From 2c6ab514fe0828075ad3a752836d66cf76e38f00 Mon Sep 17 00:00:00 2001 From: Claude Date: Sun, 4 Oct 2026 04:12:05 +0000 Subject: [PATCH] Errata for #191 and #187 from the second-provider chain reads (T1, T5) Additive errata on two merged packets; PROOF.md, checkers and RESULTS.json are unchanged in both. - frontiers/remainder_vanishing_20260930/ERRATUM_20261004.md (Math- #191): F1 density-version qualifier of Theorem R+; F2 status labels (#186 merged before v1, #187 and #188 merged since); F3 the [R] and [C7-K] source rows; F4 the c1 notation in Remark 4; O1-O3 readings. From Grok Bot agent 13's Slice C AMEND 5975809791 (Slices A-B PASS 5975858230). - frontiers/far_elder_rate_20260930/ERRATUM_20261004.md (Math- #187): the section 0 SIDE24 manuscript and F-02 audit citations are context only, not repository sources. From Grok Bot agent 6's AMEND 5975813301 (mathematics PASS). - Each README gains a pointer line; each SOURCES.json gains the erratum's identity and an errata record. Scientific effect: NONE. Co-Authored-By: Claude Opus 5.5 Claude-Session: https://claude.ai/code/session_01NMeKEismAyeqgdB4sy2NJU --- .../ERRATUM_20261004.md | 40 ++++++++ frontiers/far_elder_rate_20260930/README.md | 4 + .../far_elder_rate_20260930/SOURCES.json | 18 +++- .../ERRATUM_20261004.md | 92 +++++++++++++++++++ .../remainder_vanishing_20260930/README.md | 4 + .../remainder_vanishing_20260930/SOURCES.json | 18 +++- 6 files changed, 172 insertions(+), 4 deletions(-) create mode 100644 frontiers/far_elder_rate_20260930/ERRATUM_20261004.md create mode 100644 frontiers/remainder_vanishing_20260930/ERRATUM_20261004.md diff --git a/frontiers/far_elder_rate_20260930/ERRATUM_20261004.md b/frontiers/far_elder_rate_20260930/ERRATUM_20261004.md new file mode 100644 index 000000000..93afac3ba --- /dev/null +++ b/frontiers/far_elder_rate_20260930/ERRATUM_20261004.md @@ -0,0 +1,40 @@ +# Erratum (4 October 2026): provenance of the §0 context citations + +Object: CL-FAR-ELDER-RATE-20260930-v1, erratum 1. +Author: Anthropic Claude (the packet's author; claude.ai session `session_01NMeKEismAyeqgdB4sy2NJU`). +Scientific effect: NONE. No mathematical change. + +`PROOF.md` stays unchanged as the merged record (blob `07260114`, consumed by Math- #220 (E3.3) and #229 (E3⁺.1)). +This file records the one finding of the second-provider read of Math- #187: +- **The read.** Comment 5975813301 by Grok Bot agent 6, task T5 of main#229 5975667461. +- **Its verdict.** AMEND, provenance only. The mathematics reads PASS: Lemma 1, Theorem F and Corollaries F1–F2 are + correct as stated within the retained interfaces. + +## The finding + +§0 makes specific claims about the SIDE24 manuscript: the 30 July 2026 revision, its supplement Proposition A.3.2, +and A.3.2′ in the 2026-08-01 amendment. It also makes claims about the audit finding F-02. Neither source is in the §5 +table or `SOURCES.json`, and neither exists in the repository. No proof step uses them. + +## Erratum + +This is the reviewer's text, applied verbatim: + +> **Erratum (provenance; additive, no mathematical change).** The SIDE24 manuscript (30 July 2026 revision, supplement +> Proposition A.3.2; A.3.2′ in the 2026-08-01 amendment) and the audit finding F-02 cited in §0 and Corollary F2 are +> not repository sources: they are not pinned in §5 or `SOURCES.json`, and no step of Lemma 1, Theorem F or +> Corollaries F1–F2 uses them. The only in-repository record of F-02 is +> `reviews/d1_cde_full_depth_claude_20260929/REVIEW.md` (blob `f05700e2`, Re-derivations D1-D item 2), which records +> it as an unproven `ν^far = O(ℓ)`-type claim in the superseded 2026-08-01 line. The §0 statements about what +> Proposition A.3.2 asserts and what the audit found are context only and are not verifiable from this repository; +> Theorem F stands independently of them. + +## What is unchanged + +- `PROOF.md`, `far_elder_check.py` and `RESULTS.json`, with the same blobs. +- Every source binding in `SOURCES.json`. + +`SOURCES.json` gains only this file's identity and an `errata` record. `README.md` gains one pointer line. + +The same read's non-blocking observation is not an erratum, and nothing is changed for it. The near-pair remark of §1 +idealizes `λ = 6kr` and drops the `r²M₄/2` term, and Theorem F does not consume it. diff --git a/frontiers/far_elder_rate_20260930/README.md b/frontiers/far_elder_rate_20260930/README.md index cdb2ba17e..e0859d1e9 100644 --- a/frontiers/far_elder_rate_20260930/README.md +++ b/frontiers/far_elder_rate_20260930/README.md @@ -1,5 +1,9 @@ # Far elder density rate (CL-FAR-ELDER-RATE-20260930-v1) +**Erratum 1 (4 October 2026):** `ERRATUM_20261004.md` records that the §0 SIDE24 manuscript and audit (F-02) +citations are context only and not repository sources. It answers the second-provider read 5975813301; the mathematics +reads PASS, and no mathematical change follows. + Author-side proof candidate, Anthropic Claude, 30 September 2026. Scientific effect NONE. Nonauthor review required. **Statement.** For the periodized Gaussian field on the torus and a fixed separation `ρ`, the density (per unit diff --git a/frontiers/far_elder_rate_20260930/SOURCES.json b/frontiers/far_elder_rate_20260930/SOURCES.json index 1ff213481..6e9b8786f 100644 --- a/frontiers/far_elder_rate_20260930/SOURCES.json +++ b/frontiers/far_elder_rate_20260930/SOURCES.json @@ -107,8 +107,22 @@ }, { "path": "README.md", - "bytes": 1808, - "sha256": "c1b9fbc8db38b8deab4c48c73d4f53f28e94f4e5ea92dff35bc3d8f5c2f316c7" + "bytes": 2086, + "sha256": "f6b001862f3bf5f91afcb4d3147e1279f7eab4d816e1319452cb662427a8d733" + }, + { + "path": "ERRATUM_20261004.md", + "bytes": 2394, + "sha256": "1b030bf383c8941e6262bb46a84bed53e504764fe44f054e2032d134da23fe11" + } + ], + "errata": [ + { + "file": "ERRATUM_20261004.md", + "date": "2026-10-04", + "found_by": "Grok Bot agent 6, Math- #187 comment 5975813301 (AMEND, provenance only; mathematics PASS), task T5 of main#229 5975667461", + "corrects": "section 0 and Corollary F2: the SIDE24 manuscript (30 July 2026 revision, Proposition A.3.2, A.3.2-prime) and audit finding F-02 are context only, not repository sources; the in-repository F-02 record is reviews/d1_cde_full_depth_claude_20260929/REVIEW.md (blob f05700e2)", + "proof_unchanged": "PROOF.md bytes unchanged (blob 072601145601a1021037a2e91bf8826c1c971ecc)" } ] } diff --git a/frontiers/remainder_vanishing_20260930/ERRATUM_20261004.md b/frontiers/remainder_vanishing_20260930/ERRATUM_20261004.md new file mode 100644 index 000000000..0ffb10311 --- /dev/null +++ b/frontiers/remainder_vanishing_20260930/ERRATUM_20261004.md @@ -0,0 +1,92 @@ +# Erratum (4 October 2026): density versions, status labels, source rows and one notation clash + +Object: CL-D2-REMAINDER-VANISHING-20260930-v1.1, erratum 1. +Author: Anthropic Claude (the packet's author; claude.ai session `session_01NMeKEismAyeqgdB4sy2NJU`). +Scientific effect: NONE. No mathematical claim of the packet changes. + +`PROOF.md` stays unchanged as the merged record (blob `441152df`). This file records the corrections from the +second-provider read of Math- #191: +- Slice C (comment 5975809791, Grok Bot agent 13): AMEND, as an additive erratum, low severity. This file applies it. +- Slices A and B (comment 5975858230, Grok Bot agent 5): PASS. + +These reads answer task T1 of main#229 5975667461. Every item below concerns scope wording, status labels or source +rows. Lemma E, Theorem R+ and its proof are unaffected. + +## F1. The density versions (statement, §0) + +`PROOF.md` §0 reads: "**Theorem R+.** For every fixed `d ≥ 2`, `L > 0`, as `ℓ ↓ 0`,". It is to be read as: + +> **Theorem R+.** For every fixed `d ≥ 2`, `L > 0`, and for the canonical marked Kac–Rice density versions of [P] +> with [E2], as `ℓ ↓ 0`. These are the versions for which [Z] (Z4) is stated: `ν_cand` and `ν_eld` are [R]'s +> unrestricted densities, that is, [Z]'s `ν_cand^all` and `ν_eld^all`. + +The reason: (R+.1)–(R+.2) are pointwise in `ℓ`, and (R+.2) subtracts [Z]'s `ρ_rej`. Such statements are meaningful +only for one fixed, compatible choice of versions. §2 already works with the Kac–Rice integral versions. [R] Theorem +R, [Z] (Z4) and [C7-K] (T1) carry the same qualifier. + +The list "What is not claimed" gains: "no statement about other almost-everywhere-equal versions of the densities." + +## F2. Status labels (§0, Remarks 2 and 4, §4, `SOURCES.json`, `README.md`) + +The status as of Math- `main` `cb73b11` corrects the labels "(unmerged)" and "unmerged candidates": +- **#186.** `reviews/d2_remainder_full_depth_claude_20260930/REVIEW.md` (blob `529c5264`) was already on `main` when + this note was written. It landed on `main` in `c839f28` on 30 September at 12:53 UTC, before v1 (`f59a6e5`, + 13:44 UTC) and v1.1 (`abae6d0`, 17:06 UTC). So "(unmerged)" for #186 reads "merged, cited only". +- **#187.** It has since landed (`c2f1270`, 1 October) with `PROOF.md` blob `07260114`, not the cited `37dcf6ef`. That + version changes only §0 and §5 wording. See also #187's own erratum, `ERRATUM_20261004.md` in its folder. +- **#188.** It has since landed (`f7f083e`, 4 October) with `PROOF.md` blob `0b089b89` (Theorem G v1.1), not the + cited v1 blob `50cfbf4f`. + +None of the three is consumed by Lemma E or Theorem R+. Remark 2 stays conditional and is not claimed. The +`SOURCES.json` bindings stay as recorded: they are cited-only identities, which the workflow does not verify. + +## F3. Two rows of the §4 source table + +- **[R]**, which reads "Theorem R; §§2–6: coupling (R2)–(R5), Lemma R3.2, (R8)–(R11), the separation-variable identity + — consumed", is to be read as: + + > Theorem R; §§2–7: coupling (R2)–(R5), Lemma R3.2, (R8)–(R13), the separation-variable identity, the ledgers + > (R16)–(R18) (Remark 1) — consumed + + This matches `SOURCES.json` and Remark 1's use of [R] §§6–7. +- **[C7-K]**, which reads "§4 (T1) proof with cutoff `ρ`, (T2) — Remark 2, Remark 3", is to be read as: + + > (K2) radius `r_0^{[K]}` in `r_0^*` (§0); §4 (T1) proof with cutoff `ρ`, (T2) — Remark 2, Remark 3 + + [C7-K] enters the statement's admissible radius. + +Both sources are merged and byte-matched, so neither row records unmerged consumption. + +## F4. A notation clash in Remark 4 + +Remark 4 reads: "No `+ c_1 + o(1)` with `c_1 ≠ 0` is claimed for `ν_eld`; the claim is precisely that its constant +term is `0`." It is to be read as: + +> No nonzero constant term (`ν_eld = cℓ^{−1/3} + C_0 + o(1)` with `C_0 ≠ 0`) is claimed for `ν_eld`; the claim is +> precisely that its constant term is `0`. (The `c₁` of Math- #207 is the coefficient of `ℓ^{1/4}`, a different +> object.) + +The merged #207 uses `c₁` for the nonzero, negative coefficient of `ℓ^{1/4}`, for example +`c₁/c_{3,24} ∈ [−5.07106215, −5.07106213]` (#219). Without this reading, Remark 4 and the V3 text could look +contradictory. + +## Optional items O1–O3 of the same read, applied as readings + +- **O1.** In Remark 1 (and Remark 3), "the rejected mass at separations `≍ r_0`" reads "the rejected mass at + separations below `r_0`". That mass is `O(1)` per unit separation, hence proportional to `r_0` (R+.3, [Z] (Z18)). +- **O2.** In §2, "the near-diagonal domination that [Z] §5 records as unavailable for candidates from (R11) alone": the + words "from (R11) alone" are this note's gloss. [Z] §5 says the bound (Z15) uses the rejection factor via (K2) and + is unavailable for candidates or selected pairs. +- **O3.** In §0, `r_0^*` uses "`≤ … L/(4√2)`". [REC] §5 has the strict `r < L/(4√2)`, and the strict form is meant. For + `L = 24` this does not bind, since `24/(4√2) ≈ 4.24` exceeds [R]'s `r_0 ≤ 1`. +- **O4** (informational). `SOURCES.json`'s `read_at.branch_base` `3e0a91b` is not an ancestor of `abae6d0`; the branch + forked at `2a10ed3`. All eight bound source blobs are identical at `2a10ed3`, `3e0a91b` and `42f19d7`, so there is no + effect. + +## What is unchanged + +- `PROOF.md`, `even_contact_check.py` and `RESULTS.json`, with the same blobs. +- All bindings in `SOURCES.json`. +- The checker's outputs. + +`SOURCES.json` gains only this file's identity and an `errata` record. `README.md` gains one pointer line. diff --git a/frontiers/remainder_vanishing_20260930/README.md b/frontiers/remainder_vanishing_20260930/README.md index 097ed0e6e..4014de40c 100644 --- a/frontiers/remainder_vanishing_20260930/README.md +++ b/frontiers/remainder_vanishing_20260930/README.md @@ -1,5 +1,9 @@ # The remainder of Theorem R: `B_{d,L}` for candidates, `0` for elder pairs (CL-D2-REMAINDER-VANISHING-20260930-v1.1) +**Erratum 1 (4 October 2026):** `ERRATUM_20261004.md`. It states the density-version qualifier of Theorem R+, corrects the +"unmerged" labels for #186/#187/#188 and two source-table rows, and resolves a `c₁` notation clash. It answers the +second-provider read 5975809791; no mathematical claim changes. + Author-side proof candidate, Anthropic Claude, 30 September 2026. Scientific effect NONE. Nonauthor review required. Relative to merged, reviewed sources only ([R] Theorem R, [Z] Theorem Z, [C7-K], the reconciled [P] chain); Math- #187/#188 are cited only, for a conditional rate remark. diff --git a/frontiers/remainder_vanishing_20260930/SOURCES.json b/frontiers/remainder_vanishing_20260930/SOURCES.json index 73732cec0..cc9d3ec3d 100644 --- a/frontiers/remainder_vanishing_20260930/SOURCES.json +++ b/frontiers/remainder_vanishing_20260930/SOURCES.json @@ -135,8 +135,22 @@ }, { "path": "README.md", - "bytes": 4393, - "sha256": "f3078a42edc8a0dbe88b6cca645ddff1518366756c2423b3ffc898bb283cd02f" + "bytes": 4698, + "sha256": "c5ea317ded604ee660defa2416b1e91c41e779d3e6762199d8d3f19f3d57c41e" + }, + { + "path": "ERRATUM_20261004.md", + "bytes": 5581, + "sha256": "1d058a6f66ed48bc7c74d8c529addb143d6397be050c9d28d9b97436af164961" + } + ], + "errata": [ + { + "file": "ERRATUM_20261004.md", + "date": "2026-10-04", + "found_by": "Grok Bot agent 13, Math- #191 comment 5975809791 (Slice C AMEND; Slices A-B PASS 5975858230), task T1 of main#229 5975667461", + "corrects": "F1 density-version qualifier in Theorem R+ and not-claimed list; F2 status labels for #186 (merged before v1), #187 (merged, blob 07260114), #188 (merged, blob 0b089b89); F3 the [R] and [C7-K] source rows; F4 the c1 notation in Remark 4; O1-O3 readings", + "proof_unchanged": "PROOF.md bytes unchanged (blob 441152dfc1d8d00cb268cebdb0394212a5bfacdb)" } ] }