plus1check wording is not converted into the current schema kind mapping." + }, + { + "id": "H-KINDS", + "kind": "inventory_statement", + "record": { + "record_id": "R6054305355", + "locator": "## COMPLETE / own RELEASE — P-C candidate kinds and group table" + }, + "affects_unit_ids": [], + "affects_use_ids": [], + "text": "Descriptive candidate taxonomy was separately source-read and then frozen in A:112 premise,2context,1check. No implication or sufficiency acceptance is inferred." + }, + { + "id": "H-ALL", + "kind": "author_inventory_amendment", + "record": { + "record_id": "R6055287391", + "locator": "My explicit descriptive selection" + }, + "affects_unit_ids": [ + "B19", + "B20", + "B22", + "B23", + "B50", + "B51" + ], + "affects_use_ids": [], + "text": "The actual descriptive custodian selected the three complete recorded ALL contribution sets, preserving every owner/member list and qualifications. This is not original-proof-author assent or sufficiency review." + }, + { + "id": "H-RANGES", + "kind": "author_inventory_amendment", + "record": { + "record_id": "R6057972030", + "locator": "Exact arrays for the existing ReadingBoundary fields" + }, + "affects_unit_ids": [], + "affects_use_ids": [], + "text": "The actual descriptive source selection fixes E1/E2/REC consumed and excluded arrays; source reading is not mathematical acceptance." + }, + { + "id": "H-B-PICKUP", + "kind": "supersession_note", + "record": { + "record_id": "R6064435898", + "locator": "## Personal pickup — Stage B source companion" + }, + "affects_unit_ids": [], + "affects_use_ids": [], + "text": "This separate descendant companion binds literal landed A. It exposes named recorded pointers and unexpanded mechanisms/substitutions; all applicability review arrays are empty. Earlier A reviews are not represented as reviews of B." + }, + { + "id": "H-N45", + "kind": "supersession_note", + "record": { + "record_id": "R6049640627", + "locator": "N1–N7 are retained" + }, + "affects_unit_ids": [], + "affects_use_ids": [], + "text": "N4/N5 remain historical range labels without recovered individual payload selectors. No new annotation, use, source fact or mathematical obligation is fabricated." + } + ], + "bundles": [ + { + "id": "ALL-B20", + "combination": "ALL", + "conclusion": { + "unit_id": "B20", + "source": { + "file": { + "repository": "d6g8k5htny-coder/Math-", + "commit": "9fd261135b41daf1e377f9ef2db193fee6ec36be", + "path": "imports/lifetime_parent_20260925/UNIFORM_MATRIX_CAP_AND_LIFETIME.md", + "git_blob": "dfed3b8d318a3ab1950957f393307733a4bef3f2", + "bytes": 40261, + "sha256": "9350ad6eaba6626b93c3dedeef9e2ff816e5cdf1c8318e85fb27499141c84bc7" + }, + "lines": [ + 359, + 361 + ], + "locator": "P lines359–361", + "precision": "exact_lines" + } + }, + "group_ids": [ + "G-B19", + "G-B20" + ], + "basis": { + "text": "B19/P357 introduces the stronger difference statement displayed at B20/P359–361. G-B19’s imported pointwise-selection contribution and G-B20’s candidate-density, selection, conversion and uniform-upper-bound entries are recorded contributions read together. Preserve the compact-mark domain, the A* notation omission and its attributed upper-bound interpretation. U19.1 and U20.2 remain distinct occurrences. Mathematical sufficiency is not assessed.", + "source_refs": [], + "record_refs": [ + { + "record_id": "R6055287391", + "locator": "My explicit descriptive selection / B20" + }, + { + "record_id": "R6055282954", + "locator": "Exact source response / B20" + } + ], + "unknown_refs": [] + } + }, + { + "id": "ALL-B23", + "combination": "ALL", + "conclusion": { + "unit_id": "B23", + "source": { + "file": { + "repository": "d6g8k5htny-coder/Math-", + "commit": "9fd261135b41daf1e377f9ef2db193fee6ec36be", + "path": "imports/lifetime_parent_20260925/UNIFORM_MATRIX_CAP_AND_LIFETIME.md", + "git_blob": "dfed3b8d318a3ab1950957f393307733a4bef3f2", + "bytes": 40261, + "sha256": "9350ad6eaba6626b93c3dedeef9e2ff816e5cdf1c8318e85fb27499141c84bc7" + }, + "lines": [ + 369, + 370 + ], + "locator": "P lines369–370", + "precision": "exact_lines" + } + }, + "group_ids": [ + "G-B22", + "G-B23" + ], + "basis": { + "text": "B22/P367 introduces integration of the density versions into the following restricted-population expected per-unit-volume results, beginning with B23/(12.1)/P369–370. G-B22 and G-B23 contribute jointly with separate unchanged member lists. Preserve the common population/domain/per-volume qualification and sufficiently-small-t reading. This selected target does not assert that the lead-in concerns B23 exclusively or add assignments for later results. Mathematical sufficiency is not assessed.", + "source_refs": [], + "record_refs": [ + { + "record_id": "R6055287391", + "locator": "My explicit descriptive selection / B23" + }, + { + "record_id": "R6055282954", + "locator": "Exact source response / B23" + } + ], + "unknown_refs": [] + } + }, + { + "id": "ALL-B51", + "combination": "ALL", + "conclusion": { + "unit_id": "B51", + "source": { + "file": { + "repository": "d6g8k5htny-coder/Math-", + "commit": "9fd261135b41daf1e377f9ef2db193fee6ec36be", + "path": "imports/lifetime_parent_20260925/UNIFORM_MATRIX_CAP_AND_LIFETIME.md", + "git_blob": "dfed3b8d318a3ab1950957f393307733a4bef3f2", + "bytes": 40261, + "sha256": "9350ad6eaba6626b93c3dedeef9e2ff816e5cdf1c8318e85fb27499141c84bc7" + }, + "lines": [ + 441, + 441 + ], + "locator": "P lines441", + "precision": "exact_lines" + } + }, + "group_ids": [ + "G-B50", + "G-B51" + ], + "basis": { + "text": "B50/P439 contributes moments, the unit height Jacobian, integration and marked Kac-Rice to the far-domain chain at B51/P441, for0 Date: Thu, 8 Oct 2026 12:26:46 -0700 Subject: [PATCH 2/4] Correct named P source pointers and represented Theorem C link --- .../P_C/PROOF_SLICE.json | 106 ++++++++++++++---- 1 file changed, 84 insertions(+), 22 deletions(-) diff --git a/reviews/proof_dependencies_20261008/P_C/PROOF_SLICE.json b/reviews/proof_dependencies_20261008/P_C/PROOF_SLICE.json index 6b533db4b..a8e1c4d2e 100644 --- a/reviews/proof_dependencies_20261008/P_C/PROOF_SLICE.json +++ b/reviews/proof_dependencies_20261008/P_C/PROOF_SLICE.json @@ -2,7 +2,7 @@ "schema": "proof-slice/v0-provisional-5", "artifact_kind": "source_companion", "id": "P-C-SOURCE-COMPANION-20261008", - "read_at": "2026-10-08T17:07:50Z", + "read_at": "2026-10-08T18:26:38Z", "author": { "provider": "OpenAI", "agent": "Codex implement_proof_slice_inventory", @@ -17990,14 +17990,28 @@ }, { "id": "S-U29.1-P", - "kind": "source_section", - "unit_ids": [], + "kind": "inventory_unit", + "unit_ids": [ + "B53" + ], "source_refs": [ { "source_id": "P", - "lines": null, - "locator": "Recorded earlier-source pointer: P Theorem C: unrestricted leading density.", - "precision": "named_locator_unexpanded" + "lines": [ + 47, + 52 + ], + "locator": "Theorem C (1.3), statement and retained scope", + "precision": "exact_lines" + }, + { + "source_id": "P", + "lines": [ + 445, + 445 + ], + "locator": "P lines445", + "precision": "exact_lines" } ], "external_ref": null, @@ -18006,9 +18020,21 @@ "source_refs": [ { "source_id": "P", - "lines": null, - "locator": "Recorded earlier-source pointer: P Theorem C: unrestricted leading density.", - "precision": "named_locator_unexpanded" + "lines": [ + 47, + 52 + ], + "locator": "Theorem C (1.3), statement and retained scope", + "precision": "exact_lines" + }, + { + "source_id": "P", + "lines": [ + 445, + 445 + ], + "locator": "P lines445", + "precision": "exact_lines" } ], "record_refs": [ @@ -18017,14 +18043,10 @@ "locator": "B29/U29.1" } ], - "unknown_refs": [ - "UNKNOWN-U1" - ] + "unknown_refs": [] }, - "expansion": "unexpanded", - "unknown_refs": [ - "UNKNOWN-U1" - ] + "expansion": "in_slice", + "unknown_refs": [] }, { "id": "S-U29.2-UNNAMED", @@ -18395,13 +18417,33 @@ }, { "id": "S-U38.1-UNNAMED", - "kind": "unnamed", + "kind": "source_section", "unit_ids": [], - "source_refs": [], + "source_refs": [ + { + "source_id": "P", + "lines": [ + 148, + 149 + ], + "locator": "P (5.1): endpoint identities", + "precision": "exact_lines" + } + ], "external_ref": null, "interface": { "text": "Recorded input designation (inventory/correction transcription): P (5.1): endpoint identities.", - "source_refs": [], + "source_refs": [ + { + "source_id": "P", + "lines": [ + 148, + 149 + ], + "locator": "P (5.1): endpoint identities", + "precision": "exact_lines" + } + ], "record_refs": [ { "record_id": "R6049443374", @@ -18415,13 +18457,33 @@ }, { "id": "S-U38.2-UNNAMED", - "kind": "unnamed", + "kind": "source_section", "unit_ids": [], - "source_refs": [], + "source_refs": [ + { + "source_id": "P", + "lines": [ + 160, + 161 + ], + "locator": "P (5.3): block determinant identity", + "precision": "exact_lines" + } + ], "external_ref": null, "interface": { "text": "Recorded input designation (inventory/correction transcription): P (5.3): determinant product envelope.", - "source_refs": [], + "source_refs": [ + { + "source_id": "P", + "lines": [ + 160, + 161 + ], + "locator": "P (5.3): block determinant identity", + "precision": "exact_lines" + } + ], "record_refs": [ { "record_id": "R6049443374", From 55d91cb3b7335dc8722ebb440c2155ffd8b506c5 Mon Sep 17 00:00:00 2001 From: Dylan Roy <249851642+d6g8k5htny-coder@users.noreply.github.com> Date: Thu, 8 Oct 2026 13:02:14 -0700 Subject: [PATCH 3/4] Describe P (5.1) source locators as bounds --- reviews/proof_dependencies_20261008/P_C/PROOF_SLICE.json | 4 ++-- 1 file changed, 2 insertions(+), 2 deletions(-) diff --git a/reviews/proof_dependencies_20261008/P_C/PROOF_SLICE.json b/reviews/proof_dependencies_20261008/P_C/PROOF_SLICE.json index a8e1c4d2e..693d7bc27 100644 --- a/reviews/proof_dependencies_20261008/P_C/PROOF_SLICE.json +++ b/reviews/proof_dependencies_20261008/P_C/PROOF_SLICE.json @@ -18426,7 +18426,7 @@ 148, 149 ], - "locator": "P (5.1): endpoint identities", + "locator": "P (5.1): endpoint and transverse-block bounds", "precision": "exact_lines" } ], @@ -18440,7 +18440,7 @@ 148, 149 ], - "locator": "P (5.1): endpoint identities", + "locator": "P (5.1): endpoint and transverse-block bounds", "precision": "exact_lines" } ], From bf93325dfbe6f51987d6127fa1c33bf0255722ce Mon Sep 17 00:00:00 2001 From: Dylan Roy <249851642+d6g8k5htny-coder@users.noreply.github.com> Date: Thu, 8 Oct 2026 17:04:44 -0700 Subject: [PATCH 4/4] Clarify initial and repair-phase author attribution --- reviews/proof_dependencies_20261008/P_C/PROOF_SLICE.json | 2 +- reviews/proof_dependencies_20261008/P_C/README.md | 6 +++--- 2 files changed, 4 insertions(+), 4 deletions(-) diff --git a/reviews/proof_dependencies_20261008/P_C/PROOF_SLICE.json b/reviews/proof_dependencies_20261008/P_C/PROOF_SLICE.json index 693d7bc27..1e6b40500 100644 --- a/reviews/proof_dependencies_20261008/P_C/PROOF_SLICE.json +++ b/reviews/proof_dependencies_20261008/P_C/PROOF_SLICE.json @@ -7,7 +7,7 @@ "provider": "OpenAI", "agent": "Codex implement_proof_slice_inventory", "session": null, - "exposure": "Actual receiver pc-companion-b-author-20261008; runtime session identifier is not attested. Actual Stage B materializer; prior Stage A author and source/design discussion exposure. Descriptive serialization only; no original-proof-author or independent applicability-review identity is claimed." + "exposure": "Initial Stage B receiver pc-companion-b-author-20261008. The same actual invocation later performed the DATA-01/02 repair as receiver pc-b-datafix-author-20261008 under pickup Math-#409/6066357248, created 2026-10-08T18:23:38Z with a stated hard end of 2026-10-08T19:03:38Z. read_at 2026-10-08T18:26:38Z is the source-read cut from that repair. Runtime session identifier is not attested. Prior Stage A author and source/design discussion exposure. Descriptive serialization only; no original-proof-author or independent applicability-review identity is claimed." }, "scientific_effect": "NONE", "status_authority": false, diff --git a/reviews/proof_dependencies_20261008/P_C/README.md b/reviews/proof_dependencies_20261008/P_C/README.md index 12d9c4435..9fc2888e1 100644 --- a/reviews/proof_dependencies_20261008/P_C/README.md +++ b/reviews/proof_dependencies_20261008/P_C/README.md @@ -2,7 +2,7 @@ Inventory A is published at **92a45e1749936a19ebfe31e803289e0f4683d754**. Its unchanged inventory blob is **252f1f36bd8ddb4f6fe00c17dc1486836fe13198**, 102233 bytes, SHA-256 **bb764b4a5b440c63c176006e4187f8a9a38833cbc6086905123887f4397c17d3**. This descendant adds a separate source-companion B candidate under [offer6064392915](https://github.com/d6g8k5htny-coder/main/issues/281#issuecomment-6064392915) and [actual pickup6064435898](https://github.com/d6g8k5htny-coder/main/issues/281#issuecomment-6064435898). It preserves A's 66 ordered units, 115 use occurrences (112 premise, 2 context, 1 check), 45 owner groups, complete recorded ALL sets and all 20 zero-use units. These remain descriptive source classifications, not accepted implications or mathematical completeness. -Stage A's original [offer6057671226](https://github.com/d6g8k5htny-coder/main/issues/281#issuecomment-6057671226), [pickup6057699936](https://github.com/d6g8k5htny-coder/main/issues/281#issuecomment-6057699936), R1–R4 source/review/failure history, [landing6063483510](https://github.com/d6g8k5htny-coder/Math-/pull/406#issuecomment-6063483510) and [landed evidence6063543055](https://github.com/d6g8k5htny-coder/Math-/pull/406#issuecomment-6063543055) retain their separate scopes. Actual B materializer: the same native OpenAI/Codex invocation implement_proof_slice_inventory, now receiver pc-companion-b-author-20261008; source/design exposed, organizational-independence credit0, scientific effect NONE. No runtime session identifier or original-proof-author assent is invented. The original source performers retain their own record attribution. +Stage A's original [offer6057671226](https://github.com/d6g8k5htny-coder/main/issues/281#issuecomment-6057671226), [pickup6057699936](https://github.com/d6g8k5htny-coder/main/issues/281#issuecomment-6057699936), R1–R4 source/review/failure history, [landing6063483510](https://github.com/d6g8k5htny-coder/Math-/pull/406#issuecomment-6063483510) and [landed evidence6063543055](https://github.com/d6g8k5htny-coder/Math-/pull/406#issuecomment-6063543055) retain their separate scopes. The B materializer is the same native OpenAI/Codex invocation implement_proof_slice_inventory. Its initial receiver was pc-companion-b-author-20261008. It later performed the DATA-01/02 repair as pc-b-datafix-author-20261008 under [offer6066301760](https://github.com/d6g8k5htny-coder/main/issues/281#issuecomment-6066301760) and [pickup6066357248](https://github.com/d6g8k5htny-coder/Math-/pull/409#issuecomment-6066357248), created at 18:23:38 UTC with a stated hard end of 19:03:38 UTC on 8 October 2026. B’s read_at records the 18:26:38 source-read cut during that repair. Subsequent editing, publication and integration dates are separate. Source/design exposed, organizational-independence credit0, scientific effect NONE. No runtime session identifier or original-proof-author assent is invented. The original source performers retain their own record attribution. Separate exact-B source-data and engineering reviews, required current hosted execution and distinct integration remain necessary. A's reviews are not reviews of B's newly serialized fields. This candidate claims no completed B review, accepted proof edge, reader UI, GRAPH/STATUS/PROOF_INDEX change, proof edit, formal registration or theorem acceptance. @@ -10,7 +10,7 @@ Separate exact-B source-data and engineering reviews, required current hosted ex - EXPECTED_INVENTORY.json is the closed proof-unit-inventory/v0-provisional-5 object - PROOF_SLICE.json is the separate proof-slice/v0-provisional-5 companion, with literal A's complete FileIdentity and its own actual materializer read_at -- records/ preserves all eleven A captures unchanged and adds only the referenced B pickup capture6064435898; its body identity is2785B/SHA256139ffd12d0daa6d0dfaa4c3a1e6885c19e07c5286d25065c1163aedae9dc6792. Custody evidence is not an applicability review +- records/ preserves all eleven A captures unchanged and adds only the referenced initial B pickup capture6064435898; its body identity is2785B/SHA256139ffd12d0daa6d0dfaa4c3a1e6885c19e07c5286d25065c1163aedae9dc6792. Custody evidence is not an applicability review - ../CONTRACT.md consolidates the selected engineering contract and its source chain - ../../../tools/proof_slice_check.py provides inventory-only and paired technical validation; Stage A's paired positives were synthetic, while this phase also requires real A/B validation - ../../../tests/fixtures/proof_slice_cases.json holds reusable synthetic shape/refusal and target-comparison vectors, not a reduced real inventory @@ -68,7 +68,7 @@ Each parameter_mapping retains the attributed occurrence wording and the literal Target-bearing fields retain U08.2's E1/W1 correction, B38's E1 note, the Theorem-A/covariance-radius distinction including U30.2, E2's global marked formula/external base/diagonal-import limits, A*'s retained missing-definition qualification, sufficiently-small-t compact formulas, U46.5's fixed-mark local application, U58.4's separate conditional-density factor, and the far/B51 restrictions. CAP's excluded fixed-axis corollary and separate R12/once-counting claims are not substituted for the consumed interfaces. Source-data review must assess these actual serialized associations; successful self-consistency cannot establish that none was omitted. -The B author and pickup capture establish this materialization's custody only. No source author's agreement, future reviewer, use-bound applicability judgment or theorem acceptance is inferred from the new records. N4/N5 remain the historical selector ambiguity described above. +The retained B pickup capture records the initial Stage B phase. The dated continuation links above identify the same invocation’s later repair and source-read cut. These custody references supply no applicability review or theorem acceptance. No source author's agreement, future reviewer, use-bound applicability judgment or theorem acceptance is inferred from the new records. N4/N5 remain the historical selector ambiguity described above. ## Validation and the A/B boundary