From 5a878dcf8b057dfe874eb27b82632eb096078112 Mon Sep 17 00:00:00 2001 From: Dylan Roy Date: Tue, 29 Sep 2026 15:32:42 -0500 Subject: [PATCH 01/11] Execute reviewed D5 graph fold --- frontiers/downstream_gate_20260925/GRAPH.json | 441 +++++++++++++++++- 1 file changed, 434 insertions(+), 7 deletions(-) diff --git a/frontiers/downstream_gate_20260925/GRAPH.json b/frontiers/downstream_gate_20260925/GRAPH.json index fa6ba930f..4e1cce112 100644 --- a/frontiers/downstream_gate_20260925/GRAPH.json +++ b/frontiers/downstream_gate_20260925/GRAPH.json @@ -332,26 +332,58 @@ "math.rn-region.mesoscopic-scaled-annulus": { "layer": "D5", "kind": "region", - "classification": "OPEN_ACTIVE", + "classification": "PROVED_REVIEWED", "controlling": false, "fingerprint": "x=r y with A<=|y|<=B away from pins", - "notes": "Owned by Math- PR7 reduction; exact J0 ledger still open" + "notes": "Reviewed only at D5-d with R >= B (covers the reviewed fixed annulus); see the complete D5 reconciliation reading rule. No d>2, numerical, elder-selection, JETMOD, or witness-collision closure.", + "scope": "D5-d with R >= B (covers the reviewed fixed annulus)", + "review_source": "reviews/d5_reconciliation_20260929/RECONCILIATION.md", + "review_disposition": "ACCEPT_AT_STATED_SCOPE", + "reading_rule": [ + "math.d5-component.punctured-pin-proof", + "math.d5-component.punctured-pin-review-111", + "math.d5-component.punctured-pin-continuum-review", + "math.d5-component.punctured-pin-continuum-check", + "math.d5-component.collar-proof", + "math.d5-component.collar-review", + "math.d5-component.annulus-proof", + "math.d5-component.annulus-review" + ] }, "math.rn-region.pin-collision": { "layer": "D5", "kind": "region", - "classification": "OPEN_ACTIVE", + "classification": "PROVED_REVIEWED", "controlling": false, "fingerprint": "near +-e1/2 scaled pin sites", - "notes": "Complement of fixed-remote and fixed scaled annulus" + "notes": "Reviewed only at D5-a, D5-b, D5-d; see the complete D5 reconciliation reading rule. No d>2, numerical, elder-selection, JETMOD, or witness-collision closure.", + "scope": "D5-a, D5-b, D5-d", + "review_source": "reviews/d5_reconciliation_20260929/RECONCILIATION.md", + "review_disposition": "ACCEPT_AT_STATED_SCOPE", + "reading_rule": [ + "math.d5-component.punctured-pin-proof", + "math.d5-component.punctured-pin-review-111", + "math.d5-component.punctured-pin-continuum-review", + "math.d5-component.punctured-pin-continuum-check", + "math.d5-component.collar-proof", + "math.d5-component.collar-review" + ] }, "math.rn-region.intermediate-r-to-rho": { "layer": "D5", "kind": "region", - "classification": "OPEN_ACTIVE", + "classification": "PROVED_REVIEWED", "controlling": false, "fingerprint": "r<<|x|<2, numerical, elder-selection, JETMOD, or witness-collision closure.", + "scope": "D5-e (I3/I4, window I_r)", + "review_source": "reviews/d5_reconciliation_20260929/RECONCILIATION.md", + "review_disposition": "ACCEPT_AT_STATED_SCOPE", + "reading_rule": [ + "math.d5-component.intermediate-window-proof", + "math.d5-component.i5-review-xai", + "math.d5-component.i5-review-claude" + ] }, "math.rn-region.witness-collision": { "layer": "D5", @@ -359,7 +391,13 @@ "classification": "OPEN_ACTIVE", "controlling": false, "fingerprint": "eta->0 mutual witness separation", - "notes": "Fixed-eta factorial moments do not cover shrinking separation" + "notes": "Off-pin fixed-separation second-moment evidence is reviewed, but the shrinking pin/witness-collision mechanism and sharp full-window order remain open.", + "scope": "catalog C6", + "review_source": "reviews/d5_reconciliation_20260929/RECONCILIATION.md", + "review_disposition": "OPEN", + "reading_rule": [ + "math.d5-component.offpin-second-moment-review" + ] }, "math.rn-mesoscopic-reduction": { "layer": "D5", @@ -457,6 +495,215 @@ "fingerprint": "regional-bypass-fixed-annulus-window-v1", "scope": "fixed d=2 scaled annulus; compact positive gaps; between-pin height window", "notes": "For this scope only, the reviewed analytic route bypasses CH-LIFT / Piece-2 / OBL-H5-JETMOD. Historical predicates remain OPEN/ABSENT in their original replay scopes." + }, + "math.d5-pin-neighborhood-first-moment": { + "layer": "D5", + "kind": "candidate", + "classification": "PROVED_REVIEWED", + "controlling": false, + "scope": "D5-a..D5-f of RECONCILIATION.md section 2; existential constants; fixed T; compact marks with k >= k_- > 0; d = 2", + "source": "reviews/d5_reconciliation_20260929/RECONCILIATION.md" + }, + "math.d5-component.punctured-pin-proof": { + "layer": "D5", + "kind": "reading_rule_component", + "classification": "PROVED_REVIEWED", + "controlling": false, + "component_of": "math.d5-pin-neighborhood-first-moment", + "component_role": "proof", + "author_provider": "OpenAI", + "fingerprint": "f972e50bc07674ebce9d971d1a1bd4dba2f8036dde37ecb57d8a44a35650f76a", + "source": "reviews/d5_local_collar_20260928/PUNCTURED_PIN_PROOF.md", + "review_basis": [ + { + "review": "#111", + "provider": "xAI", + "verdict": "ACCEPT algebra; continuum HOLD", + "depth": "algebraic" + }, + { + "review": "d5_punctured_pin_continuum_claude_20260929", + "provider": "Anthropic", + "verdict": "ACCEPT existential", + "depth": "full" + } + ] + }, + "math.d5-component.punctured-pin-review-111": { + "layer": "D5", + "kind": "reading_rule_component", + "classification": "PROVED_REVIEWED", + "controlling": false, + "component_of": "math.d5-pin-neighborhood-first-moment", + "component_role": "review_record", + "author_provider": "xAI", + "fingerprint": "668d74825f156c929177bc1a3481cf421de4dd7874e7b25b2aece6c10aa7dc0e", + "source": "reviews/d5_punctured_pin_nonauthor_20260928/REVIEW.md" + }, + "math.d5-component.punctured-pin-continuum-review": { + "layer": "D5", + "kind": "reading_rule_component", + "classification": "PROVED_REVIEWED", + "controlling": false, + "component_of": "math.d5-pin-neighborhood-first-moment", + "component_role": "review_record", + "author_provider": "Anthropic", + "fingerprint": "124c472cc064ba24021cb4bb8da1002836a4ce26c8df506228f5c20609f6575a", + "source": "reviews/d5_punctured_pin_continuum_claude_20260929/REVIEW.md" + }, + "math.d5-component.punctured-pin-continuum-check": { + "layer": "D5", + "kind": "reading_rule_component", + "classification": "PROVED_REVIEWED", + "controlling": false, + "component_of": "math.d5-pin-neighborhood-first-moment", + "component_role": "review_checker", + "author_provider": "Anthropic", + "fingerprint": "57bc87d11271b47ebccec6ea73abf823fa90e3a8c3c7d7cd2165bdc6f7e4175c", + "source": "reviews/d5_punctured_pin_continuum_claude_20260929/pp_continuum_check.py" + }, + "math.d5-component.collar-proof": { + "layer": "D5", + "kind": "reading_rule_component", + "classification": "PROVED_REVIEWED", + "controlling": false, + "component_of": "math.d5-pin-neighborhood-first-moment", + "component_role": "proof", + "author_provider": "OpenAI", + "fingerprint": "794babe0fd039c3a93c401c0b8978316331af009fad45f953e63fbe7e1e31aab", + "source": "reviews/d5_local_collar_20260928/COLLAR_PROOF.md", + "review_basis": [ + { + "review": "d5_collar_count_20260928", + "provider": "not named in record", + "verdict": "ACCEPT existential", + "depth": "full" + }, + { + "review": "Math-#105 comment 5872932723 (external)", + "provider": "Anthropic", + "verdict": "CONFIRMED", + "depth": "full" + } + ] + }, + "math.d5-component.collar-review": { + "layer": "D5", + "kind": "reading_rule_component", + "classification": "PROVED_REVIEWED", + "controlling": false, + "component_of": "math.d5-pin-neighborhood-first-moment", + "component_role": "review_record", + "author_provider": "not named in record", + "fingerprint": "8c8c30cc3b19601a7421341d5da8cb6c982fbc1fcc5ae4791acafa11cc81ee4e", + "source": "reviews/d5_collar_count_20260928/REVIEW.md" + }, + "math.d5-component.annulus-proof": { + "layer": "D5", + "kind": "reading_rule_component", + "classification": "PROVED_REVIEWED", + "controlling": false, + "component_of": "math.d5-pin-neighborhood-first-moment", + "component_role": "proof", + "author_provider": "OpenAI", + "fingerprint": "d55e2c03bb17e7977ff94130cc1ff21e54840cd1e20dc4e41ea9ad52228beb05", + "source": "frontiers/rn_annulus_bridge_20260925/PROOF.md", + "review_basis": [ + { + "review": "pr28_annulus_bridge_nonauthor_20260925", + "provider": "xAI", + "verdict": "ACCEPT R1-R7", + "depth": "full" + } + ] + }, + "math.d5-component.annulus-review": { + "layer": "D5", + "kind": "reading_rule_component", + "classification": "PROVED_REVIEWED", + "controlling": false, + "component_of": "math.d5-pin-neighborhood-first-moment", + "component_role": "review_record", + "author_provider": "xAI", + "fingerprint": "69ea7a479a9e8a5150cbe07b373772ab22413a1d81194d5a6a78adf6ada5f03f", + "source": "reviews/pr28_annulus_bridge_nonauthor_20260925/REVIEW.md" + }, + "math.d5-component.intermediate-window-proof": { + "layer": "D5", + "kind": "reading_rule_component", + "classification": "PROVED_REVIEWED", + "controlling": false, + "component_of": "math.d5-pin-neighborhood-first-moment", + "component_role": "proof", + "author_provider": "OpenAI", + "fingerprint": "b3eb9456d7058b5b78149cfca4e072679beda85cd1a0293d209664a542db66cf", + "source": "frontiers/intermediate_window_20260928/PROOF.md", + "review_basis": [ + { + "review": "d5_i5_planar_f_20260928", + "provider": "xAI", + "verdict": "ACCEPT existential", + "depth": "full" + }, + { + "review": "d5_intermediate_window_claude_20260928", + "provider": "Anthropic", + "verdict": "ACCEPT", + "depth": "full" + } + ] + }, + "math.d5-component.i5-review-xai": { + "layer": "D5", + "kind": "reading_rule_component", + "classification": "PROVED_REVIEWED", + "controlling": false, + "component_of": "math.d5-pin-neighborhood-first-moment", + "component_role": "review_record", + "author_provider": "xAI", + "fingerprint": "527d66e72b079ef7c854987f7e9d44f2252b81aa0e8d9e7ef3b45deb02388659", + "source": "reviews/d5_i5_planar_f_20260928/REVIEW.md" + }, + "math.d5-component.i5-review-claude": { + "layer": "D5", + "kind": "reading_rule_component", + "classification": "PROVED_REVIEWED", + "controlling": false, + "component_of": "math.d5-pin-neighborhood-first-moment", + "component_role": "review_record", + "author_provider": "Anthropic", + "fingerprint": "fb3207802bf2d92ad138bc338a36f39bcd3a94440669b9aba9558e566f767976", + "source": "reviews/d5_intermediate_window_claude_20260928/REVIEW.md" + }, + "math.d5-component.remote-window-proof": { + "layer": "D5", + "kind": "reading_rule_component", + "classification": "PROVED_REVIEWED", + "controlling": false, + "component_of": "math.d5-pin-neighborhood-first-moment", + "component_role": "proof", + "author_provider": "OpenAI", + "fingerprint": "a332bae9bdc0106ce17047f7e0409cc3d94eb610a0c7b74ba5ba2d01a1620cb7", + "source": "frontiers/remote_window_20260924/PROOF.md", + "review_basis": [ + { + "review": "STATUS D4 (main#76, external)", + "provider": "nonauthor", + "verdict": "ACCEPT", + "depth": "full" + } + ] + }, + "math.d5-component.offpin-second-moment-review": { + "layer": "D5", + "kind": "reading_rule_component", + "classification": "PROVED_REVIEWED", + "controlling": false, + "component_of": "math.rn-region.witness-collision", + "component_role": "review_record", + "author_provider": "nonauthor", + "fingerprint": "43beb4ef7da5bf71e15164d5c4bc1862db387d83f906aebdf9831625b1ca6369", + "source": "reviews/d5_offpin_second_moment_20260928/REVIEW.md" } }, "edges": [ @@ -609,6 +856,186 @@ "to": "hist.OBL-H5-JETMOD", "required": false, "relation": "regional_bypass_only" + }, + { + "from": "math.d5-pin-neighborhood-first-moment", + "to": "math.d5-component.punctured-pin-proof", + "required": true, + "relation": "requires_evidence" + }, + { + "from": "math.d5-pin-neighborhood-first-moment", + "to": "math.d5-component.punctured-pin-review-111", + "required": true, + "relation": "requires_evidence" + }, + { + "from": "math.d5-pin-neighborhood-first-moment", + "to": "math.d5-component.punctured-pin-continuum-review", + "required": true, + "relation": "requires_evidence" + }, + { + "from": "math.d5-pin-neighborhood-first-moment", + "to": "math.d5-component.punctured-pin-continuum-check", + "required": true, + "relation": "requires_evidence" + }, + { + "from": "math.d5-pin-neighborhood-first-moment", + "to": "math.d5-component.collar-proof", + "required": true, + "relation": "requires_evidence" + }, + { + "from": "math.d5-pin-neighborhood-first-moment", + "to": "math.d5-component.collar-review", + "required": true, + "relation": "requires_evidence" + }, + { + "from": "math.d5-pin-neighborhood-first-moment", + "to": "math.d5-component.annulus-proof", + "required": true, + "relation": "requires_evidence" + }, + { + "from": "math.d5-pin-neighborhood-first-moment", + "to": "math.d5-component.annulus-review", + "required": true, + "relation": "requires_evidence" + }, + { + "from": "math.d5-pin-neighborhood-first-moment", + "to": "math.d5-component.intermediate-window-proof", + "required": true, + "relation": "requires_evidence" + }, + { + "from": "math.d5-pin-neighborhood-first-moment", + "to": "math.d5-component.i5-review-xai", + "required": true, + "relation": "requires_evidence" + }, + { + "from": "math.d5-pin-neighborhood-first-moment", + "to": "math.d5-component.i5-review-claude", + "required": true, + "relation": "requires_evidence" + }, + { + "from": "math.d5-pin-neighborhood-first-moment", + "to": "math.d5-component.remote-window-proof", + "required": true, + "relation": "requires_evidence" + }, + { + "from": "math.rn-region.pin-collision", + "to": "math.d5-component.punctured-pin-proof", + "required": true, + "relation": "requires_evidence" + }, + { + "from": "math.rn-region.pin-collision", + "to": "math.d5-component.punctured-pin-review-111", + "required": true, + "relation": "requires_evidence" + }, + { + "from": "math.rn-region.pin-collision", + "to": "math.d5-component.punctured-pin-continuum-review", + "required": true, + "relation": "requires_evidence" + }, + { + "from": "math.rn-region.pin-collision", + "to": "math.d5-component.punctured-pin-continuum-check", + "required": true, + "relation": "requires_evidence" + }, + { + "from": "math.rn-region.pin-collision", + "to": "math.d5-component.collar-proof", + "required": true, + "relation": "requires_evidence" + }, + { + "from": "math.rn-region.pin-collision", + "to": "math.d5-component.collar-review", + "required": true, + "relation": "requires_evidence" + }, + { + "from": "math.rn-region.mesoscopic-scaled-annulus", + "to": "math.d5-component.punctured-pin-proof", + "required": true, + "relation": "requires_evidence" + }, + { + "from": "math.rn-region.mesoscopic-scaled-annulus", + "to": "math.d5-component.punctured-pin-review-111", + "required": true, + "relation": "requires_evidence" + }, + { + "from": "math.rn-region.mesoscopic-scaled-annulus", + "to": "math.d5-component.punctured-pin-continuum-review", + "required": true, + "relation": "requires_evidence" + }, + { + "from": "math.rn-region.mesoscopic-scaled-annulus", + "to": "math.d5-component.punctured-pin-continuum-check", + "required": true, + "relation": "requires_evidence" + }, + { + "from": "math.rn-region.mesoscopic-scaled-annulus", + "to": "math.d5-component.collar-proof", + "required": true, + "relation": "requires_evidence" + }, + { + "from": "math.rn-region.mesoscopic-scaled-annulus", + "to": "math.d5-component.collar-review", + "required": true, + "relation": "requires_evidence" + }, + { + "from": "math.rn-region.mesoscopic-scaled-annulus", + "to": "math.d5-component.annulus-proof", + "required": true, + "relation": "requires_evidence" + }, + { + "from": "math.rn-region.mesoscopic-scaled-annulus", + "to": "math.d5-component.annulus-review", + "required": true, + "relation": "requires_evidence" + }, + { + "from": "math.rn-region.intermediate-r-to-rho", + "to": "math.d5-component.intermediate-window-proof", + "required": true, + "relation": "requires_evidence" + }, + { + "from": "math.rn-region.intermediate-r-to-rho", + "to": "math.d5-component.i5-review-xai", + "required": true, + "relation": "requires_evidence" + }, + { + "from": "math.rn-region.intermediate-r-to-rho", + "to": "math.d5-component.i5-review-claude", + "required": true, + "relation": "requires_evidence" + }, + { + "from": "math.rn-region.witness-collision", + "to": "math.d5-component.offpin-second-moment-review", + "required": true, + "relation": "requires_evidence" } ] } From 506f315d44951c5beadba975b11c6257bd8a7ad8 Mon Sep 17 00:00:00 2001 From: Dylan Roy Date: Tue, 29 Sep 2026 15:32:43 -0500 Subject: [PATCH 02/11] Publish reviewed D5 and C6 proof paths --- PROOF_INDEX.md | 6 +++--- 1 file changed, 3 insertions(+), 3 deletions(-) diff --git a/PROOF_INDEX.md b/PROOF_INDEX.md index dc7cea156..652d2b725 100644 --- a/PROOF_INDEX.md +++ b/PROOF_INDEX.md @@ -24,6 +24,8 @@ The shared [public inventory](https://github.com/d6g8k5htny-coder/main/tree/main - D5 two-scale S6-S21: proof [frontiers/rn_thin_tube_20260925/TWO_SCALE_ADDENDUM.md](frontiers/rn_thin_tube_20260925/TWO_SCALE_ADDENDUM.md); review [reviews/replacement_20260925_pr19_pr21/TWO_SCALE_REVIEW.md](reviews/replacement_20260925_pr19_pr21/TWO_SCALE_REVIEW.md). - D5 inner-belt gradient density: proof [frontiers/axial_density_20260925/PROOF.md](frontiers/axial_density_20260925/PROOF.md); review [reviews/replacement_20260925_pr19_pr21/REVIEW.md](reviews/replacement_20260925_pr19_pr21/REVIEW.md) accepts corollary (1) on `|z|<=W r^2`. That acceptance is the density bound only. - D5 fixed-transverse chart: proof [reviews/downstream_boundary_20260925/TRANSVERSE_BOUND_CANDIDATE.md](reviews/downstream_boundary_20260925/TRANSVERSE_BOUND_CANDIDATE.md) (byte-for-byte import of commit `32b80ee085dc6a40113d1e46e333cda50d57ba21`, blob `024d927779f79fadaf932541ea6474f2995f8c50`); review [reviews/pr16_fixed_transverse_nonauthor_20260925/REVIEW.md](reviews/pr16_fixed_transverse_nonauthor_20260925/REVIEW.md). +- D5 planar pin/collar/intermediate first moment: the [source-bound reconciliation](reviews/d5_reconciliation_20260929/RECONCILIATION.md) composes the punctured pin disks, nested microdisks, collar, fixed annulus, window-only intermediate shells, and remote window into D5-a–D5-f. The reviewed scope is fixed `d=2` and `T`, compact birth/gap marks with `k>=k_->0`, all frames and critical indices, existential constants, all heights for D5-a–D5-d and the height window `I_r` for D5-e–D5-f. The exact component nodes and 30 required evidence edges are in [the downstream graph](frontiers/downstream_gate_20260925/GRAPH.json). The xAI planar continuum check is [Math-#141 comment 5894512272](https://github.com/d6g8k5htny-coder/Math-/pull/141#issuecomment-5894512272); it grants no `d>2` transfer and no independent collar proof. Shrinking multiple-witness collision, sharp factorial order, numerical constants, elder pairing, RN/24-jet and JETMOD remain open. +- C6 planar Fourier upper bound: [full proof](frontiers/c6_fourier_cutoff_20260929/PROOF.md), [source-bound reading note](reviews/c6_fourier_completion_20260929/READING_NOTE.md), and [Anthropic nonauthor review 5356335148](https://github.com/d6g8k5htny-coder/Math-/pull/148#pullrequestreview-5356335148) record `E_{Q_r^W}N(N-1)<=C r^3 log(1/r)` for fixed planar `T`, compact positive-gap marks and existential constants, using the complete planar D5/I5 reading rule. This is an upper bound, not `Theta(r^3)`; the Palm/size-biased route, `d>=3` first moment, numerical cutoffs and shrinking-collision mechanism remain open. - Cumulative transfer correction: proof [reviews/collision_mechanism_20260925/CUMULATIVE_TRANSFER_CORRECTION.md](reviews/collision_mechanism_20260925/CUMULATIVE_TRANSFER_CORRECTION.md); review [reviews/d2_cumulative_correction_20260925/REVIEW.md](reviews/d2_cumulative_correction_20260925/REVIEW.md) accepts this correction only. - P15 demand-one extension: exact counterexample [frontiers/three_fronts_20260924/P15_PRICE_BOUNDARY.md](frontiers/three_fronts_20260924/P15_PRICE_BOUNDARY.md); review pointer in [claims/LANDING_CLAIMS.json](claims/LANDING_CLAIMS.json) is [main #67](https://github.com/d6g8k5htny-coder/main/issues/67), disposition EXACT_COUNTEREXAMPLE. - D6 P15 full price theorem: proof [frontiers/full_price_20260924/PROOF.md](frontiers/full_price_20260924/PROOF.md); [reviews/p15_full_price_nonauthor_20260926/REVIEW.md](reviews/p15_full_price_nonauthor_20260926/REVIEW.md) records ACCEPT for Theorem F on the stated realized disjoint-capacity/clutter family, with demands at least two, independent probabilities, and the same palette. That review leaves the landing disposition untouched; it does not accept arbitrary downsets, demand-one extension, or an unrestricted prize claim. ASCII `3e-2` in (F1)/(F11) means `3*e-2`; see [ASCII_3E_MINUS_2.md](frontiers/full_price_20260924/ASCII_3E_MINUS_2.md). @@ -40,9 +42,7 @@ The shared [public inventory](https://github.com/d6g8k5htny-coder/main/tree/main ## Open obligations without a complete proof yet -- D5 pin neighborhoods: retained derivations are [reviews/d5_finite_r_hermite_repair_20260925/REPAIR.md](reviews/d5_finite_r_hermite_repair_20260925/REPAIR.md) and [reviews/d5_finite_r_hermite_repair_20260925/C6_REMAINDERS.md](reviews/d5_finite_r_hermite_repair_20260925/C6_REMAINDERS.md), with M1–M7 and S1–S4 accepted in [reviews/replacement_20260925_pr19_pr21/REVIEW.md](reviews/replacement_20260925_pr19_pr21/REVIEW.md). The newer public [PR53 reconnaissance note](https://github.com/d6g8k5htny-coder/Math-/blob/9a6f8a660d4508ec273b67d67e6b3871ddf2aa19/reviews/pin_neighborhood_recon_20260926/NOTE.md) has an [AMEND review in PR55](https://github.com/d6g8k5htny-coder/Math-/blob/4e188e25b1e1ef560f3eeb75c0d354d2ccf0ea22/reviews/d5_pin_neighborhood_20260926/REVIEW.md). These sources are on unmerged branches. **NO COMPLETE PROOF YET:** the inner microdisk bound and the open collar to the reviewed annulus are not supplied by that reconnaissance. [Math #58](https://github.com/d6g8k5htny-coder/Math-/issues/58) tracks the microdisk derivation; the claimed summed pin-neighborhood bound remains AMEND. -- D5 intermediate scale r << |x| << rho: bounded on opposite sides by [frontiers/remote_window_20260924/PROOF.md](frontiers/remote_window_20260924/PROOF.md) and by the reviewed fixed-annulus proofs [frontiers/rn_annulus_bridge_20260925/PROOF.md](frontiers/rn_annulus_bridge_20260925/PROOF.md) and [frontiers/rn_thin_tube_20260925/FIXED_ANNULUS_CANDIDATE.md](frontiers/rn_thin_tube_20260925/FIXED_ANNULUS_CANDIDATE.md). NO COMPLETE PROOF YET: uniform growing-scaled-radius bridge. -- D5 shrinking multiple-witness collision: fixed-separation machinery is [frontiers/remote_window_20260924/PROOF.md](frontiers/remote_window_20260924/PROOF.md) section 6, (15)–(16), at fixed `eta>0`. NO COMPLETE PROOF YET: shrinking-separation factorial-moment/collision estimate. +- D5 shrinking multiple-witness collision: fixed-separation machinery is [frontiers/remote_collision_20260928/PROOF.md](frontiers/remote_collision_20260928/PROOF.md), while the reviewed [global Fourier C6 upper bound](frontiers/c6_fourier_cutoff_20260929/PROOF.md) gives `O(r^3 log(1/r))` without resolving this regional mechanism. **NO COMPLETE SHARP PROOF YET:** the shrinking-separation/size-biased Palm estimate needed for `Theta(r^3)` remains open. - D0 historical CH-LIFT/Piece-2/24-jet obligations outside reviewed regional bypasses: see [frontiers/downstream_gate_20260925/GRAPH.json](frontiers/downstream_gate_20260925/GRAPH.json). NO COMPLETE PROOF YET where not explicitly superseded; absent historical carriers remain ABSENT. ## Repository rule From e61347250e653213583da59fc0e76ff1d1099b65 Mon Sep 17 00:00:00 2001 From: Dylan Roy Date: Tue, 29 Sep 2026 15:32:45 -0500 Subject: [PATCH 03/11] Record reviewed planar C6 upper bound --- .../candidates_pending_20260928/CANDIDATES.md | 37 ++++++++++++------- 1 file changed, 23 insertions(+), 14 deletions(-) diff --git a/reviews/candidates_pending_20260928/CANDIDATES.md b/reviews/candidates_pending_20260928/CANDIDATES.md index e3fc1a310..c6ea2c91e 100644 --- a/reviews/candidates_pending_20260928/CANDIDATES.md +++ b/reviews/candidates_pending_20260928/CANDIDATES.md @@ -72,26 +72,35 @@ was integrated at `4b2aa45b2f995fc27c16ec37cccb081821eda74c` with a scoped nonauthor review, but its proof explicitly omits the height law. This new height candidate does not inherit acceptance from that merge. -## C6. Torus-wide second factorial moment: open optimal order +## C6. Torus-wide second factorial moment: reviewed upper bound; sharp order open -The global `O(r^5)` extension is not an unqualified theorem target. There is a -**CONDITIONAL OBSTRUCTION** from C2: pointwise for every nonnegative integer `N`, +The reviewed planar Fourier-cutoff theorem now supplies, for fixed `T`, compact +positive-gap marks and existential constants, - N(N-1) >= 2*1{N>=2}. + E_{Q_r^W}[N(N-1)] <= C r^3 log(1/r). -Thus a proved lower bound `P(N>=2)>=c r^3` would force -`E[N(N-1)]>=2c r^3`, incompatible with a uniform `O(r^5)` upper bound as `r->0`. -This is not an accepted disproof until C2's analytic lower mechanism is validated. -No global factorial upper bound or optimal order is supplied here. +Full proof: `frontiers/c6_fourier_cutoff_20260929/PROOF.md` at Math main +`4d062e2a976abc8800a1ae63a49a943526b6bc0d`. The source-bound reading note is +`reviews/c6_fourier_completion_20260929/READING_NOTE.md`; Anthropic nonauthor +review 5356335148 ACCEPTs the stated planar composition. The complete planar +D5/I5 reading rule is load-bearing. Tests and the merge do not substitute for +that analytic review. -The fixed-remote `O(r^5)` result remains separate: both witnesses stay a fixed -distance from the pins. Source: `frontiers/remote_collision_20260928/PROOF.md` -at `5a5b97d2c518dd5c04c89d17029ec96e721d3b78`, Corollary D / P_eta. +The global `O(r^5)` extension is not an unqualified theorem target. Pointwise, +`N(N-1)>=2*1{N>=2}`; therefore a future proved lower bound +`P(N>=2)>=c r^3` would force an order-`r^3` lower bound. The current Fourier +result is only an upper bound with one logarithm. It does not prove +`Theta(r^3)`, validate C2's lower mechanism, or close the shrinking +pin/witness-collision or size-biased Palm estimate. The `d>=3` factorial +composition remains conditional on its separate first-moment input. -Open task: determine a valid full-window factorial upper bound with the -pin-neighborhood collisions included, compatible with the eventual disposition -of C2. Cauchy-Schwarz on the first moment (I5) does not supply such a bound. +The fixed-remote `O(r^5)` result remains separate: both witnesses stay a fixed +distance from the pins. Source: `frontiers/remote_collision_20260928/PROOF.md`. +Open task: determine the sharp full-window order, with the pin-neighborhood +collisions included. Mean plus a stretched/exponential total-count cap alone +cannot remove the logarithm; an appropriate marked or size-biased estimate is +still required. ## C7. Unrestricted selection-difference rate Candidate: Theorem C's unrestricted densities satisfy From 07a624059be2ea6011154a41c997fab9f494b3ee Mon Sep 17 00:00:00 2001 From: Dylan Roy Date: Tue, 29 Sep 2026 15:32:46 -0500 Subject: [PATCH 04/11] Add D5 graph fold negative controls --- reviews/d5_graph_fold_20260929/verify.py | 76 ++++++++++++++++++++++++ 1 file changed, 76 insertions(+) create mode 100644 reviews/d5_graph_fold_20260929/verify.py diff --git a/reviews/d5_graph_fold_20260929/verify.py b/reviews/d5_graph_fold_20260929/verify.py new file mode 100644 index 000000000..536960a94 --- /dev/null +++ b/reviews/d5_graph_fold_20260929/verify.py @@ -0,0 +1,76 @@ +#!/usr/bin/env python3 +"""Fail-closed checks for the D5 graph/proof-index/C6 catalog fold.""" +import copy +import json +import pathlib +import sys +import unittest + +ROOT=pathlib.Path(__file__).resolve().parents[2] +GRAPH=ROOT/"frontiers/downstream_gate_20260925/GRAPH.json" +PROP=ROOT/"reviews/d5_reconciliation_20260929/PROPOSED_TRANSITIONS.json" +INDEX=ROOT/"PROOF_INDEX.md" +CAND=ROOT/"reviews/candidates_pending_20260928/CANDIDATES.md" + +def load(path): + def pairs(items): + out={} + for k,v in items: + if k in out: raise ValueError("duplicate JSON key: "+k) + out[k]=v + return out + return json.loads(path.read_text(encoding="utf-8"),object_pairs_hook=pairs, + parse_constant=lambda x: (_ for _ in ()).throw(ValueError("nonfinite JSON: "+x))) + +def realized(graph,proposal): + nodes=graph["nodes"]; edges=graph["edges"] + if len({(e["from"],e["to"],e.get("relation")) for e in edges})!=len(edges): return False + for n in proposal["proposed_graph_nodes"]: + actual=nodes.get(n["id"]) + if actual is None: return False + for k,v in n.items(): + if k!="id" and actual.get(k)!=v: return False + have={(e["from"],e["to"],e.get("relation"),e.get("required")) for e in edges} + for e in proposal["proposed_graph_edges"]: + if (e["from"],e["to"],e.get("relation"),True) not in have: return False + for tr in proposal["graph"]: + if nodes.get(tr["node"],{}).get("classification")!=tr["proposed"]: return False + return nodes["math.rn-region.witness-collision"]["classification"]=="OPEN_ACTIVE" + +class FoldTests(unittest.TestCase): + @classmethod + def setUpClass(cls): + cls.g=load(GRAPH); cls.p=load(PROP) + cls.index=INDEX.read_text(encoding="utf-8") + cls.cand=CAND.read_text(encoding="utf-8") + def test_proposal_realized(self): self.assertTrue(realized(self.g,self.p)) + def test_missing_node_rejected(self): + g=copy.deepcopy(self.g);g["nodes"].pop("math.d5-component.collar-proof") + self.assertFalse(realized(g,self.p)) + def test_stale_fingerprint_rejected(self): + g=copy.deepcopy(self.g);g["nodes"]["math.d5-component.punctured-pin-proof"]["fingerprint"]="0"*64 + self.assertFalse(realized(g,self.p)) + def test_missing_edge_rejected(self): + g=copy.deepcopy(self.g);g["edges"]=[e for e in g["edges"] if not (e["from"]=="math.d5-pin-neighborhood-first-moment" and e["to"]=="math.d5-component.collar-proof")] + self.assertFalse(realized(g,self.p)) + def test_witness_closure_rejected(self): + g=copy.deepcopy(self.g);g["nodes"]["math.rn-region.witness-collision"]["classification"]="PROVED_REVIEWED" + self.assertFalse(realized(g,self.p)) + def test_index_scope_and_open_boundary(self): + self.assertIn("D5 planar pin/collar/intermediate first moment",self.index) + self.assertIn("C6 planar Fourier upper bound",self.index) + self.assertIn("NO COMPLETE SHARP PROOF YET",self.index) + self.assertNotIn("the claimed summed pin-neighborhood bound remains AMEND",self.index) + def test_catalog_records_only_reviewed_bound(self): + sec=self.cand.split("## C6.",1)[1].split("\n## C7.",1)[0] + self.assertIn("r^3 log(1/r)",sec) + self.assertIn("sharp full-window order",sec) + self.assertIn("does not prove",sec) + self.assertNotIn("No global factorial upper bound",sec) + def test_declarative_source_preserved(self): + self.assertIs(self.p["declarative"],True) + self.assertIs(self.p["executed"],False) + +if __name__=="__main__": + result=unittest.TextTestRunner(verbosity=2).run(unittest.defaultTestLoader.loadTestsFromTestCase(FoldTests)) + raise SystemExit(0 if result.wasSuccessful() else 1) From f71fb6ea1850d3e6158db6391159be17112d4c27 Mon Sep 17 00:00:00 2001 From: Dylan Roy Date: Tue, 29 Sep 2026 15:32:47 -0500 Subject: [PATCH 05/11] Document D5 graph fold scope --- reviews/d5_graph_fold_20260929/README.md | 19 +++++++++++++++++++ 1 file changed, 19 insertions(+) create mode 100644 reviews/d5_graph_fold_20260929/README.md diff --git a/reviews/d5_graph_fold_20260929/README.md b/reviews/d5_graph_fold_20260929/README.md new file mode 100644 index 000000000..e0696b0fe --- /dev/null +++ b/reviews/d5_graph_fold_20260929/README.md @@ -0,0 +1,19 @@ +# D5 graph/proof-index fold — 2026-09-29 + +This additive integration executes the already reviewed, declarative D5 reconciliation against the live downstream graph and repairs the public proof index/catalog. It does not alter proof bodies, `STATUS.md`, `LANDING_CLAIMS.json`, prizes or scientific Booleans. + +Scope: +- planar `d=2`, fixed `T`, compact marks with `k>=k_->0`, existential constants; +- D5-a–D5-d all-height first moments and D5-e–D5-f window-only first moments; +- reviewed planar C6 upper bound `E N(N-1)<=C r^3 log(1/r)`. + +Explicitly open: shrinking witness collision, sharp `Theta(r^3)`, Palm/size-biased repair, `d>=3` first moments, numerical constants, RN/24-jet/JETMOD and elder selection. + +Run: + +```sh +python -B -S reviews/d5_graph_fold_20260929/verify.py +python -B -O -S reviews/d5_graph_fold_20260929/verify.py +``` + +The verifier checks exact proposed nodes/edges and negative controls for a missing node, stale fingerprint, missing edge and accidental witness closure. Passing software checks are not mathematical acceptance. From 417462382e644d9b9ac2f9c70113df3f4f52465b Mon Sep 17 00:00:00 2001 From: Dylan Roy Date: Tue, 29 Sep 2026 15:38:21 -0500 Subject: [PATCH 06/11] Regenerate downstream gate result for D5 graph fold --- frontiers/downstream_gate_20260925/RESULTS.json | 16 ++++++++-------- 1 file changed, 8 insertions(+), 8 deletions(-) diff --git a/frontiers/downstream_gate_20260925/RESULTS.json b/frontiers/downstream_gate_20260925/RESULTS.json index 65b2bdb3f..ea31ef67e 100644 --- a/frontiers/downstream_gate_20260925/RESULTS.json +++ b/frontiers/downstream_gate_20260925/RESULTS.json @@ -6,7 +6,7 @@ "hist.rnu_env.py" ], "illegal_controlling_count": 0, - "open_or_author_side_count": 20 + "open_or_author_side_count": 17 }, "d0_ci_unblock": { "ci_error": "PROBLEM packet: unexpected files ['DOWNSTREAM_CROSSWALK_20260925.md']", @@ -39,32 +39,32 @@ "no_event_to_expectation_reversal": true, "open_complement": [ { - "classification": "OPEN_ACTIVE", + "classification": "PROVED_REVIEWED", "coverage_source": null, "fingerprint": "r<<|x|<2, numerical, elder-selection, JETMOD, or witness-collision closure." }, { - "classification": "OPEN_ACTIVE", + "classification": "PROVED_REVIEWED", "coverage_source": null, "fingerprint": "x=r y with A<=|y|<=B away from pins", "id": "math.rn-region.mesoscopic-scaled-annulus", - "notes": "Owned by Math- PR7 reduction; exact J0 ledger still open" + "notes": "Reviewed only at D5-d with R >= B (covers the reviewed fixed annulus); see the complete D5 reconciliation reading rule. No d>2, numerical, elder-selection, JETMOD, or witness-collision closure." }, { - "classification": "OPEN_ACTIVE", + "classification": "PROVED_REVIEWED", "coverage_source": null, "fingerprint": "near +-e1/2 scaled pin sites", "id": "math.rn-region.pin-collision", - "notes": "Complement of fixed-remote and fixed scaled annulus" + "notes": "Reviewed only at D5-a, D5-b, D5-d; see the complete D5 reconciliation reading rule. No d>2, numerical, elder-selection, JETMOD, or witness-collision closure." }, { "classification": "OPEN_ACTIVE", "coverage_source": null, "fingerprint": "eta->0 mutual witness separation", "id": "math.rn-region.witness-collision", - "notes": "Fixed-eta factorial moments do not cover shrinking separation" + "notes": "Off-pin fixed-separation second-moment evidence is reviewed, but the shrinking pin/witness-collision mechanism and sharp full-window order remain open." } ] }, From 41fcd31731422e0ee6f3a7f36eb385972dd90a00 Mon Sep 17 00:00:00 2001 From: Dylan Roy Date: Tue, 29 Sep 2026 15:38:22 -0500 Subject: [PATCH 07/11] Rebind downstream gate sources after D5 graph fold --- frontiers/downstream_gate_20260925/SOURCE_FILES.json | 8 ++++---- 1 file changed, 4 insertions(+), 4 deletions(-) diff --git a/frontiers/downstream_gate_20260925/SOURCE_FILES.json b/frontiers/downstream_gate_20260925/SOURCE_FILES.json index 19363814c..6a5e7a3ea 100644 --- a/frontiers/downstream_gate_20260925/SOURCE_FILES.json +++ b/frontiers/downstream_gate_20260925/SOURCE_FILES.json @@ -5,16 +5,16 @@ "sha256": "2423fa7d3519a5ba06739cb43cc72e26db70020350338a1fa508e5adfb109643" }, "GRAPH.json": { - "bytes": 22830, - "sha256": "53057a110d64e8bf135a19b8e7681a594c3c3fda18b1133136ba1b0ebba7ce20" + "bytes": 38676, + "sha256": "e0a5287a14b601eef1ea7883e0b4ad99788d165754d145c002dafd6102c03146" }, "README.md": { "bytes": 4025, "sha256": "13fc1accebebd6017f34b0e5473bf6338f2604948c25a002051b5f0620fc327a" }, "RESULTS.json": { - "bytes": 6535, - "sha256": "a513d80f0e54e229955cd2f63e1119e029ee13105c5531359cda1cb411801545" + "bytes": 6979, + "sha256": "5f27315797c57a1a5c9f37ba00667246f7a6e45e275998f79dc793d9e8efde3e" }, "SCOPE.md": { "bytes": 2218, From d3d8677f99f2a9c8adef4b480b140221f3cca53f Mon Sep 17 00:00:00 2001 From: Dylan Roy Date: Tue, 29 Sep 2026 15:45:48 -0500 Subject: [PATCH 08/11] Repair reviewed-region reporting after D5 graph fold --- frontiers/downstream_gate_20260925/RESULTS.json | 16 +++++++++------- .../downstream_gate_20260925/SOURCE_FILES.json | 12 ++++++------ frontiers/downstream_gate_20260925/hard_gate.py | 6 +++++- .../downstream_gate_20260925/test_hard_gate.py | 12 ++++++++---- 4 files changed, 28 insertions(+), 18 deletions(-) diff --git a/frontiers/downstream_gate_20260925/RESULTS.json b/frontiers/downstream_gate_20260925/RESULTS.json index ea31ef67e..62ac6f07c 100644 --- a/frontiers/downstream_gate_20260925/RESULTS.json +++ b/frontiers/downstream_gate_20260925/RESULTS.json @@ -38,6 +38,15 @@ "meaning": "region inventory for #76/#86 D4-D5; each covered region retains its source scope", "no_event_to_expectation_reversal": true, "open_complement": [ + { + "classification": "OPEN_ACTIVE", + "coverage_source": null, + "fingerprint": "eta->0 mutual witness separation", + "id": "math.rn-region.witness-collision", + "notes": "Off-pin fixed-separation second-moment evidence is reviewed, but the shrinking pin/witness-collision mechanism and sharp full-window order remain open." + } + ], + "proved_reviewed_regions": [ { "classification": "PROVED_REVIEWED", "coverage_source": null, @@ -58,13 +67,6 @@ "fingerprint": "near +-e1/2 scaled pin sites", "id": "math.rn-region.pin-collision", "notes": "Reviewed only at D5-a, D5-b, D5-d; see the complete D5 reconciliation reading rule. No d>2, numerical, elder-selection, JETMOD, or witness-collision closure." - }, - { - "classification": "OPEN_ACTIVE", - "coverage_source": null, - "fingerprint": "eta->0 mutual witness separation", - "id": "math.rn-region.witness-collision", - "notes": "Off-pin fixed-separation second-moment evidence is reviewed, but the shrinking pin/witness-collision mechanism and sharp full-window order remain open." } ] }, diff --git a/frontiers/downstream_gate_20260925/SOURCE_FILES.json b/frontiers/downstream_gate_20260925/SOURCE_FILES.json index 6a5e7a3ea..41642a97c 100644 --- a/frontiers/downstream_gate_20260925/SOURCE_FILES.json +++ b/frontiers/downstream_gate_20260925/SOURCE_FILES.json @@ -13,8 +13,8 @@ "sha256": "13fc1accebebd6017f34b0e5473bf6338f2604948c25a002051b5f0620fc327a" }, "RESULTS.json": { - "bytes": 6979, - "sha256": "5f27315797c57a1a5c9f37ba00667246f7a6e45e275998f79dc793d9e8efde3e" + "bytes": 7018, + "sha256": "5421ed4d334b75d3bd80bb23e64fd63bb0fbd1c4eda1e7f3da3f47569904a0c6" }, "SCOPE.md": { "bytes": 2218, @@ -29,8 +29,8 @@ "sha256": "393d407c2e35d2b6f3230f5a60a9aaa7691172544d3b59f72cc880c81be20701" }, "hard_gate.py": { - "bytes": 26557, - "sha256": "1954723d143a3d68cbf3834b2c18e4198fd89ba49145f012bdc425c80050d052" + "bytes": 26735, + "sha256": "a78f3e25f3b0cfe113e618a4c31a7a25d7f22af638c46dec1ecba221fa333ac8" }, "patches/d0_packet_allowlist.patch": { "bytes": 3096, @@ -41,8 +41,8 @@ "sha256": "276e69c2b29e012c386db615ed64e24badf3726a9f122fd9d77776a9c4f00711" }, "test_hard_gate.py": { - "bytes": 22691, - "sha256": "0f28ed996a50a1676b91a17198cf090086976e9eaf6a61aa9652f03acc427cf0" + "bytes": 22820, + "sha256": "a3376481d6029c7db25562ad25d1a5610e683e4d8a924768eb72a136afdc485d" }, "test_transition_contract.py": { "bytes": 12679, diff --git a/frontiers/downstream_gate_20260925/hard_gate.py b/frontiers/downstream_gate_20260925/hard_gate.py index 52ec00305..3a334f11e 100644 --- a/frontiers/downstream_gate_20260925/hard_gate.py +++ b/frontiers/downstream_gate_20260925/hard_gate.py @@ -486,6 +486,7 @@ def d4_region_complement(graph: dict[str, Any]) -> dict[str, Any]: """Explicit D4/D5 region map with coverage attributed to its exact source.""" fixed_remote = [] other_scoped = [] + proved_reviewed = [] open_regions = [] for nid, node in sorted(graph['nodes'].items()): if node.get('kind') != 'region': @@ -502,11 +503,14 @@ def d4_region_complement(graph: dict[str, Any]) -> dict[str, Any]: fixed_remote.append(entry) else: other_scoped.append(entry) + elif node['classification'] == 'PROVED_REVIEWED': + proved_reviewed.append(entry) else: open_regions.append(entry) return { 'covered_by_fixed_remote_candidate': fixed_remote, 'covered_by_other_scoped_candidates': other_scoped, + 'proved_reviewed_regions': proved_reviewed, 'open_complement': open_regions, 'no_event_to_expectation_reversal': True, 'legacy_24jet_discharged': False, @@ -657,4 +661,4 @@ def main() -> None: if __name__ == '__main__': - main() \ No newline at end of file + main() diff --git a/frontiers/downstream_gate_20260925/test_hard_gate.py b/frontiers/downstream_gate_20260925/test_hard_gate.py index 1c8c9f63e..293103064 100644 --- a/frontiers/downstream_gate_20260925/test_hard_gate.py +++ b/frontiers/downstream_gate_20260925/test_hard_gate.py @@ -226,6 +226,7 @@ def test_d4_region_complement(self): regions = m.d4_region_complement(self.graph) covered_ids = {r['id'] for r in regions['covered_by_fixed_remote_candidate']} scoped_ids = {r['id'] for r in regions['covered_by_other_scoped_candidates']} + reviewed_ids = {r['id'] for r in regions['proved_reviewed_regions']} open_ids = {r['id'] for r in regions['open_complement']} self.assertEqual(covered_ids, {'math.rn-region.fixed-remote'}) self.assertEqual(scoped_ids, {'math.rn-region.fixed-annulus-window'}) @@ -233,9 +234,12 @@ def test_d4_region_complement(self): regions['covered_by_other_scoped_candidates'][0]['coverage_source'], 'math.rn-fixed-annulus-window', ) - self.assertIn('math.rn-region.mesoscopic-scaled-annulus', open_ids) - self.assertIn('math.rn-region.pin-collision', open_ids) - self.assertIn('math.rn-region.intermediate-r-to-rho', open_ids) + self.assertEqual(reviewed_ids, { + 'math.rn-region.mesoscopic-scaled-annulus', + 'math.rn-region.pin-collision', + 'math.rn-region.intermediate-r-to-rho', + }) + self.assertTrue(reviewed_ids.isdisjoint(open_ids)) self.assertIn('math.rn-region.witness-collision', open_ids) self.assertFalse(regions['legacy_24jet_discharged']) self.assertTrue(regions['no_event_to_expectation_reversal']) @@ -445,4 +449,4 @@ def test_duplicate_edge_fails_closed(self): if __name__ == '__main__': - unittest.main() \ No newline at end of file + unittest.main() From 42db0ef59340a06af52354222ef26cbc6d1e7140 Mon Sep 17 00:00:00 2001 From: Dylan Roy Date: Tue, 29 Sep 2026 18:00:48 -0500 Subject: [PATCH 09/11] Repair D5 catalog review crosswalk --- frontiers/downstream_gate_20260925/GRAPH.json | 2 +- .../downstream_gate_20260925/RESULTS.json | 2 +- .../SOURCE_FILES.json | 12 ++-- .../test_hard_gate.py | 5 ++ .../candidates_pending_20260928/CANDIDATES.md | 69 +++++++++++++------ reviews/d5_graph_fold_20260929/verify.py | 14 ++++ 6 files changed, 74 insertions(+), 30 deletions(-) diff --git a/frontiers/downstream_gate_20260925/GRAPH.json b/frontiers/downstream_gate_20260925/GRAPH.json index 4e1cce112..220b56867 100644 --- a/frontiers/downstream_gate_20260925/GRAPH.json +++ b/frontiers/downstream_gate_20260925/GRAPH.json @@ -391,7 +391,7 @@ "classification": "OPEN_ACTIVE", "controlling": false, "fingerprint": "eta->0 mutual witness separation", - "notes": "Off-pin fixed-separation second-moment evidence is reviewed, but the shrinking pin/witness-collision mechanism and sharp full-window order remain open.", + "notes": "Off-pin fixed-separation second-moment evidence is reviewed and sharp global order is reviewed and merged through Math-#145, but the regional shrinking pin/witness-collision mechanism and its source-bound graph fold remain open.", "scope": "catalog C6", "review_source": "reviews/d5_reconciliation_20260929/RECONCILIATION.md", "review_disposition": "OPEN", diff --git a/frontiers/downstream_gate_20260925/RESULTS.json b/frontiers/downstream_gate_20260925/RESULTS.json index 62ac6f07c..657594914 100644 --- a/frontiers/downstream_gate_20260925/RESULTS.json +++ b/frontiers/downstream_gate_20260925/RESULTS.json @@ -43,7 +43,7 @@ "coverage_source": null, "fingerprint": "eta->0 mutual witness separation", "id": "math.rn-region.witness-collision", - "notes": "Off-pin fixed-separation second-moment evidence is reviewed, but the shrinking pin/witness-collision mechanism and sharp full-window order remain open." + "notes": "Off-pin fixed-separation second-moment evidence is reviewed and sharp global order is reviewed and merged through Math-#145, but the regional shrinking pin/witness-collision mechanism and its source-bound graph fold remain open." } ], "proved_reviewed_regions": [ diff --git a/frontiers/downstream_gate_20260925/SOURCE_FILES.json b/frontiers/downstream_gate_20260925/SOURCE_FILES.json index 41642a97c..1fa1e59e4 100644 --- a/frontiers/downstream_gate_20260925/SOURCE_FILES.json +++ b/frontiers/downstream_gate_20260925/SOURCE_FILES.json @@ -5,16 +5,16 @@ "sha256": "2423fa7d3519a5ba06739cb43cc72e26db70020350338a1fa508e5adfb109643" }, "GRAPH.json": { - "bytes": 38676, - "sha256": "e0a5287a14b601eef1ea7883e0b4ad99788d165754d145c002dafd6102c03146" + "bytes": 38753, + "sha256": "8822e9618678321a342d69cd0b8ae6552de1b5d578c331de5072b2892ee9dd09" }, "README.md": { "bytes": 4025, "sha256": "13fc1accebebd6017f34b0e5473bf6338f2604948c25a002051b5f0620fc327a" }, "RESULTS.json": { - "bytes": 7018, - "sha256": "5421ed4d334b75d3bd80bb23e64fd63bb0fbd1c4eda1e7f3da3f47569904a0c6" + "bytes": 7095, + "sha256": "0b95624e08e3eff7ca386a68534960b89ef63b10312ad5120159c0e29961264a" }, "SCOPE.md": { "bytes": 2218, @@ -41,8 +41,8 @@ "sha256": "276e69c2b29e012c386db615ed64e24badf3726a9f122fd9d77776a9c4f00711" }, "test_hard_gate.py": { - "bytes": 22820, - "sha256": "a3376481d6029c7db25562ad25d1a5610e683e4d8a924768eb72a136afdc485d" + "bytes": 23161, + "sha256": "c444e6c347da680aff5bef7f43900e45d52a0cc45081fb7b4def45266d97aac1" }, "test_transition_contract.py": { "bytes": 12679, diff --git a/frontiers/downstream_gate_20260925/test_hard_gate.py b/frontiers/downstream_gate_20260925/test_hard_gate.py index 293103064..0c8263e96 100644 --- a/frontiers/downstream_gate_20260925/test_hard_gate.py +++ b/frontiers/downstream_gate_20260925/test_hard_gate.py @@ -241,6 +241,11 @@ def test_d4_region_complement(self): }) self.assertTrue(reviewed_ids.isdisjoint(open_ids)) self.assertIn('math.rn-region.witness-collision', open_ids) + witness = next(r for r in regions['open_complement'] + if r['id'] == 'math.rn-region.witness-collision') + self.assertIn('sharp global order is reviewed and merged through Math-#145', + witness['notes']) + self.assertNotIn('sharp full-window order remain open', witness['notes']) self.assertFalse(regions['legacy_24jet_discharged']) self.assertTrue(regions['no_event_to_expectation_reversal']) diff --git a/reviews/candidates_pending_20260928/CANDIDATES.md b/reviews/candidates_pending_20260928/CANDIDATES.md index a733b50a5..70a703661 100644 --- a/reviews/candidates_pending_20260928/CANDIDATES.md +++ b/reviews/candidates_pending_20260928/CANDIDATES.md @@ -1,8 +1,11 @@ -# Theorem candidates pending review and test +# Historical theorem-candidate intake with current review crosswalk Scientific effect: **NONE**. Publication of this list is not acceptance. -Algebra already checked is noted. Continuum or missing public tests are the pending obligation. +This file began as the 28 September 2026 intake list. The source descriptions below +are preserved, while each section now states the source-bound disposition known on +29 September 2026. A later review does not recover the absent original `algebra.py`, +and tests or integration do not substitute for the cited analytic review. ## C1. Planar elder-failure lower bound (Math-#116) @@ -17,23 +20,33 @@ for small r, hence with the parent upper bound `1-p_r = Theta(r^3)` and Finite identities checked: cubic `G_k` pins correctly; path nodes evaluate to `0`, `-7k/32`, `-7k/32`, `+17k/64`; extra saddles at `X=-3/4`, `Z^2=15/8`, height `-7k/32`. -Pending: 10-jet covariance floor; `Q_r` box mass `>= c r`; `W_r >= c r^4` on that box; comparison with `Z_r <= C r^2`; public runnable suite (`algebra.py` is not in the PR). +Current disposition: Anthropic's source-bound +[`reviews/d1_elder_lower_claude_20260928/REVIEW.md`](../d1_elder_lower_claude_20260928/REVIEW.md) +accepts the ten-jet Schur floor and box mass (L9--L11), conditional `C^4` +control (L12--L13), determinant/normalizer ledger (L5/L14), and Theorem E1. +The review packet was integrated by Math-#124. The original author's +`algebra.py` remains absent, so its historical execution claim is still not +publicly reproducible; the review's distinct checker does not recover it. ## C2. Local window multiplicity (Math-#116) Source: `frontiers/window_multiplicity_laws_20260928/LOCAL_MULTIPLICITY.md` at `0507e3a1dbd3dede84cbeb805947c70aa16ebc36`. -Candidate: `P(N_global >= 2) = Theta(r^3)` in the planar height window. +Original candidate: `P(N_global >= 2) = Theta(r^3)` in the planar height window. The same global order conclusion is now available by the separate reviewed Palm route in `frontiers/c6_palm_route_20260929/PROOF.md`; that theorem does not -validate this candidate's local jet-box mechanism. If the mechanism here were -established with its stated first-moment upper bound, it would give an independent -local explanation of the failure of global conditional uniqueness. This is not an -acceptance transfer from the Palm theorem. - -Pending for this candidate: the jet-box probability lower bound together with the -planar first-moment upper bound (I5), as a matched local mechanism, plus public -tests. +validate this candidate's local jet-box mechanism. The separate C1/C2 review cited +below does validate that mechanism with its stated first-moment upper bound, giving +an independent local explanation of the failure of global conditional uniqueness. +That acceptance is not transferred from the Palm theorem. + +Current disposition: the same source-bound +[`reviews/d1_elder_lower_claude_20260928/REVIEW.md`](../d1_elder_lower_claude_20260928/REVIEW.md) +accepts Theorem L, including the jet-box lower event and the I5 first-moment +upper composition. This reviewed local mechanism remains distinct from the open +regional `math.rn-region.witness-collision` graph predicate. The absent original +`algebra.py` remains a publication/execution limitation, not an unreviewed +Gaussian step. ## C3. Remote ordered-pair kernel and beta-gap law (Math-#116) @@ -55,7 +68,10 @@ little-o is for fixed `E`, not arbitrary oscillatory `E_r`. Finite identities checked: Beta(2/3, 2) has mean `1/4` and variance `9/176`. -Pending: the contact Gaussian coefficient, extra-conditioned weight limit, overlap `(k-s^3|t|)_+`, L1 translation, and public tests. +Current disposition: Anthropic's source-bound +[`reviews/remote_pair_law_claude_20260928/REVIEW.md`](../remote_pair_law_claude_20260928/REVIEW.md) +records the analytic verdict integrated by Math-#129. Its exact fixed-remote, +fixed-Borel scope remains controlling; it is not a shrinking-region statement. ## C4. Distance-moment transition (Math-#116) @@ -63,7 +79,11 @@ Source: `frontiers/window_multiplicity_laws_20260928/REMOTE_DISTANCE_MOMENTS.md` Candidate: for each fixed moment order `p>=0`, ordered-pair distance moments `M_p` scale as `r^{5+p} A_p` for `0<=p<1`, `r^6(A_1+B_1)` at `p=1`, and `r^6 B_p` for `p>1`. -Pending: radial envelope `C(r^{12} delta^{-8}+r^6)`, equal-height contact kernel, loss of uniform integrability at moment order 1, public tests. +Current disposition: the amended source-bound +[`reviews/remote_distance_moments_claude_20260929/REVIEW.md`](../remote_distance_moments_claude_20260929/REVIEW.md) +records the accepted moment transition integrated with Math-#130. The finite-r +microscopic and limiting moment ranges remain those stated in the integration +receipt; no pair-event-conditioned law is inferred. ## C5. Remote singleton height mark (Math-#116) @@ -71,10 +91,12 @@ Source: `frontiers/window_multiplicity_laws_20260928/HEIGHT_MARKS.md` at `0507e3 Candidate: conditional on a remote occurrence, height in the window is asymptotically uniform and independent of the joint location/index mark, at `O(r)` TV. -Pending: source-bound use of the pre-height-integrated remote kernel. Math-#115 -was integrated at `4b2aa45b2f995fc27c16ec37cccb081821eda74c` with a scoped -nonauthor review, but its proof explicitly omits the height law. This new height -candidate does not inherit acceptance from that merge. +Current disposition: Anthropic's source-bound +[`reviews/remote_height_marks_claude_20260929/REVIEW.md`](../remote_height_marks_claude_20260929/REVIEW.md) +records the accepted singleton height-mark statement integrated with Math-#130. +The acceptance comes from that review, not from Math-#115; it retains the fixed +remote and deterministic varying positive-volume-set scope recorded in +[`docs/integration/2026-09-29-reviewed-window-and-inverse.md`](../../docs/integration/2026-09-29-reviewed-window-and-inverse.md). ## C6. Torus-wide factorial moments: reviewed global order; regional mechanism open @@ -115,7 +137,7 @@ Open task: prove or refute the shrinking-separation witness-collision mechanism encoded by the open graph node, without inferring it from the global Palm bound. Numerical constants and a unique limiting cluster law also remain outside the reviewed packets cited above. -## C7. Unrestricted selection-difference rate +## C7. Unrestricted selection-difference rate (still open as of 2026-09-29) Candidate: Theorem C's unrestricted densities satisfy @@ -125,13 +147,16 @@ Written support: the compact-mark case is the parent difference estimate under Theorem A in `imports/lifetime_parent_20260925/UNIFORM_MATRIX_CAP_AND_LIFETIME.md` at `5a5b97d2c518dd5c04c89d17029ec96e721d3b78`. #116 C1 would make the compact exponent sharp. -Pending: a rate in the unbounded-mark dominated-convergence argument of parent §13; parent text presently does not claim this unrestricted remainder. +Current disposition: **OPEN**. A rate in the unbounded-mark dominated-convergence +argument of parent §13 is still missing; the parent text does not claim this +unrestricted remainder. -## C8. Numerical constants +## C8. Numerical constants (still open as of 2026-09-29) Candidates: explicit finite `C`, `r_*`, `z_*`, `c_{B,K}`, `c_{d,L}` on a declared compact-mark / torus band. -Pending: a certified covariance-enclosure / finite-band program. No numerical value is recorded here. +Current disposition: **OPEN**. A certified covariance-enclosure / finite-band +program is still missing. No numerical value is recorded here. ## Not candidates diff --git a/reviews/d5_graph_fold_20260929/verify.py b/reviews/d5_graph_fold_20260929/verify.py index 1e357a5bf..f9f38ad64 100644 --- a/reviews/d5_graph_fold_20260929/verify.py +++ b/reviews/d5_graph_fold_20260929/verify.py @@ -82,6 +82,20 @@ def test_later_packets_are_separate_from_open_regional_mechanism(self): self.assertRegex(sec,r"They do\s+not close the regional shrinking-witness mechanism") heading=self.cand.split("## C6.",1)[1].splitlines()[0] self.assertNotIn("sharp order open",heading) + def test_catalog_current_review_crosswalk(self): + c1=self.cand.split("## C1.",1)[1].split("\n## C2.",1)[0] + c2=self.cand.split("## C2.",1)[1].split("\n## C3.",1)[0] + self.assertIn("reviews/d1_elder_lower_claude_20260928/REVIEW.md",c1) + self.assertIn("Theorem E1",c1) + self.assertNotIn("Pending:",c1) + self.assertIn("reviews/d1_elder_lower_claude_20260928/REVIEW.md",c2) + self.assertIn("Theorem L",c2) + self.assertNotIn("Pending for this candidate",c2) + def test_graph_note_separates_global_order_from_regional_gap(self): + note=self.g["nodes"]["math.rn-region.witness-collision"]["notes"] + self.assertIn("sharp global order is reviewed and merged through Math-#145",note) + self.assertIn("regional shrinking pin/witness-collision mechanism",note) + self.assertNotIn("sharp full-window order remain open",note) def test_declarative_source_preserved(self): self.assertIs(self.p["declarative"],True) self.assertIs(self.p["executed"],False) From 573a51095ee1dad9972c39375e196794f5192530 Mon Sep 17 00:00:00 2001 From: Dylan Roy Date: Tue, 29 Sep 2026 18:07:19 -0500 Subject: [PATCH 10/11] Mark historical C7 proposal refuted --- .../candidates_pending_20260928/CANDIDATES.md | 23 ++++++++++++------- reviews/d5_graph_fold_20260929/verify.py | 6 +++++ 2 files changed, 21 insertions(+), 8 deletions(-) diff --git a/reviews/candidates_pending_20260928/CANDIDATES.md b/reviews/candidates_pending_20260928/CANDIDATES.md index 70a703661..7d96d86bf 100644 --- a/reviews/candidates_pending_20260928/CANDIDATES.md +++ b/reviews/candidates_pending_20260928/CANDIDATES.md @@ -137,19 +137,26 @@ Open task: prove or refute the shrinking-separation witness-collision mechanism encoded by the open graph node, without inferring it from the global Palm bound. Numerical constants and a unique limiting cluster law also remain outside the reviewed packets cited above. -## C7. Unrestricted selection-difference rate (still open as of 2026-09-29) +## C7. Unrestricted selection-difference rate (historical proposal — REFUTED) -Candidate: Theorem C's unrestricted densities satisfy +Historical candidate: Theorem C's unrestricted densities satisfy 0 <= nu_cand^{all}(ell) - nu_eld^{all}(ell) <= C ell^{2/3}. -Written support: the compact-mark case is the parent difference estimate under +The compact-mark case is the parent difference estimate under Theorem A in `imports/lifetime_parent_20260925/UNIFORM_MATRIX_CAP_AND_LIFETIME.md` -at `5a5b97d2c518dd5c04c89d17029ec96e721d3b78`. #116 C1 would make the compact exponent sharp. - -Current disposition: **OPEN**. A rate in the unbounded-mark dominated-convergence -argument of parent §13 is still missing; the parent text does not claim this -unrestricted remainder. +at `5a5b97d2c518dd5c04c89d17029ec96e721d3b78`; it is not contradicted by +the unrestricted counterexample. + +Current disposition: **REFUTED**. Theorem U in +[`frontiers/unrestricted_selection_difference_20260929/PROOF.md`](../../frontiers/unrestricted_selection_difference_20260929/PROOF.md) +proves that the unrestricted difference is bounded below by a positive constant, +so its ratio to `ell^alpha` diverges for every `alpha>0`. The source-bound +[`reviews/c7_nonvanishing_openai_20260929/REVIEW.md`](../c7_nonvanishing_openai_20260929/REVIEW.md) +accepts that conclusion at fixed `d,L,r_0`; the packet landed via Math-#149 at +`21244e5ea0b0ab26884d8f933f9391acfa2b3697`. This does not assert an +individual expansion for `nu_eld` or transfer the compact-mark rate to the +unrestricted densities. ## C8. Numerical constants (still open as of 2026-09-29) diff --git a/reviews/d5_graph_fold_20260929/verify.py b/reviews/d5_graph_fold_20260929/verify.py index f9f38ad64..e871f6a02 100644 --- a/reviews/d5_graph_fold_20260929/verify.py +++ b/reviews/d5_graph_fold_20260929/verify.py @@ -96,6 +96,12 @@ def test_graph_note_separates_global_order_from_regional_gap(self): self.assertIn("sharp global order is reviewed and merged through Math-#145",note) self.assertIn("regional shrinking pin/witness-collision mechanism",note) self.assertNotIn("sharp full-window order remain open",note) + def test_catalog_c7_historical_proposal_is_refuted(self): + c7=self.cand.split("## C7.",1)[1].split("\n## C8.",1)[0] + self.assertIn("REFUTED",c7) + self.assertIn("frontiers/unrestricted_selection_difference_20260929/PROOF.md",c7) + self.assertIn("reviews/c7_nonvanishing_openai_20260929/REVIEW.md",c7) + self.assertNotIn("Current disposition: **OPEN**",c7) def test_declarative_source_preserved(self): self.assertIs(self.p["declarative"],True) self.assertIs(self.p["executed"],False) From 64a170fe7ff86f14f4f9b180abea7a376f7d7567 Mon Sep 17 00:00:00 2001 From: Dylan Roy Date: Tue, 29 Sep 2026 18:09:31 -0500 Subject: [PATCH 11/11] Correct C7 refutation provenance --- reviews/candidates_pending_20260928/CANDIDATES.md | 4 ++-- reviews/d5_graph_fold_20260929/verify.py | 3 +++ 2 files changed, 5 insertions(+), 2 deletions(-) diff --git a/reviews/candidates_pending_20260928/CANDIDATES.md b/reviews/candidates_pending_20260928/CANDIDATES.md index 7d96d86bf..02455f056 100644 --- a/reviews/candidates_pending_20260928/CANDIDATES.md +++ b/reviews/candidates_pending_20260928/CANDIDATES.md @@ -153,8 +153,8 @@ Current disposition: **REFUTED**. Theorem U in proves that the unrestricted difference is bounded below by a positive constant, so its ratio to `ell^alpha` diverges for every `alpha>0`. The source-bound [`reviews/c7_nonvanishing_openai_20260929/REVIEW.md`](../c7_nonvanishing_openai_20260929/REVIEW.md) -accepts that conclusion at fixed `d,L,r_0`; the packet landed via Math-#149 at -`21244e5ea0b0ab26884d8f933f9391acfa2b3697`. This does not assert an +accepts that conclusion at fixed `d,L,r_0`; the packet landed via Math-#133 at +`5bd924969bb261241885cd224d5dfb31acf64509`. This does not assert an individual expansion for `nu_eld` or transfer the compact-mark rate to the unrestricted densities. diff --git a/reviews/d5_graph_fold_20260929/verify.py b/reviews/d5_graph_fold_20260929/verify.py index e871f6a02..989033732 100644 --- a/reviews/d5_graph_fold_20260929/verify.py +++ b/reviews/d5_graph_fold_20260929/verify.py @@ -101,6 +101,9 @@ def test_catalog_c7_historical_proposal_is_refuted(self): self.assertIn("REFUTED",c7) self.assertIn("frontiers/unrestricted_selection_difference_20260929/PROOF.md",c7) self.assertIn("reviews/c7_nonvanishing_openai_20260929/REVIEW.md",c7) + self.assertIn("Math-#133",c7) + self.assertIn("5bd924969bb261241885cd224d5dfb31acf64509",c7) + self.assertNotIn("Math-#149",c7) self.assertNotIn("Current disposition: **OPEN**",c7) def test_declarative_source_preserved(self): self.assertIs(self.p["declarative"],True)