C52 in every d ≥ 2: E[K_τ; K_τ ≥ 2] = o(τ^{2/3}), occurrence probability L^d(3/2)c_{d,L}τ^{2/3}, singleton and field-first laws on T_L^d (extends #235; scientific effect NONE)

.github/workflows/ordinary-short-bar-occurrence-all-d.yml

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+name: Ordinary short-bar occurrence (all d) exact controls
+on:
+  pull_request:
+    paths:
+      - 'frontiers/ordinary_short_bar_occurrence_all_d_20261001/**'
+      - 'frontiers/three_fronts_20260924/LIFETIME_REMAINDER.md'
+      - 'frontiers/short_bar_endpoint_law_20261001/PROOF.md'
+      - 'frontiers/ordinary_short_bar_occurrence_20261001/FOLD_ISOLATION.md'
+      - 'frontiers/ordinary_short_bar_occurrence_20261001/PROOF.md'
+      - 'imports/lifetime_parent_20260925/**'
+      - 'reviews/d1_section9_borel_repair_20260925/REPAIR.md'
+      - 'reviews/d1_chain_reconciliation_20260928/RECONCILIATION.md'
+      - '.github/workflows/ordinary-short-bar-occurrence-all-d.yml'
+  push:
+    branches: [main]
+    paths:
+      - 'frontiers/ordinary_short_bar_occurrence_all_d_20261001/**'
+      - 'frontiers/three_fronts_20260924/LIFETIME_REMAINDER.md'
+      - 'frontiers/short_bar_endpoint_law_20261001/PROOF.md'
+      - 'frontiers/ordinary_short_bar_occurrence_20261001/FOLD_ISOLATION.md'
+      - 'frontiers/ordinary_short_bar_occurrence_20261001/PROOF.md'
+      - 'imports/lifetime_parent_20260925/**'
+      - 'reviews/d1_section9_borel_repair_20260925/REPAIR.md'
+      - 'reviews/d1_chain_reconciliation_20260928/RECONCILIATION.md'
+      - '.github/workflows/ordinary-short-bar-occurrence-all-d.yml'
+  workflow_dispatch:
+permissions:
+  contents: read
+concurrency:
+  group: ordinary-short-bar-occurrence-all-d-${{ github.ref }}
+  cancel-in-progress: true
+jobs:
+  exact:
+    runs-on: ubuntu-latest
+    timeout-minutes: 10
+    strategy:
+      matrix:
+        mode: [normal, optimized]
+    steps:
+      - uses: actions/checkout@3d3c42e5aac5ba805825da76410c181273ba90b1
+        with:
+          fetch-depth: 0
+          persist-credentials: false
+      - uses: actions/setup-python@5fda3b95a4ea91299a34e894583c3862153e4b97
+        with:
+          python-version: '3.11'
+      - name: Verify sources and run exact controls
+        env:
+          PYTHON_MODE: ${{ matrix.mode }}
+        run: |
+          D=frontiers/ordinary_short_bar_occurrence_all_d_20261001
+          if [ "$PYTHON_MODE" = optimized ]; then F="-B -O -S"; else F="-B -S"; fi
+          python3 $F $D/verify_sources.py
+          python3 $F $D/check.py
+          python3 $F $D/test_check.py -v
+      - name: Reject implementation mutants in both Python modes
+        if: matrix.mode == 'normal'
+        run: python3 -B -S frontiers/ordinary_short_bar_occurrence_all_d_20261001/test_check.py --mutants

frontiers/ordinary_short_bar_occurrence_all_d_20261001/README.md

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+# Ordinary short-bar occurrence in every dimension
+
+This packet extends OpenAI/Codex's planar C52 theorem (Math-#235) to the periodized Gaussian field on `T_L^d` for every
+`d >= 2`. A field that contains a sufficiently short ordinary finite superlevel H0 bar asymptotically contains only one
+such bar. The probability that one occurs has the same leading coefficient, `L^d (3/2) c_{d,L} tau^(2/3)`, as the
+expected count. Sampling a bar after conditioning the field on occurrence has the same limiting mark law as the
+intensity calculation.
+
+[Theorem and proof](NOTE.md) · [Exact sources](SOURCES.json)
+
+**What is new.** The only new step is ordinary-fold isolation in dimension `d` (NOTE §2):
+- the transverse ridge on a ball;
+- the identities `g''' = D³F[v,v,v]` and `g'' = Schur complement`;
+- Haynsworth inertia for the pin types;
+- the `{lambda_max(A) = 0}` null boundary;
+- the general-`d` mesh counts.
+
+The consumer (NOTE §§3–4) is C52's, written out with `L^d`, `S^(d-1)` and `c_{d,L}`. For `d = 2` it is C52's Theorem O.
+
+**Conditional.** The theorem retains the imported elder-pairing, Kac–Rice and Gaussian interfaces of the seven pinned
+sources, all of which are stated for every `d >= 2`.
+
+**Not supplied:**
+- a rate;
+- factorial moments or a Poisson law;
+- an increasing-volume limit;
+- uniformity in `d`.
+
+Scientific effect NONE; C8 OPEN.
+
+Run from the repository root:
+
+```sh
+python3 -B -S frontiers/ordinary_short_bar_occurrence_all_d_20261001/verify_sources.py
+python3 -B -S frontiers/ordinary_short_bar_occurrence_all_d_20261001/check.py
+python3 -B -S frontiers/ordinary_short_bar_occurrence_all_d_20261001/test_check.py -v
+python3 -B -O -S frontiers/ordinary_short_bar_occurrence_all_d_20261001/test_check.py -v
+python3 -B -S frontiers/ordinary_short_bar_occurrence_all_d_20261001/test_check.py --mutants
+```
+
+The exact rational controls check the finite identities for `d = 2..6`. They do not prove the continuum analysis.
+
+Author lane: Anthropic / Claude, under Dylan Roy's delegation; personal reading PENDING. Every lane uses the same
+account, so organizational-independence credit is 0.

frontiers/ordinary_short_bar_occurrence_all_d_20261001/SOURCES.json

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+{
+ "version": 1,
+ "object": "C52-ALL-D-ORDINARY-SHORT-BAR-OCCURRENCE-20261001-v1",
+ "scientific_effect": "NONE",
+ "status": "additive conditional consumer; mandatory P/CAP/E1/E2/REC reading rule retained; no source reacceptance",
+ "current_required": [
+  {
+   "key": "P",
+   "path": "imports/lifetime_parent_20260925/UNIFORM_MATRIX_CAP_AND_LIFETIME.md",
+   "commit": "7fe06b01489af8181e53f26d520810829f146094",
+   "blob": "dfed3b8d318a3ab1950957f393307733a4bef3f2",
+   "bytes": 40261,
+   "sha256": "9350ad6eaba6626b93c3dedeef9e2ff816e5cdf1c8318e85fb27499141c84bc7",
+   "local_path": "imports/lifetime_parent_20260925/UNIFORM_MATRIX_CAP_AND_LIFETIME.md",
+   "role": "lifetime parent: Sections 2-5, 8, 10, 13-15 in every d>=2"
+  },
+  {
+   "key": "CAP",
+   "path": "imports/lifetime_parent_20260925/MARKED_CYLINDER_CAP_PROOF.md",
+   "commit": "7fe06b01489af8181e53f26d520810829f146094",
+   "blob": "0633aca3c2a2882b0de4399da0a75d64c2e6b2e1",
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+   "sha256": "0bf922b9203c29088b12388807aa0e2ecd020485eb0f6e919679841b5b2636fc",
+   "local_path": "imports/lifetime_parent_20260925/MARKED_CYLINDER_CAP_PROOF.md",
+   "role": "deterministic cap predecessor (d>=2)"
+  },
+  {
+   "key": "E1",
+   "path": "imports/lifetime_parent_20260925/ERRATUM_CONGRUENCE.md",
+   "commit": "7fe06b01489af8181e53f26d520810829f146094",
+   "blob": "213594d6ca6a86fb938110f4d166d9ce275a02d0",
+   "bytes": 1782,
+   "sha256": "bad7ef609c4ad8c41ad6af562c1b6807921e19a9d556ed793ad1a0db6e202028",
+   "local_path": "imports/lifetime_parent_20260925/ERRATUM_CONGRUENCE.md",
+   "role": "corrected endpoint congruence"
+  },
+  {
+   "key": "E2",
+   "path": "reviews/d1_section9_borel_repair_20260925/REPAIR.md",
+   "commit": "7fe06b01489af8181e53f26d520810829f146094",
+   "blob": "fe9b9ce4999908bb3814b500ee2d0ceb0c6f704a",
+   "bytes": 9062,
+   "sha256": "845abf9f9c99d672c2a10a887b5a2e7206a3d2de3d876f35f75ff6e2dc13e62f",
+   "local_path": "reviews/d1_section9_borel_repair_20260925/REPAIR.md",
+   "role": "replacement Section 9: Borel elder mark in weighted pair Kac-Rice"
+  },
+  {
+   "key": "REC",
+   "path": "reviews/d1_chain_reconciliation_20260928/RECONCILIATION.md",
+   "commit": "7fe06b01489af8181e53f26d520810829f146094",
+   "blob": "75da2597971510f843f8d90c743950cb8c177342",
+   "bytes": 23312,
+   "sha256": "451b9d7ffee072a73fc904cab891b6693e3f233808b89df10cce1b57036b65da",
+   "local_path": "reviews/d1_chain_reconciliation_20260928/RECONCILIATION.md",
+   "role": "mandatory reading rule, W1, embedding radius; fixed d>=2"
+  },
+  {
+   "key": "R",
+   "path": "frontiers/three_fronts_20260924/LIFETIME_REMAINDER.md",
+   "local_path": "frontiers/three_fronts_20260924/LIFETIME_REMAINDER.md",
+   "commit": "7fe06b01489af8181e53f26d520810829f146094",
+   "bytes": 17734,
+   "sha256": "380b7d0abdb0fe2de5a6564565af9560d3f1b1ce22fd5538927db0c52f4f3a4a",
+   "blob": "247b3ecf80bfbe896948d5d489b2d5842a81c481",
+   "role": "Section 2 whole-field regression coupling formula"
+  },
+  {
+   "key": "T",
+   "path": "frontiers/short_bar_endpoint_law_20261001/PROOF.md",
+   "local_path": "frontiers/short_bar_endpoint_law_20261001/PROOF.md",
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+   "bytes": 13815,
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+   "blob": "0d47dbc1d92863d8c51b918aa47d1fa8b605cfdc",
+   "role": "Proposition 3 / (T4): ordinary-bar marked intensity law in every d>=2"
+  }
+ ],
+ "cited": [
+  {
+   "key": "C52-FOLD",
+   "path": "frontiers/ordinary_short_bar_occurrence_20261001/FOLD_ISOLATION.md",
+   "pr": "Math-#235",
+   "commit": "7e2344166e989ae94e5732e445f445598fc75c4c",
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+   "bytes": 20771,
+   "sha256": "3889a0898901d03716d277e3afc2964bdbc7566d3a85803c4ad73673bdff1b52",
+   "role": "source of the planar argument generalized here; cited, not consumed as a premise; merged to main at 7e23441; d=2 case",
+   "local_path": "frontiers/ordinary_short_bar_occurrence_20261001/FOLD_ISOLATION.md"
+  },
+  {
+   "key": "C52-PROOF",
+   "path": "frontiers/ordinary_short_bar_occurrence_20261001/PROOF.md",
+   "pr": "Math-#235",
+   "commit": "7e2344166e989ae94e5732e445f445598fc75c4c",
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+   "role": "source of the planar consumer (Sections 3-6) generalized here; cited, not consumed as a premise; merged to main at 7e23441",
+   "local_path": "frontiers/ordinary_short_bar_occurrence_20261001/PROOF.md"
+  }
+ ]
+}