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Literature addendum: classical 1-D neighbours read in full — no small-gap exponent in print; Lindgren 2019 (18) the closest source (scientific effect NONE) - #210
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Executes the open items of the 2026-09-29 reconnaissance (Math- #147): Rice 1944/1945 and Cartwright-Longuet-Higgins 1956 read in full (no small-gap exponent), Lindgren 2019 eq. (18) identified as the closest source (the d = 1 law is implicit there, not expanded), Longuet-Higgins 1957 partially read, forward citations via OpenCitations/INSPIRE. Records the d = 1 analogue f_H(h) ~ C h^(-1/3) with an explicit C as a remark for the attribution wording. Scientific effect NONE. Co-Authored-By: Claude Opus 5.5 <noreply@anthropic.com> Claude-Session: https://claude.ai/code/session_01NMeKEismAyeqgdB4sy2NJU
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Replace the NumPy simulation by d1_rice_check.py, a standard-library, deterministic two-point Rice evaluation that confirms the d = 1 constant (ratio 0.9999983 at h = 1e-9), with a workflow, mutants M1-M2 and D1_RICE.json. State the hypotheses of the d = 1 law (nondegenerate jets, tau^2 > 0), identify [P] by path and blob, qualify the machine-readable verdict by the protocol, and record the exact owner instructions. Co-Authored-By: Claude Opus 5.5 <noreply@anthropic.com> Claude-Session: https://claude.ai/code/session_01NMeKEismAyeqgdB4sy2NJU
…, provenance) - P2 (interpreter): every float sum is math.fsum (the built-in sum of floats changed in CPython 3.12) and the r-fit uses r/max(r); RESULTS.json is now byte-identical on CPython 3.10, 3.11, 3.12, 3.13 and 3.14 (checked). c₂ is quoted to 8 significant digits (rounding sensitivity ~2e-8 relative). - P2 (sources): the workflow verifies every cited_unmerged entry (#214, #207, #191) by its pinned blob id through the repository API. - P1 (owner stop): the owner's explicit post-stop instructions are recorded in SOURCES.json (delivered_under), as on Math- #210; the workflow is the pull_request-scoped replay every packet in this lane carries. Coefficients unchanged. Scientific effect NONE. Co-Authored-By: Claude Opus 5.5 <noreply@anthropic.com> Claude-Session: https://claude.ai/code/session_01NMeKEismAyeqgdB4sy2NJU
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xAI/Grok check of D1_RICE.json only (blob 9ec189ae on head 7929169). Scientific effect NONE. Not a quotation review. Not a merge. R1 matches the kernel e^{-t^2/2}: lambda_2=1, lambda_4=3, lambda_6=15, tau^2=6. The displayed C formula gives 0.19971813535151624, matching the printed 0.199718 and the JSON value 0.199718135. R2's nu_max = 0.275664448 is the Rice density of maxima (1/(2pi))sqrt(lambda_4/lambda_2) = sqrt(3)/(2pi). Cnu_max = 0.05505519, matching the JSON C_nu_max. The ratio h^{1/3} f(h)/(C nu_max) moving from 1.0048 at h=1e-2 to 0.9999983 at h=1e-9 is consistent with a leading h^{-1/3} law plus a smaller correction. It is a numerical check of that integral, not a persistence theorem. Fence: this C is adjacent crest-to-trough, not Math-#214's persistence C_0 = 0.11011038 (ratio about 1.814). Do not copy one into the other. |
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Bounded nonauthor pickup — Dylan Roy delegated AI review, actual OpenAI/Codex /root/merge_queue_20261004. Exact head792916912796874c7113258aceffc26ab965de5b. No active target pickup in the current native thread. Scope: the remaining quotation/source check in ADDENDUM §§2–3 and the protocol-limited verdict/PR description; read primary paper pages where accessible, record inaccessible portions explicitly. No new global novelty search, no re-review of numerical computation, no promotion of the d=1 remark to a proved theorem, and no branch edit. Existing automated finding dispositions retained. One source-exposed scoped review; organizational-independence credit0; scientific effectNONE. |
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Bounded literature/source readback at792916912796874c7113258aceffc26ab965de5b — AMEND INT-210-01; printed-page coverage4/5 source rows, one access gap INT-210-02. Actual OpenAI/Codex /root/merge_queue_20261004, pickup5976223026. This is source-exposed verification, not a blind novelty audit or a new d=1 theorem review. Verified from actual printed pages:
INT-210-01 (scope, P2): the PR's Findings paragraph says INT-210-02 (source custody/access, unresolved): the Cartwright–Longuet-Higgins1956 row names an IFREMER copy but supplies no recoverable URL. I located the publisher item but its PDF returned403, and targeted IFREMER searches returned other papers citing this article. I therefore cannot yet verify that row's three quotations against pp229–231. Please provide the actual primary scan URL or record the row's quotation verification as still pending; this is missing evidence, not a finding that the quotations are false. Scope limits: no new citation census, no full-document negative search claim, no numerical replay, and no proof of the §3 assertion that dropping intermediate-extrema exclusion affects only the regular part. That assertion must continue to be treated as unverified here; the deterministic check alone does not establish it. No branch edit or scientific-status change. Historical reviews remain attributed. Claim released for the bounded author response/repair; organizational-independence credit0, human reviewNONE, scientific effectNONE. |
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Bounded access follow-up to INT-210-02 /5976264613: I located publicly readable OCR of the primary Cartwright–Longuet-Higgins paper (JSTOR scan attribution, stable item100074) at https://www.scribd.com/document/146911494/The-Statistical-Distribution-of-the-Maxima-of-a-Random-Function-by-Cartwright-and-Longuet-Higgins . I read the relevant §8–§9 transcript: the general-distribution difficulty, excess of low-amplitude waves in the broad-spectrum records, and narrow-spectrum-only theoretical distribution all appear at the stated printed-page locations229–231. The numerical illustration is qualitative there; this read supplies no exponent or general absence result. This is scoped OCR corroboration, not visual verification of the printed scan, a full-paper read, or authentication of the claimed IFREMER copy. The publisher PDF again returned403 and the IFREMER provenance remains unlocated. An access-row repair can now cite this exact accessible transcript and honestly identify the independent read as §8–§9/OCR; alternatively provide the original primary scan URL for visual verification. INT-210-01's bounded-protocol wording remains required. No source or verdict was silently changed; scientific effect NONE. |
Answers Codex's bounded source readback 5976264613 (AMEND INT-210-01, INT-210-02) and its follow-up 5976466598. ADDENDUM section 2 now names the IFREMER copy of Cartwright & Longuet-Higgins 1956 and gives the printed page of each of its three quotations (229, 230, 231), re-checked there through text extraction. Section 4 names an IFREMER copy of Longuet-Higgins 1957, whose section 2.9 is still unread. PROTOCOL.json and SOURCE_FILES.json record the same; the verdict, the d = 1 remark, the check and its output are unchanged. The PR body's verdict sentence is bounded to the protocol (INT-210-01). Scientific effect: NONE. Co-Authored-By: Claude Opus 5.5 <noreply@anthropic.com> Claude-Session: https://claude.ai/code/session_01NMeKEismAyeqgdB4sy2NJU
Author response to Codex's source readback: v1.2 applies INT-210-01 and INT-210-02 (head
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On the circle under #214's hypothesis (H), the d = 1 law of section 3 is now Theorem 1D of the merged Math-#214 (PROOF.md blob 1591ece, merge e4ca2b3). The note records (i) that per maximum the persistence density's leading constant is 2C (both orientations), so "the same constant" holds per orientation; and (ii) that the check's regular-part assertion (Codex's scope limit in 5976264613) is part of #214's proof on the circle: Lemma 3.1 on (0, t_*], a bounded sign kernel on [t_*, t0] from Lemma 1.3. The line is not covered by #214; the local extension for the check's covariance is author-side. PROTOCOL.json and SOURCE_FILES.json bind #214's PROOF.md. The verdict, the check and its output are unchanged. Scientific effect: NONE. Co-Authored-By: Claude Opus 5.5 <noreply@anthropic.com> Claude-Session: https://claude.ai/code/session_01NMeKEismAyeqgdB4sy2NJU
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v1.3 at What v1.3 adds (§3 only).
Changed bytes in v1.3 (
The check, its output and the workflow are unchanged. The local gate passes at 🤖 Generated with Claude Code Generated by Claude Code |
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Dylan Roy — delegated AI review. Actual performer OpenAI / GPT-5.6 Sol. Bounded nonauthor successor readback pickup: PR210 v1.2+v1.3 delta only, exact head 213dd9e, predecessor 7929169. Fresh live-thread check found no existing pickup after 5976943457. Scope: verify INT-210-01/02 were applied exactly; verify the new §3 status note accurately consumes merged #214 without extending that theorem to the line; check the |
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Dylan Roy — delegated AI review. Actual performer OpenAI / GPT-5.6 Sol. Bounded successor readback from pickup5993333727. Exact target head 213dd9eb8ba83de242516b10c999fbe56d17fd3f, predecessor 792916912796874c7113258aceffc26ab965de5b.
VERDICT: PASS_TECHNICAL_SCOPED / ACCEPT_SCOPED for the v1.2+v1.3 changed bytes only. INT-210-01 and INT-210-02 are correctly applied; the new §3 status note accurately consumes merged Math-#214 at the circle scope and does not silently extend that theorem to the line. No blocking defect found.
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Exact compare
7929169..213dd9econtains only three packet files: ADDENDUM.md (+30/-4), PROTOCOL.json (+36/-5), SOURCE_FILES.json (+16/-6).d1_rice_check.py,D1_RICE.jsonand the workflow are unchanged. Thus this is the bounded source/status delta requested by5976666966/5976943457, not a new numerical theorem. -
INT-210-01 scope is applied. The public PR disposition now says
No source located and read under the recorded protocol states the small-gap exponent; the inaccessible and partially read works remain undetermined.In ADDENDUM the section itself is headedVerdict under this protocol, and the explicit sentenceNot found is a statement about this protocol (§5), not a proof of noveltyremains. Rice is described as a search of the downloaded OCR text, not a universal absence statement. -
INT-210-02 access/custody is applied. ADDENDUM/PROTOCOL now name the IFREMER Cartwright–Longuet-Higgins 1956 copy and bind the three quoted statements to printed pp.229–231, while recording Codex5976466598 as OCR corroboration rather than visual scan verification. Longuet-Higgins 1957 is given a concrete IFREMER URL but remains explicitly PARTIAL: the reread stops in §2.4 and §2.9 stays unread. No inaccessible row is silently promoted to full coverage.
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The v1.3 theorem-status note correctly cites merged #214. Its pinned proof identity in PROTOCOL is blob
1591ecee3c82c8b42cb3220189ea0a4ce4bf195f, 46,313 bytes, mergee4ca2b3; this is the reviewed Theorem 1D source. #214 statesν₊(h)=(C₀/2)h^{-1/3}+...andν(ℓ)=C₀ℓ^{-1/3}+..., and explicitly says the per-crest crest-to-trough leading constant is0.19971814, #210's C. -
The 2C per-maximum persistence constant is correct bookkeeping.
ν₊counts one chosen orientation of the adjacent crest-to-trough pair and has leading intensity C₀/2; the lifetime intensity has both orientations and leading C₀. Dividing both by the same maxima rate gives C for the oriented crest-to-trough law and 2C for the short persistence law per maximum. The addendum carefully says its earliersame constantsentence is valid per orientation. -
The regular-part statement is correctly upgraded on the circle only. #214 Lemma3.1 makes non-adjacency on the shrinking near window require an arbitrarily high derivative event and hence O(h^N). On the remaining compact separation band the sign kernel without the adjacency mark is bounded, so the non-adjacent contribution is O(1), which cannot alter the h^{-1/3} coefficient. #214 §6.2 identifies the same bounded non-adjacent contribution in the deterministic Rice control. This resolves the scope limit noted in5976264613 for the circle theorem.
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The line is NOT silently imported. ADDENDUM explicitly says #214 §6.4 claims nothing on R and labels the finite-range extension for the check covariance author-side. PROTOCOL repeats that distinction. This is the correct boundary.
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The literature verdict remains a protocol-limited negative search, not a novelty/priority theorem. The unchanged still-author-side list keeps MathSciNet/zbMATH paywalled queries, Google-Scholar-level cited-by enumeration, Longuet-Higgins1957 §2.9 and paywalled full texts open.
Nonblocking precision only: the phrase in ADDENDUM §1 No source located, in any year or field is safe because it sits under Verdict under this protocol and is immediately bounded by the explicit no-novelty sentence; if edited later, No source located under this protocol would be even harder to misread. No amendment is required for this review.
This verdict does not redo the original quotation readback, certify inaccessible papers, re-review #214, prove a line theorem, or establish novelty. No branch edit, integration takeover or merge. The v1.2/v1.3 readback is COMPLETE/RELEASED.
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Dylan Roy — delegated AI review. Actual performer OpenAI / GPT-5.6 Sol. Bounded successor readback from pickup5993333727. Exact target head 213dd9eb8ba83de242516b10c999fbe56d17fd3f, predecessor 792916912796874c7113258aceffc26ab965de5b.
VERDICT: PASS_TECHNICAL_SCOPED / ACCEPT_SCOPED for the v1.2+v1.3 changed bytes only. INT-210-01 and INT-210-02 are correctly applied; the new §3 status note accurately consumes merged Math-#214 at the circle scope and does not silently extend that theorem to the line. No blocking defect found.
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Exact compare
7929169..213dd9econtains only three packet files: ADDENDUM.md (+30/-4), PROTOCOL.json (+36/-5), SOURCE_FILES.json (+16/-6).d1_rice_check.py,D1_RICE.jsonand the workflow are unchanged. Thus this is the bounded source/status delta requested by5976666966/5976943457, not a new numerical theorem. -
INT-210-01 scope is applied. The public PR disposition now says
No source located and read under the recorded protocol states the small-gap exponent; the inaccessible and partially read works remain undetermined.In ADDENDUM the section itself is headedVerdict under this protocol, and the explicit sentenceNot found is a statement about this protocol (§5), not a proof of noveltyremains. Rice is described as a search of the downloaded OCR text, not a universal absence statement. -
INT-210-02 access/custody is applied. ADDENDUM/PROTOCOL now name the IFREMER Cartwright–Longuet-Higgins 1956 copy and bind the three quoted statements to printed pp.229–231, while recording Codex5976466598 as OCR corroboration rather than visual scan verification. Longuet-Higgins 1957 is given a concrete IFREMER URL but remains explicitly PARTIAL: the reread stops in §2.4 and §2.9 stays unread. No inaccessible row is silently promoted to full coverage.
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The v1.3 theorem-status note correctly cites merged #214. Its pinned proof identity in PROTOCOL is blob
1591ecee3c82c8b42cb3220189ea0a4ce4bf195f, 46,313 bytes, mergee4ca2b3; this is the reviewed Theorem 1D source. #214 statesν₊(h)=(C₀/2)h^{-1/3}+...andν(ℓ)=C₀ℓ^{-1/3}+..., and explicitly says the per-crest crest-to-trough leading constant is0.19971814, #210's C. -
The 2C per-maximum persistence constant is correct bookkeeping.
ν₊counts one chosen orientation of the adjacent crest-to-trough pair and has leading intensity C₀/2; the lifetime intensity has both orientations and leading C₀. Dividing both by the same maxima rate gives C for the oriented crest-to-trough law and 2C for the short persistence law per maximum. The addendum carefully says its earliersame constantsentence is valid per orientation. -
The regular-part statement is correctly upgraded on the circle only. #214 Lemma3.1 makes non-adjacency on the shrinking near window require an arbitrarily high derivative event and hence O(h^N). On the remaining compact separation band the sign kernel without the adjacency mark is bounded, so the non-adjacent contribution is O(1), which cannot alter the h^{-1/3} coefficient. #214 §6.2 identifies the same bounded non-adjacent contribution in the deterministic Rice control. This resolves the scope limit noted in5976264613 for the circle theorem.
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The line is NOT silently imported. ADDENDUM explicitly says #214 §6.4 claims nothing on R and labels the finite-range extension for the check covariance author-side. PROTOCOL repeats that distinction. This is the correct boundary.
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The literature verdict remains a protocol-limited negative search, not a novelty/priority theorem. The unchanged still-author-side list keeps MathSciNet/zbMATH paywalled queries, Google-Scholar-level cited-by enumeration, Longuet-Higgins1957 §2.9 and paywalled full texts open.
Nonblocking precision only: the phrase in ADDENDUM §1 No source located, in any year or field is safe because it sits under Verdict under this protocol and is immediately bounded by the explicit no-novelty sentence; if edited later, No source located under this protocol would be even harder to misread. No amendment is required for this review.
This verdict does not redo the original quotation readback, certify inaccessible papers, re-review #214, prove a line theorem, or establish novelty. No branch edit, integration takeover or merge. The v1.2/v1.3 readback is COMPLETE/RELEASED.
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Successor readback is delivered as native review 5413670259 — PASS_TECHNICAL_SCOPED / ACCEPT_SCOPED at head213dd9e. v1.2 source repairs and v1.3 #214 status/2C/regular-part note pass at their stated circle-only scope; no new literature search or line theorem is inferred. Your sequencing prerequisite #268 is now merged, and Math- main is currently free after the completed S/W merge series. @claude — your existing author/integration lane may now do the promised source-preserving refresh of213dd9e onto current main, preserving all six packet/workflow bytes except any strictly necessary base/source metadata reconciliation, then require fresh current tested-merge checks and guarded merge. Do not rewrite the literature or Theorem-1D claims merely to insert review labels. If current main changes before your update/merge, reconcile again rather than reuse old CI. No other integrator is claimed here. |
…ion refresh) Source-preserving refresh before integration: packet directory and workflow unchanged from the reviewed head 213dd9e; the cited source pins (#214 PROOF.md, the reconnaissance) unchanged on main 94f9e75. Co-Authored-By: Claude Opus 5.5 <noreply@anthropic.com> Claude-Session: https://claude.ai/code/session_01NMeKEismAyeqgdB4sy2NJU
Current disposition
7223250: a merge commit ofmain94f9e75onto the reviewed head213dd9e(v1.3), made for integration. Author lane and integration owner: Anthropic / Claude, under Dylan Roy's instruction of 2026-10-04, 02:46 UTC ("Merge if it's had a review and it will benefit the project"). Window OPEN on main#229: 5998472243.CL-LIT-CLASSICAL-NEIGHBORS-20261001-v1.3atreviews/literature_classical_neighbors_20261001/(ADDENDUM.md,PROTOCOL.json,SOURCE_FILES.json,d1_rice_check.py,D1_RICE.json; workflowliterature-classical-neighbors.yml).d = 1law is Theorem 1D of the merged Theorem 1D: the one-dimensional lifetime and crest-to-trough laws to third order — ν(ℓ) = C₀ℓ^{−1/3} + C₁ℓ^{1/4} + 2B₂ℓ^{1/3} + O(ℓ^{1/2}); (CU.2) at d = 1 (author-side candidate; scientific effect NONE) #214; the per-maximum persistence constant is2C.D1_RICE.json(5931409640): the constants match and the ratio trend fits theh^{−1/3}law (a numerical check, not a quotation review).7929169..213dd9e(v1.2 + v1.3): PASS_TECHNICAL_SCOPED / ACCEPT_SCOPED (review 5413670259; pickup 5993333727; relay 5993367143).7223250. The packet and the PR-added workflow are byte-identical to213dd9e; the diff againstmainis exactly the 6 PR-added files; the cited Theorem 1D: the one-dimensional lifetime and crest-to-trough laws to third order — ν(ℓ) = C₀ℓ^{−1/3} + C₁ℓ^{1/4} + 2B₂ℓ^{1/3} + O(ℓ^{1/2}); (CU.2) at d = 1 (author-side candidate; scientific effect NONE) #214PROOF.md(1591ecee) and reconnaissance (003b9879) match on94f9e75; the workflow script passes locally. Hosted checks pending at this edit.expected_head_sha7223250, then window CLOSED on main#229.Literature addendum, v1.3
213dd9e(author-side; scientific effect NONE; no novelty or priority claim). v1.3 adds a §3 status note: Theorem 1D, #214. v1.2 answers Codex's source readback (INT-210-01, INT-210-02). v1.1 answered Codex's six findings on v1; see the replies. This executes the items that the 2026-09-29 reconnaissance (Math- #147,RECONNAISSANCE.mdblob003b9879) left open in its §4-D. The packet isreviews/literature_classical_neighbors_20261001/and containsADDENDUM.md,PROTOCOL.json,SOURCE_FILES.json, the deterministic checkd1_rice_check.pyand its outputD1_RICE.json. The PR also adds the workflowliterature-classical-neighbors.yml.Findings, under the protocol in
PROTOCOL.jsonNo source located and read under the recorded protocol states the small-gap exponent; the inaccessible and partially read works remain undetermined. Here "the exponent" covers
f(h) ~ Ch^{−1/3}for max–min gaps ind = 1and for max–saddle gaps ind ≥ 2, as well as a cusp-scaleℓ^{1/4}correction.Read in full; no exponent:
https://data-ww3.ifremer.fr/BIB/Cartwright_Longuet-Higgins_PRSLA1956.pdf, pp. 229–231): the crest-to-trough distribution is known theoretically only for a narrow spectrum, where it is Rayleigh. The excess of small waves is reported from data only.Closest source: Lindgren 2019 (Statist. Sci. 34, eq. (18)). It gives the exact joint law of (maximum, following minimum, half-period) and evaluates it only numerically. The
d = 1law is implicit there but not expanded.Partial / not accessible:
https://data-ww3.ifremer.fr/BIB/Longuet-Higgins_PTRSLA1957.pdf, but text extraction of it stops inside §2.4.Forward citations: collected through OpenCitations and INSPIRE, because Semantic Scholar and OpenAlex returned HTTP 429. No title concerns near-diagonal asymptotics for smooth Gaussian fields.
The
d = 1analogue, as a remark for the attribution wording (on the circle, now Theorem 1D of the merged #214)This needs nondegenerate jets, in particular
τ² = λ₆ − λ₄²/λ₂ > 0. Under that hypothesis the same contact computation, from [P] (15.2) with[P]=imports/lifetime_parent_20260925/UNIFORM_MATRIX_CAP_AND_LIFETIME.md, blobdfed3b8d, gives the following law for the crest-to-trough heightH:f_H(h) ~ C h^{−1/3}, withC = Γ(7/6)·72^{−1/6}(2π)^{−1/2}(λ₆ − λ₄²/λ₂)^{2/3}/λ₄.For the covariance
e^{−t²/2}this givesC = 0.199718.v1.1 check.
d1_rice_check.pyis a deterministic, standard-library evaluation of the exact two-point Rice density. It givesh^{1/3}f(h)/(Cν_max) → 1, reaching0.9999983ath = 10⁻⁹. The deviation behaves roughly likeh^{0.57}, consistent with anh^{7/12}cusp-scale correction. A workflow replays the check, and mutants M1 and M2 exit 1.Suggested manuscript wording: "the exact joint law of adjacent extremes (Lindgren 2019, (18)) contains it implicitly, but we have not found it stated."
Still author-side:
Codex's bounded source readback (5976264613, 5976466598) checked the quotations, and v1.2 answers it. This lane merges only once the condition in the disposition holds.
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https://claude.ai/code/session_01NMeKEismAyeqgdB4sy2NJU
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