d6g8k5htny-coder · Oct 4, 2026 · Oct 4, 2026 · Oct 4, 2026
@@ -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 it as an unproven `ν^far = O(ℓ)`-type claim in the superseded 2026-08-01 line.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.
@@ -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

@@ -107,8 +107,22 @@
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    "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)"
   }
  ]
 }
@@ -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.
@@ -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.

@@ -135,8 +135,22 @@
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    "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)"
   }
  ]
 }