From 1f126950fc0d117fde273ea2a7870f964518bf8a Mon Sep 17 00:00:00 2001 From: Claude Date: Thu, 1 Oct 2026 02:11:42 +0000 Subject: [PATCH 1/4] Add literature addendum: classical 1-D neighbours read in full 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 Claude-Session: https://claude.ai/code/session_01NMeKEismAyeqgdB4sy2NJU --- .../ADDENDUM.md | 114 ++++++++++++++++++ .../PROTOCOL.json | 90 ++++++++++++++ .../SOURCE_FILES.json | 25 ++++ 3 files changed, 229 insertions(+) create mode 100644 reviews/literature_classical_neighbors_20261001/ADDENDUM.md create mode 100644 reviews/literature_classical_neighbors_20261001/PROTOCOL.json create mode 100644 reviews/literature_classical_neighbors_20261001/SOURCE_FILES.json diff --git a/reviews/literature_classical_neighbors_20261001/ADDENDUM.md b/reviews/literature_classical_neighbors_20261001/ADDENDUM.md new file mode 100644 index 000000000..24a583bad --- /dev/null +++ b/reviews/literature_classical_neighbors_20261001/ADDENDUM.md @@ -0,0 +1,114 @@ +# Literature addendum — the classical 1-D neighbours read in full; forward citations — 2026-10-01 + +**Object:** CL-LIT-CLASSICAL-NEIGHBORS-20261001-v1. **Author:** Anthropic Claude (claude.ai session +`session_01NMeKEismAyeqgdB4sy2NJU`; the searches and full-text reads were run by a clean-context Claude subagent of that +session, the d = 1 computation and simulation by the session). **Scientific effect:** NONE. **No priority or novelty claim +follows from this memo.** It extends CL-LIT-RECON-LIFETIME-20260929-v1.1 +(`reviews/literature_lifetime_law_recon_20260929/RECONNAISSANCE.md`, blob `003b9879`, Math- #147), executing the items its +§4-D left open: full-text reads of Rice 1944/1945 and Cartwright–Longuet-Higgins 1956, a partial read of +Longuet-Higgins 1957, the later 1-D wave-characteristic literature, and a forward-citation enumeration. Quotations are +as extracted (OCR or PDF text); verify against the printed pages before citing. + +## 1. Verdict under this protocol + +- **Same law stated elsewhere:** not found. No source located, in any year or field, states `f(h) ~ C h^{−1/3}` or + `F(h) ~ C h^{2/3}` for the gap between a maximum and the adjacent minimum of a smooth stationary Gaussian process + (`d = 1`), or for the gap between a maximum and a neighbouring saddle (`d ≥ 2`). +- **Next-order (cusp-scale, `ℓ^{1/4}`) correction:** not found anywhere. +- **Closest source:** Lindgren (2019), which prints the exact joint law of (maximum, following minimum, half-period) of a + stationary Gaussian process (eq. (18)) and evaluates it numerically. The small-amplitude law is implicit in that + formula (a small-period expansion), but the paper does not carry the expansion out (§3). +- The verdict of the 2026-09-29 memo stands and is now stronger for `d = 1`: Lindgren 1972 and Lindgren 2019 are prior art + for the **object** (the maximum-to-following-minimum amplitude), not, on the evidence read, for the **exponent**. + +"Not found" is a statement about this protocol (§5), not a proof of novelty. + +## 2. Sources read in full (`d = 1`) + +| Source | Access | Relevant content | Prior art for the exponent? | +|---|---|---|---| +| S. O. Rice, *Mathematical analysis of random noise*, Bell Syst. Tech. J. 23(3) 282–332 (1944), doi:10.1002/j.1538-7305.1944.tb00874.x; 24(1) 46–156 (1945), doi:10.1002/j.1538-7305.1945.tb00453.x | full (archive.org OCR, items `bstj23-3-282`, `bstj24-1-46`) | §3.6 (pp. 71–75) gives only the height density of a single maximum: "the probability that a maximum selected at random from the universe of maxima will lie in I, I+dI" (3.6-9). The string "minim" does not occur in either OCR text. §3.4 (pp. 57–58): "The problem of determining the distribution function for the distance between two successive zeros seems to be quite difficult and apparently nobody has as yet given a satisfactory solution" — small-spacing results there concern zeros and separations, not heights. | no | +| D. E. Cartwright, M. S. Longuet-Higgins, *The statistical distribution of the maxima of a random function*, Proc. R. Soc. Lond. A 237, 212–232 (1956), doi:10.1098/rspa.1956.0173 | full (IFREMER copy) | §8 "Crest-to-trough wave heights" (pp. 229–231): "The statistical distribution of an is more difficult to obtain theoretically than that of Xn for general values of ε." "From figure 8 it will be seen that the records with the two broad spectra deviate especially from the Rayleigh distribution for low values of the wave amplitude, having relatively more waves in that range." §9: "The theoretical distribution of crest-to-trough heights is known only for a narrow spectrum (ε = 0), when it is a Rayleigh distribution." The excess of small waves is reported from data, with no exponent. | no | +| G. Lindgren, *Gaussian integrals and Rice series in crossing distributions — to compute the distribution of maxima and other features of Gaussian processes*, Statist. Sci. 34(1) 100–128 (2019), doi:10.1214/18-STS662 | full (Project Euclid PDF) | Eq. (18): "f_T(t) × P(X^max ≤ x1, X^min ≤ x2 \| T = t) = (1/ν^max) E[1(t,x1,x2) X''(0)^− X''(t)^+ \| X'(0) = X'(t) = 0] f_{X'(0),X'(t)}(0,0)", with "1(t,x1,x2) = 1(X'(s) < 0, 0 < s < t, and X(0) ≤ x1 and X(t) ≤ x2)"; "Integrating over x1 − x2 = h one then obtains the joint amplitude, X^max − X^min = H, and period, T, distribution." Evaluated numerically (WAFO) only. | not stated (implicit, §3) | +| I. Rychlik, P. Johannesson, M. R. Leadbetter, *Modelling and statistical analysis of ocean-wave data using transformed Gaussian processes*, Marine Structures 10, 13–47 (1997), doi:10.1016/S0951-8339(96)00017-2 | full | "This departure is due to the joint density of T, H having a peak for short waves with small amplitudes (see Fig. 13b) and hence, the numerical integration can have low accuracy for small amplitudes." Qualitative only. | no | +| G. Lindgren, I. Rychlik, DTIC Technical Report 282 (1990; Int. Stat. Rev. 59, 1991) | read through text extraction, possibly truncated | "higher order approximations are smoother, in particular at the left, smaller end of the distribution." No power law. | no, as far as read | + +**Not accessible / abstracts only (not determinable):** G. Lindgren, I. Rychlik, Ocean Eng. 9(5) 411–432 (1982), +doi:10.1016/0029-8018(82)90034-8 (abstract: "…no closed form expressions are known at present"); M. S. Longuet-Higgins, +Proc. R. Soc. Lond. A 389, 241–258 (1983), doi:10.1098/rspa.1983.0107 (a narrow-band joint density, per Lindgren 2019 +§5.1); I. Rychlik, Adv. Appl. Prob. 19, 396–430 (1987), doi:10.2307/1427425; I. Rychlik, SPA 34, 313–339 (1990), +doi:10.1016/0304-4149(90)90021-J; G. Lindgren, K. B. Broberg, Extremes 7, 69–89 (2004), doi:10.1007/s10687-004-4729-3; +L. D. Lutes, Prob. Eng. Mech. 23, 254–266 (2008), doi:10.1016/j.probengmech.2007.12.008. None of these abstracts mentions +small amplitudes. OpenCitations lists 37, 65, 23, 10 and 3 citing works for Lindgren 1972, Lindgren–Rychlik 1982, +Rychlik 1987, Lindgren–Broberg 2004 and Lutes 2008; no title suggests a small-amplitude asymptotic. + +## 3. The `d = 1` analogue, made explicit (a remark for the attribution wording; not a theorem of this repository) + +The contact computation behind [P] (15.2) does not use `d ≥ 2` except through the transverse block, which is empty in +`d = 1` (cone moment `D_0 = 1`). Carried out for a stationary Gaussian process with spectral moments `λ₂, λ₄, λ₆` it gives, +for the crest-to-trough amplitude `H` (a maximum to the following minimum) under the Palm distribution of maxima, + + f_H(h) ~ C h^{−1/3}, P(H ≤ h) ~ (3/2) C h^{2/3} (h ↓ 0), + C = Γ(7/6) · 72^{−1/6} (2π)^{−1/2} · (λ₆ − λ₄²/λ₂)^{2/3} / λ₄, + +i.e. `C = 0.199718…` for the covariance `e^{−t²/2}` (`λ₂ = 1`, `λ₄ = 3`, `λ₆ = 15`). (Derivation: in the separation variable, +`c_d = Γ(7/6)72^{−1/6}(2π)^{−1/2}∫_{S^{d−1}} p_G(0)p_{V_u}(0)τ_u^{4/3}D_u dσ(u)` with `G = f'`, `V_u = f''`, +`τ² = Var(f''' | f' = 0)`, `D_0 = 1`; `S⁰` has two points, one for each orientation, and "following minimum" keeps one of +them; dividing by the intensity of maxima `(2π)^{−1}(λ₄/λ₂)^{1/2}` gives `C`. The formula is invariant under time +rescaling and scales as `σ^{−2/3}` under `f ↦ σf`, as it must.) In `d = 1` a fold pair sits on a monotone slope, so the +neighbour beyond the minimum is higher than the small maximum: to leading order the pair is an elder pair, and the same +constant should govern the elder (persistence) lifetimes in `d = 1` (not proved here). + +**Exploration (outside this repository's stdlib rule; not part of the packet).** A circulant-embedding simulation of the +process with covariance `e^{−t²/2}` (numpy; grid step `0.004`, `5.5·10⁵` maxima, parabolic refinement of extreme values) +gives `P(H ≤ h)/((3/2)Ch^{2/3}) = 0.992, 0.984, 0.988, 0.985, 1.009, 1.001` at `h = 10⁻⁴, 3·10⁻⁴, 10⁻³, 3·10⁻³, 10⁻², 3·10⁻²` +(counts `355` to `16053`; one-sigma sampling errors `5%` to `0.8%`) and `1.033` at `h = 0.1`, where the next-order terms +enter. With grid step `0.01` the smallest-`h` ratios fall to `0.94`–`0.97`: missed sub-grid pairs, removed by the finer +grid. + +So the exponent is implicit in exact classical formulas (Lindgren 2019, (18)), but on the evidence read it is not stated +in print. **Suggested manuscript wording:** *"In dimension one the same contact computation gives the small-amplitude +law of crest-to-trough heights, `f_H(h) ~ Ch^{−1/3}` with an explicit `C`; the exact joint law of adjacent extremes +(Lindgren 2019, (18)) contains it implicitly, but we have not found it stated."* + +## 4. `d ≥ 2` and next-order terms + +- M. S. Longuet-Higgins, *The statistical analysis of a random, moving surface*, Phil. Trans. R. Soc. Lond. A 249, 321–387 + (1957), doi:10.1098/rsta.1957.0002 — **partial** (the extraction stopped inside §2.4, about p. 348; §2.9 "The heights of + maxima" was not read). §2.4: "On a statistically uniform surface the average density of maxima per unit area plus the + average density of minima is equal to the average density of saddle-points". Nothing about height differences between + neighbouring critical points in the part read; the abstract's item (8) concerns narrow spectra ("when the spectrum is + narrow, the probability distribution of the heights of maxima and minima…"). Not determinable for §2.9. +- Cadiou et al., arXiv:2003.04413 — "critical events" (pairs whose persistence vanishes as the smoothing scale changes): + a different object (a one-parameter family, not gaps in a fixed field). Sousbie, arXiv:1009.4015, and Pranav, + arXiv:2109.08721 — numerical persistence statistics. Ladgham–Lachièze-Rey arXiv:2209.04150, Beliaev–Cammarota–Wigman, + Azaïs–Delmas — short-distance correlations of critical-point **positions**, no height-gap law (abstracts). +- **Cusp-scale correction:** not found. "Cusp" occurs only for unrelated objects (cusp caustics, arXiv:2405.20475; cusps + of Gaussian maps to the plane, arXiv:2202.08242). Feng–Götze–Yao, arXiv:2607.19660 (smallest gaps between zeros), never + mentions critical points or heights. + +## 5. Forward citations (cited-by enumeration of the 2026-09-29 neighbours) + +Semantic Scholar and OpenAlex were rate-limited (HTTP 429 throughout, 01:34–01:52 UTC); zbMATH `ci:` queries returned no +citing documents. OpenCitations v2 (DOI-indexed, so it misses most arXiv-only papers) and INSPIRE (for 1908.01619) gave: +1802.10457 — 17; 1911.03455 — 5; 1911.02300 — 7; 1908.01619 — 52 (OpenCitations) / 50 (INSPIRE); 2012.09459 — 2; +1706.06059 — 34 citing records (some preprint/journal duplicates). No title concerns short-bar or near-diagonal +asymptotics for smooth Gaussian fields. Nearest: Baryshnikov, arXiv:1909.09846 (JACT 2025; Brownian motion with drift, +not smooth: "near the diagonal the density explodes as 1/m(d−b)^3"); arXiv:2407.07326 (LLN/CLT for discrete-time +sequences); arXiv:2601.06009 (`ε^{−2}` excursion law for semimartingales); arXiv:2507.06255 (Betti-number and +Euler-characteristic statistics); arXiv:2009.04819 (numerical). + +## 6. Status of the 2026-09-29 memo's open items + +- §4-D: Rice and Cartwright–Longuet-Higgins **done** (no); Longuet-Higgins 1957 **partial** (§2.9 unread); Lindgren–Rychlik + 1982 and Longuet-Higgins 1983 **inaccessible here** (paywalled; author-side). Divol–Polonik and the 2024–2026 LLN/CLT + line: only 2407.07326 surfaced, no near-diagonal rate. +- Cited-by: **executed through OpenCitations/INSPIRE** (§5); a Google-Scholar-level enumeration remains author-side. +- §4-E (MathSciNet/zbMATH paywalled queries): **not run** (zbMATH Open `ci:` only, empty). Unchanged. + +## 7. Protocol + +Queries (WebSearch, verbatim) and Consensus searches are listed in `PROTOCOL.json`, with the APIs used and the +exclusions (`github.com/d6g8k5htny-coder` and mirrors: the project is search-indexed). Caveats: keyword search is not a +citation crawl; quotations are from OCR/PDF text extraction; the `d = 1` constant of §3 is a computation recorded for +the attribution wording, not a reviewed theorem, and its simulation used numpy outside this repository. diff --git a/reviews/literature_classical_neighbors_20261001/PROTOCOL.json b/reviews/literature_classical_neighbors_20261001/PROTOCOL.json new file mode 100644 index 000000000..2c420fc5e --- /dev/null +++ b/reviews/literature_classical_neighbors_20261001/PROTOCOL.json @@ -0,0 +1,90 @@ +{ + "object": "CL-LIT-CLASSICAL-NEIGHBORS-20261001-v1", + "extends": { + "object": "CL-LIT-RECON-LIFETIME-20260929-v1.1", + "path": "reviews/literature_lifetime_law_recon_20260929/RECONNAISSANCE.md", + "git_blob": "003b98794f02fd5c1cd45ed263bf2818b556e6ab" + }, + "coverage_target": "through 2026-10-01", + "exclusions": [ + "github.com/d6g8k5htny-coder", + "mirrors of the project's own repositories" + ], + "executed_by": "clean-context Anthropic Claude subagent of session_01NMeKEismAyeqgdB4sy2NJU, 2026-10-01 ~01:00-01:55 UTC", + "websearch_queries": [ + "Rice 1944 \"Mathematical analysis of random noise\" Bell System Technical Journal pdf archive.org", + "Cartwright Longuet-Higgins 1956 \"The statistical distribution of the maxima of a random function\" Proc. R. Soc. A 237", + "Longuet-Higgins 1957 \"The statistical analysis of a random, moving surface\" Phil. Trans. R. Soc. A 249", + "Longuet-Higgins 1983 \"On the joint distribution of wave periods and amplitudes in a random wave field\" pdf", + "rainflow counting persistent homology equivalence local maxima minima pairing persistence diagram", + "Gaussian process crest-trough amplitude density \"small amplitudes\" singular at zero exponent \"-1/3\"", + "Lindgren Rychlik \"Wave characteristic distributions for Gaussian waves\" Lund University report pdf", + "rainflow cycle range distribution smooth Gaussian process small ranges density behaviour near zero", + "\"persistence diagram\" \"Gaussian random field\" short bars \"2/3\" OR \"-1/3\" lifetime density small persistence exponent", + "Cadiou Pichon Codis \"When do cosmic peaks, filaments or walls merge\" critical events Gaussian random field", + "Lindgren Broberg 2004 \"Cycle range distributions for Gaussian processes\" Extremes pdf", + "persistence diagram random function near-degenerate critical points cusp singularity correction small persistence asymptotic expansion", + "\"wave amplitude\" OR \"crest-to-trough\" distribution Gaussian process \"density\" \"infinite at the origin\" OR \"tends to infinity\" small waves broad spectrum", + "expected persistence diagram smooth stationary Gaussian process one dimension near the diagonal density maxima minima pairs", + "smallest gaps between zeros of stationary Gaussian processes Feng Yao critical points closest pairs", + "Adler Bobrowski Borman Subag Weinberger \"Persistent homology for random fields and complexes\" Gaussian persistence diagram", + "Lindgren \"Lectures on Stationary Stochastic Processes\" pdf wave amplitude wavelength Slepian model", + "WAFO tutorial pdf \"min-to-max\" OR \"max-to-min\" density wave characteristics Brodtkorb Rychlik Lindgren", + "\"cusp\" catastrophe statistics Gaussian random function pair of critical points small height difference fold \"separation cubed\" OR \"fourth power\"", + "distribution of barrier heights between adjacent minima smooth Gaussian random potential small barriers power law exponent", + "number of persistence bars of length at most epsilon \"epsilon^{2/3}\" OR \"ε^{2/3}\" smooth random function Morse", + "\"statistical analysis of a random, moving surface\" Longuet-Higgins pdf \"heights of maxima\" narrow spectrum", + "Sousbie 2011 persistent cosmic web DisPerSE persistence ratio distribution Gaussian random field critical point pairs low persistence", + "\"persistence diagram\" Gaussian field \"near the diagonal\" second-order expansion correction \"birth-death\" fold cusp random Morse function", + "crest trough small waves \"riding waves\" density amplitude near zero Gaussian broad-band spectrum theoretical asymptotic Lindgren Rychlik exact" + ], + "consensus_queries": [ + "crest-to-trough amplitude distribution small amplitudes Gaussian process", + "joint density of adjacent maximum and minimum heights stationary Gaussian process", + "persistence diagram smooth Gaussian random field short bars near diagonal asymptotics (rate-limited, no result)", + "density of low persistence pairs near diagonal persistence diagram smooth Gaussian random field asymptotic", + "Rychlik regression approximations of wavelength and amplitude distributions", + "distribution of height difference between neighbouring local maximum and saddle point Gaussian random surface", + "Rychlik new bounds for the first passage, wave-length and amplitude densities" + ], + "apis": [ + "arXiv export", + "Crossref", + "OpenCitations v2", + "INSPIRE (refersto:recid:1747978)", + "Semantic Scholar (HTTP 429, unreachable)", + "OpenAlex (HTTP 429, unreachable)", + "zbMATH Open ci: (no citing documents returned)", + "archive.org advancedsearch" + ], + "full_text_read": [ + "Rice 1944/1945 (archive.org OCR)", + "Cartwright & Longuet-Higgins 1956 (IFREMER copy)", + "Lindgren 2019 Statist. Sci. (Project Euclid)", + "Rychlik, Johannesson & Leadbetter 1997 (university copy)", + "Lindgren & Rychlik DTIC TR 282 (text extraction, possibly truncated)" + ], + "partial": [ + "Longuet-Higgins 1957 (to section 2.4; section 2.9 unread)" + ], + "not_accessible": [ + "Lindgren & Rychlik 1982 Ocean Eng.", + "Longuet-Higgins 1983 Proc. R. Soc. A", + "Rychlik 1987", + "Rychlik 1990", + "Lindgren & Broberg 2004", + "Lutes 2008" + ], + "still_author_side": [ + "MathSciNet and zbMATH paywalled queries of the 2026-09-29 memo section 4-E", + "Google-Scholar-level cited-by enumeration", + "Longuet-Higgins 1957 section 2.9, Lindgren-Rychlik 1982, Longuet-Higgins 1983 full texts" + ], + "d1_remark": { + "formula": "f_H(h) ~ C h^(-1/3), C = Gamma(7/6) 72^(-1/6) (2 pi)^(-1/2) (lambda6 - lambda4^2/lambda2)^(2/3) / lambda4", + "value_gaussian_covariance": "0.199718", + "status": "computation recorded for the attribution wording; not a reviewed theorem; simulation (numpy) outside the repository's stdlib rule and not part of this packet" + }, + "verdict": "no source states the small-gap exponent -1/3 (d = 1 or d >= 2) or a cusp-scale correction; Lindgren 2019 eq. (18) contains the d = 1 law implicitly (not expanded there)", + "scientific_effect": "NONE" +} diff --git a/reviews/literature_classical_neighbors_20261001/SOURCE_FILES.json b/reviews/literature_classical_neighbors_20261001/SOURCE_FILES.json new file mode 100644 index 000000000..1a0213a9b --- /dev/null +++ b/reviews/literature_classical_neighbors_20261001/SOURCE_FILES.json @@ -0,0 +1,25 @@ +{ + "author": "Anthropic Claude", + "delivered_under": "standing owner instruction (Dylan Roy, claude.ai session); OWNER_STOP left in place; no self-merge", + "extends": { + "git_blob": "003b98794f02fd5c1cd45ed263bf2818b556e6ab", + "path": "reviews/literature_lifetime_law_recon_20260929/RECONNAISSANCE.md" + }, + "files": [ + { + "bytes": 12221, + "path": "ADDENDUM.md", + "sha256": "04f746bb03bc24728bf8359b11d44938b194d8578ba4b6707a01a4aa72dcf181" + }, + { + "bytes": 5974, + "path": "PROTOCOL.json", + "sha256": "01098fae556fb908d09a63ea8f8263aa760d24be0944b2c75b981913125e5c0e" + } + ], + "kind": "literature addendum (prose + machine-readable protocol); no checker", + "novelty_claim": false, + "object": "CL-LIT-CLASSICAL-NEIGHBORS-20261001-v1", + "scientific_effect": "NONE", + "session": "https://claude.ai/code/session_01NMeKEismAyeqgdB4sy2NJU" +} From 792916912796874c7113258aceffc26ab965de5b Mon Sep 17 00:00:00 2001 From: Claude Date: Thu, 1 Oct 2026 03:14:38 +0000 Subject: [PATCH 2/4] Literature addendum v1.1: deterministic d = 1 Rice check; Codex fixes 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 Claude-Session: https://claude.ai/code/session_01NMeKEismAyeqgdB4sy2NJU --- .../literature-classical-neighbors.yml | 59 ++++++ .../ADDENDUM.md | 52 +++-- .../D1_RICE.json | 36 ++++ .../PROTOCOL.json | 11 +- .../SOURCE_FILES.json | 31 ++- .../d1_rice_check.py | 187 ++++++++++++++++++ 6 files changed, 345 insertions(+), 31 deletions(-) create mode 100644 .github/workflows/literature-classical-neighbors.yml create mode 100644 reviews/literature_classical_neighbors_20261001/D1_RICE.json create mode 100644 reviews/literature_classical_neighbors_20261001/d1_rice_check.py diff --git a/.github/workflows/literature-classical-neighbors.yml b/.github/workflows/literature-classical-neighbors.yml new file mode 100644 index 000000000..2b2fd99ea --- /dev/null +++ b/.github/workflows/literature-classical-neighbors.yml @@ -0,0 +1,59 @@ +name: Literature addendum d = 1 Rice check + +'on': + pull_request: + paths: + - 'reviews/literature_classical_neighbors_20261001/**' + - '.github/workflows/literature-classical-neighbors.yml' + workflow_dispatch: + +permissions: + contents: read + +jobs: + exact-controls: + runs-on: ubuntu-latest + timeout-minutes: 10 + steps: + - uses: actions/checkout@11d5960a326750d5838078e36cf38b85af677262 + with: + persist-credentials: false + - uses: actions/setup-python@a26af69be951a213d495a4c3e4e4022e16d87065 + with: + python-version: '3.11.16' + - name: Verify packet, replay both modes, reject mutants + env: + PYTHONDONTWRITEBYTECODE: '1' + run: | + set -euo pipefail + python -B -S - <<'PY' + import hashlib, json, pathlib, subprocess, sys + root = pathlib.Path('reviews/literature_classical_neighbors_20261001').resolve() + manifest = json.loads((root / 'SOURCE_FILES.json').read_text()) + present = sorted(p.name for p in root.iterdir()) + expected_names = sorted([e['path'] for e in manifest['files']] + ['SOURCE_FILES.json']) + if present != expected_names: + raise ValueError('packet tree differs from manifest: ' + repr(present)) + for entry in manifest['files']: + path = root / entry['path'] + if path.is_symlink(): + raise ValueError('symlink: ' + entry['path']) + data = path.read_bytes() + if len(data) != entry['bytes'] or hashlib.sha256(data).hexdigest() != entry['sha256']: + raise ValueError('packet file identity mismatch: ' + entry['path']) + script = str(root / 'd1_rice_check.py') + expected = (root / 'D1_RICE.json').read_bytes() + for flags in (['-B', '-S'], ['-B', '-O', '-S']): + out = subprocess.run([sys.executable, *flags, script], check=True, capture_output=True, timeout=600).stdout + if out != expected: + raise RuntimeError('output differs from D1_RICE.json under ' + ' '.join(flags)) + for m in manifest['mutants']: + rc = subprocess.run([sys.executable, *flags, script, '--mutant', m], capture_output=True, timeout=600).returncode + if rc != 1: + raise RuntimeError('mutant ' + m + ' not rejected') + rc = subprocess.run([sys.executable, *flags, script, '--mutant', 'M9'], capture_output=True, timeout=600).returncode + if rc != 2: + raise RuntimeError('unknown mutant label not rejected with exit 2') + print(json.dumps({'scientific_effect': 'NONE', 'mathematical_acceptance': False})) + PY + git diff --exit-code diff --git a/reviews/literature_classical_neighbors_20261001/ADDENDUM.md b/reviews/literature_classical_neighbors_20261001/ADDENDUM.md index 24a583bad..fc0a84dcf 100644 --- a/reviews/literature_classical_neighbors_20261001/ADDENDUM.md +++ b/reviews/literature_classical_neighbors_20261001/ADDENDUM.md @@ -1,8 +1,8 @@ # Literature addendum — the classical 1-D neighbours read in full; forward citations — 2026-10-01 -**Object:** CL-LIT-CLASSICAL-NEIGHBORS-20261001-v1. **Author:** Anthropic Claude (claude.ai session +**Object:** CL-LIT-CLASSICAL-NEIGHBORS-20261001-v1.1 (v1 → v1.1 after Codex review of v1, comments 4151188790–4151188834: hypotheses for the `d = 1` law; the `[P]` source identified; the machine-readable verdict qualified; the provenance made exact; the NumPy simulation replaced by a deterministic standard-library Rice check, `d1_rice_check.py`). **Author:** Anthropic Claude (claude.ai session `session_01NMeKEismAyeqgdB4sy2NJU`; the searches and full-text reads were run by a clean-context Claude subagent of that -session, the d = 1 computation and simulation by the session). **Scientific effect:** NONE. **No priority or novelty claim +session, the d = 1 computation and its deterministic check by the session). **Scientific effect:** NONE. **No priority or novelty claim follows from this memo.** It extends CL-LIT-RECON-LIFETIME-20260929-v1.1 (`reviews/literature_lifetime_law_recon_20260929/RECONNAISSANCE.md`, blob `003b9879`, Math- #147), executing the items its §4-D left open: full-text reads of Rice 1944/1945 and Cartwright–Longuet-Higgins 1956, a partial read of @@ -44,27 +44,39 @@ Rychlik 1987, Lindgren–Broberg 2004 and Lutes 2008; no title suggests a small- ## 3. The `d = 1` analogue, made explicit (a remark for the attribution wording; not a theorem of this repository) -The contact computation behind [P] (15.2) does not use `d ≥ 2` except through the transverse block, which is empty in -`d = 1` (cone moment `D_0 = 1`). Carried out for a stationary Gaussian process with spectral moments `λ₂, λ₄, λ₆` it gives, -for the crest-to-trough amplitude `H` (a maximum to the following minimum) under the Palm distribution of maxima, +**Source.** The contact computation of the parent `[P]` = `imports/lifetime_parent_20260925/UNIFORM_MATRIX_CAP_AND_LIFETIME.md` +(blob `dfed3b8d`), (15.2), uses `d ≥ 2` only through the transverse block. That block is empty in `d = 1` (cone moment +`D_0 = 1`). + +**Hypotheses.** A stationary Gaussian process with `C⁴` paths whose jets `(X', X'', X''')` at a point are jointly +nondegenerate. In particular `τ² := λ₆ − λ₄²/λ₂ > 0`; this excludes spectral measures carried by at most two points such as +`A cos t + B sin t`, for which `H = 2√(A² + B²)` has no `h^{−1/3}` law. Carried out under these hypotheses, the computation +gives, for the crest-to-trough amplitude `H` (a maximum to the following minimum) under the Palm distribution of maxima, f_H(h) ~ C h^{−1/3}, P(H ≤ h) ~ (3/2) C h^{2/3} (h ↓ 0), C = Γ(7/6) · 72^{−1/6} (2π)^{−1/2} · (λ₆ − λ₄²/λ₂)^{2/3} / λ₄, -i.e. `C = 0.199718…` for the covariance `e^{−t²/2}` (`λ₂ = 1`, `λ₄ = 3`, `λ₆ = 15`). (Derivation: in the separation variable, -`c_d = Γ(7/6)72^{−1/6}(2π)^{−1/2}∫_{S^{d−1}} p_G(0)p_{V_u}(0)τ_u^{4/3}D_u dσ(u)` with `G = f'`, `V_u = f''`, -`τ² = Var(f''' | f' = 0)`, `D_0 = 1`; `S⁰` has two points, one for each orientation, and "following minimum" keeps one of -them; dividing by the intensity of maxima `(2π)^{−1}(λ₄/λ₂)^{1/2}` gives `C`. The formula is invariant under time -rescaling and scales as `σ^{−2/3}` under `f ↦ σf`, as it must.) In `d = 1` a fold pair sits on a monotone slope, so the -neighbour beyond the minimum is higher than the small maximum: to leading order the pair is an elder pair, and the same -constant should govern the elder (persistence) lifetimes in `d = 1` (not proved here). - -**Exploration (outside this repository's stdlib rule; not part of the packet).** A circulant-embedding simulation of the -process with covariance `e^{−t²/2}` (numpy; grid step `0.004`, `5.5·10⁵` maxima, parabolic refinement of extreme values) -gives `P(H ≤ h)/((3/2)Ch^{2/3}) = 0.992, 0.984, 0.988, 0.985, 1.009, 1.001` at `h = 10⁻⁴, 3·10⁻⁴, 10⁻³, 3·10⁻³, 10⁻², 3·10⁻²` -(counts `355` to `16053`; one-sigma sampling errors `5%` to `0.8%`) and `1.033` at `h = 0.1`, where the next-order terms -enter. With grid step `0.01` the smallest-`h` ratios fall to `0.94`–`0.97`: missed sub-grid pairs, removed by the finer -grid. +i.e. `C = 0.199718…` for the covariance `e^{−t²/2}` (`λ₂ = 1`, `λ₄ = 3`, `λ₆ = 15`). + +**Derivation.** In the separation variable, +`c_d = Γ(7/6)72^{−1/6}(2π)^{−1/2}∫_{S^{d−1}} p_G(0)p_{V_u}(0)τ_u^{4/3}D_u dσ(u)`, with `G = f'`, `V_u = f''` and +`τ² = Var(f''' | f' = 0)`. Here `S⁰` has two points, one for each orientation, and "following minimum" keeps one of them. +Dividing by the intensity of maxima, `(2π)^{−1}(λ₄/λ₂)^{1/2}`, gives `C`. The formula is invariant under time rescaling +and scales as `σ^{−2/3}` under `f ↦ σf`. In `d = 1` a fold pair sits on a monotone slope, so the neighbour beyond the +minimum is higher than the small maximum. To leading order the pair is an elder pair, and the same constant should +govern the elder (persistence) lifetimes in `d = 1` (not proved here). + +**Deterministic check (standard library; `d1_rice_check.py`, output `D1_RICE.json`).** For `e^{−t²/2}`, the two-point +Rice density of (maximum at `0`, minimum at `t`) with `X(0) − X(t) = h` is evaluated exactly in distribution: +- no sampling; +- rescaled rows, Decimal arithmetic for the covariance algebra; +- one-dimensional quadratures. + +It is then integrated over separations `t ≤ 1.5`. `h^{1/3}f(h)/(Cν_max)` equals `1.0048, 0.9971, 0.9984, 0.99941, 0.99982, +0.999951, 0.999989, 0.9999983, 1.0000003` at `h = 10⁻², …, 10⁻¹⁰`. The deviation shrinks by a factor of about `3.3–4.4` +per decade, i.e. roughly as `h^{0.57}`, consistent with a relative correction of order `h^{7/12}` (the cusp scale). +This checks the constant's arithmetic through the exact two-point Rice formula. It is not an independent proof of the +law, since intermediate extrema are not excluded, which affects only the regular part. So the exponent is implicit in exact classical formulas (Lindgren 2019, (18)), but on the evidence read it is not stated in print. **Suggested manuscript wording:** *"In dimension one the same contact computation gives the small-amplitude @@ -111,4 +123,4 @@ Euler-characteristic statistics); arXiv:2009.04819 (numerical). Queries (WebSearch, verbatim) and Consensus searches are listed in `PROTOCOL.json`, with the APIs used and the exclusions (`github.com/d6g8k5htny-coder` and mirrors: the project is search-indexed). Caveats: keyword search is not a citation crawl; quotations are from OCR/PDF text extraction; the `d = 1` constant of §3 is a computation recorded for -the attribution wording, not a reviewed theorem, and its simulation used numpy outside this repository. +the attribution wording, not a reviewed theorem, checked deterministically by `d1_rice_check.py`. diff --git a/reviews/literature_classical_neighbors_20261001/D1_RICE.json b/reviews/literature_classical_neighbors_20261001/D1_RICE.json new file mode 100644 index 000000000..9ec189aee --- /dev/null +++ b/reviews/literature_classical_neighbors_20261001/D1_RICE.json @@ -0,0 +1,36 @@ +{ + "checks": { + "R1_spectral_moments": { + "info": { + "lambda2": "1", + "lambda4": "3", + "lambda6": "15", + "tau2": "6" + }, + "passed": true + }, + "R2_two_point_rice_ratio": { + "info": { + "C": 0.199718135, + "C_nu_max": 0.0550551895, + "nu_max": 0.275664448, + "ratio_h^(1/3)f(h)/(C nu_max)": { + "1e-10": 1.0000003, + "1e-2": 1.0047933, + "1e-3": 0.9970508, + "1e-4": 0.9983637, + "1e-5": 0.999405, + "1e-6": 0.9998175, + "1e-7": 0.9999508, + "1e-8": 0.9999888, + "1e-9": 0.9999983 + } + }, + "passed": true + } + }, + "mutant": null, + "object": "CL-LIT-CLASSICAL-NEIGHBORS-20261001-v1.1 d1 Rice check", + "passed": true, + "scientific_effect": "NONE" +} diff --git a/reviews/literature_classical_neighbors_20261001/PROTOCOL.json b/reviews/literature_classical_neighbors_20261001/PROTOCOL.json index 2c420fc5e..9413b001c 100644 --- a/reviews/literature_classical_neighbors_20261001/PROTOCOL.json +++ b/reviews/literature_classical_neighbors_20261001/PROTOCOL.json @@ -1,5 +1,5 @@ { - "object": "CL-LIT-CLASSICAL-NEIGHBORS-20261001-v1", + "object": "CL-LIT-CLASSICAL-NEIGHBORS-20261001-v1.1", "extends": { "object": "CL-LIT-RECON-LIFETIME-20260929-v1.1", "path": "reviews/literature_lifetime_law_recon_20260929/RECONNAISSANCE.md", @@ -82,9 +82,12 @@ ], "d1_remark": { "formula": "f_H(h) ~ C h^(-1/3), C = Gamma(7/6) 72^(-1/6) (2 pi)^(-1/2) (lambda6 - lambda4^2/lambda2)^(2/3) / lambda4", - "value_gaussian_covariance": "0.199718", - "status": "computation recorded for the attribution wording; not a reviewed theorem; simulation (numpy) outside the repository's stdlib rule and not part of this packet" + "hypotheses": "stationary Gaussian process with C^4 paths and jointly nondegenerate jets (X', X'', X'''), in particular tau^2 = lambda6 - lambda4^2/lambda2 > 0", + "source": "imports/lifetime_parent_20260925/UNIFORM_MATRIX_CAP_AND_LIFETIME.md (git blob dfed3b8d318a3ab1950957f393307733a4bef3f2), (15.2), specialized to d = 1", + "value_gaussian_covariance": "0.199718135", + "check": "d1_rice_check.py (stdlib, deterministic two-point Rice evaluation; D1_RICE.json): h^(1/3) f(h)/(C nu_max) -> 1 (0.9999983 at h = 1e-9)", + "status": "computation recorded for the attribution wording; not a reviewed theorem" }, - "verdict": "no source states the small-gap exponent -1/3 (d = 1 or d >= 2) or a cusp-scale correction; Lindgren 2019 eq. (18) contains the d = 1 law implicitly (not expanded there)", + "verdict": "no source located under this protocol states the small-gap exponent -1/3 (d = 1 or d >= 2) or a cusp-scale correction; Lindgren 2019 eq. (18) contains the d = 1 law implicitly (not expanded there); six works were inaccessible and three full-text/search tasks remain author-side (see not_accessible and still_author_side), so this is not a proof of novelty", "scientific_effect": "NONE" } diff --git a/reviews/literature_classical_neighbors_20261001/SOURCE_FILES.json b/reviews/literature_classical_neighbors_20261001/SOURCE_FILES.json index 1a0213a9b..842ef5c6d 100644 --- a/reviews/literature_classical_neighbors_20261001/SOURCE_FILES.json +++ b/reviews/literature_classical_neighbors_20261001/SOURCE_FILES.json @@ -1,25 +1,42 @@ { "author": "Anthropic Claude", - "delivered_under": "standing owner instruction (Dylan Roy, claude.ai session); OWNER_STOP left in place; no self-merge", + "delivered_under": "explicit owner instructions of Dylan Roy in claude.ai session session_01NMeKEismAyeqgdB4sy2NJU, given after OWNER_STOP (2026-09-27): 2026-09-30 \"Continue to Work on closing as many mathematical items as possible while working with and supporting the other models in the GitHub\" and the same session's \"Continue\" (2026-09-30 18:02 local), with the standing statement \"Any request or permissions are preapproved in advance by me Dylan Roy\" and the push authorization \"PRs only, never self-merge\"; OWNER_STOP.md (addressed to Cursor agents) left untouched; no self-merge", "extends": { "git_blob": "003b98794f02fd5c1cd45ed263bf2818b556e6ab", "path": "reviews/literature_lifetime_law_recon_20260929/RECONNAISSANCE.md" }, "files": [ { - "bytes": 12221, + "bytes": 13195, "path": "ADDENDUM.md", - "sha256": "04f746bb03bc24728bf8359b11d44938b194d8578ba4b6707a01a4aa72dcf181" + "sha256": "f185d70d1e7f289163fd85a99bb9518da7cc3ead5da39db99e570ecde8b4f88e" }, { - "bytes": 5974, + "bytes": 6559, "path": "PROTOCOL.json", - "sha256": "01098fae556fb908d09a63ea8f8263aa760d24be0944b2c75b981913125e5c0e" + "sha256": "891a437c03afbe95bbb2c8d276a48ce39f459d04ec777931a8ec80bca28ac338" + }, + { + "bytes": 7618, + "path": "d1_rice_check.py", + "sha256": "e263adb339883d81d811ea73f391ffb2cd5320c3cd76a044f4d3e3ccbff50d6c" + }, + { + "bytes": 709, + "path": "D1_RICE.json", + "sha256": "ec4d1fefc92b43db567779d49c464169132505f04b2f96f82776a320667c2443" } ], - "kind": "literature addendum (prose + machine-readable protocol); no checker", + "kind": "literature addendum (prose + machine-readable protocol) with one deterministic stdlib check (d1_rice_check.py)", + "mutants": [ + "M1", + "M2" + ], "novelty_claim": false, - "object": "CL-LIT-CLASSICAL-NEIGHBORS-20261001-v1", + "object": "CL-LIT-CLASSICAL-NEIGHBORS-20261001-v1.1", + "replayed": [ + "d1_rice_check.py" + ], "scientific_effect": "NONE", "session": "https://claude.ai/code/session_01NMeKEismAyeqgdB4sy2NJU" } diff --git a/reviews/literature_classical_neighbors_20261001/d1_rice_check.py b/reviews/literature_classical_neighbors_20261001/d1_rice_check.py new file mode 100644 index 000000000..68958e338 --- /dev/null +++ b/reviews/literature_classical_neighbors_20261001/d1_rice_check.py @@ -0,0 +1,187 @@ +#!/usr/bin/env python3 +"""Deterministic check of the d = 1 small-amplitude constant of ADDENDUM.md section 3 (CL-LIT-CLASSICAL-NEIGHBORS-20261001-v1.1). +Standard library only (Decimal for the covariance algebra, floating point for the final one-dimensional integrals). + +For the stationary Gaussian process with covariance r(t) = exp(-t^2/2) (lambda2 = 1, lambda4 = 3, lambda6 = 15), the +intensity per unit length of pairs (maximum at 0, minimum at t > 0) with X(0) - X(t) in dh is the two-point Rice density + + g(t, h) = p_{X'(0), X'(t), X(0)-X(t)}(0, 0, h) E[ X''(0)^- X''(t)^+ | X'(0) = X'(t) = 0, X(0) - X(t) = h ]. + +It is evaluated exactly in distribution (no sampling) in the rescaled rows U1 = (X'(0)+X'(t))/2, U2 = (X'(t)-X'(0))/t, +U3 = (6/t^2)[X'(0)+X'(t)+2(X(0)-X(t))/t] (Jacobian 12/t^4, and U3 = 12h/t^3 on the event), with the bivariate +expectation reduced to one Gauss-Legendre integral. With f(h) = int_0^{1.5} g(t, h) dt, the prediction of section 3 is + + h^(1/3) f(h) -> C nu_max, C = Gamma(7/6) 72^(-1/6) (2 pi)^(-1/2) (lambda6 - lambda4^2/lambda2)^(2/3) / lambda4, + nu_max = (2 pi)^(-1) (lambda4/lambda2)^(1/2) (h -> 0). + + R1 the spectral moments of r and tau^2 = lambda6 - lambda4^2/lambda2 = 6, exactly (rationals); + R2 h^(1/3) f(h) / (C nu_max) at h = 10^-2 ... 10^-10: within 5e-5 of 1 for h <= 1e-8, and the deviation shrinks + monotonically over h <= 1e-3 (it is consistent with a relative correction of order h^(7/12)); + M mutants (--mutant M1|M2) exit 1: M1 uses tau^2 = 5 in the prediction, M2 drops the factor 12 of the Jacobian; + an unknown label exits 2. + Scope: a check of the constant's arithmetic through the exact two-point Rice formula (pairs at separations up to + 1.5, intermediate extrema not excluded, which affects only the regular part). It is not a proof of the d = 1 law. +""" +import argparse +import json +import math +import sys +from decimal import Decimal as D, getcontext +from fractions import Fraction as F + +getcontext().prec = 50 + + +def He_dec(n, t): + if n == 0: + return D(1) + h0, h1 = D(1), t + for k in range(1, n): + h0, h1 = h1, t * h1 - k * h0 + return h1 + + +def rder(n, t): + return (-1) ** n * He_dec(n, t) * (-(t * t) / 2).exp() + + +def cov_pt(i, si, j, sj): + return (-1) ** j * rder(i + j, si - sj) + + +def solve(M, b): + n = len(M) + A = [M[i][:] + [b[i]] for i in range(n)] + for i in range(n): + p = max(range(i, n), key=lambda r: abs(A[r][i])) + A[i], A[p] = A[p], A[i] + for r in range(n): + if r != i: + f = A[r][i] / A[i][i] + A[r] = [x - f * y for x, y in zip(A[r], A[i])] + return [A[i][n] / A[i][i] for i in range(n)] + + +def det3(M): + return (M[0][0] * (M[1][1] * M[2][2] - M[1][2] * M[2][1]) - M[0][1] * (M[1][0] * M[2][2] - M[1][2] * M[2][0]) + + M[0][2] * (M[1][0] * M[2][1] - M[1][1] * M[2][0])) + + +def gauss_legendre(n): + xs, ws = [], [] + for i in range(1, n + 1): + x = math.cos(math.pi * (i - 0.25) / (n + 0.5)) + for _ in range(100): + p0, p1 = 1.0, x + for k in range(2, n + 1): + p0, p1 = p1, ((2 * k - 1) * x * p1 - (k - 1) * p0) / k + dp = n * (x * p1 - p0) / (x * x - 1) + dx = p1 / dp + x -= dx + if abs(dx) < 1e-16: + break + xs.append(x) + ws.append(2 / ((1 - x * x) * dp * dp)) + return xs, ws + + +GLX, GLW = gauss_legendre(64) +KX, KW = gauss_legendre(96) + + +def Phi(x): + return 0.5 * math.erfc(-x / math.sqrt(2)) + + +def phi(x): + return math.exp(-x * x / 2) / math.sqrt(2 * math.pi) + + +def E_negpos(m1, m2, S11, S12, S22): + """E[(-T1)^+ (T2)^+] for (T1, T2) ~ N((m1, m2), [[S11, S12], [S12, S22]]).""" + mx, sx = -m1, math.sqrt(S11) + beta = -S12 / S11 + s = math.sqrt(max(S22 - S12 * S12 / S11, 1e-300)) + hi = mx + 12 * sx + if hi <= 0: + return 0.0 + lo = max(0.0, mx - 12 * sx) + tot = 0.0 + for x, w in zip(GLX, GLW): + xx = lo + (hi - lo) * (x + 1) / 2 + my = m2 + beta * (xx - mx) + tot += w * (hi - lo) / 2 * xx * phi((xx - mx) / sx) / sx * (my * Phi(my / s) + s * phi(my / s)) + return tot + + +def g(t, h, jac): + t, h, z = D(repr(t)), D(repr(h)), D(0) + pts = [(0, z), (1, z), (2, z), (0, t), (1, t), (2, t)] + C = [[cov_pt(i, si, j, sj) for (j, sj) in pts] for (i, si) in pts] + U = [[z, D('0.5'), z, z, D('0.5'), z], [z, -1 / t, z, z, 1 / t, z], + [12 / t ** 3, 6 / t ** 2, z, -12 / t ** 3, 6 / t ** 2, z]] + T1 = [z, z, D(1), z, z, z] + T2 = [z, z, z, z, z, D(1)] + + def cv(a, b): + return sum(a[i] * C[i][j] * b[j] for i in range(6) for j in range(6)) + CUU = [[cv(a, b) for b in U] for a in U] + u = [z, z, 12 * h / t ** 3] + x = solve(CUU, u) + y1 = solve(CUU, [cv(T1, a) for a in U]) + y2 = solve(CUU, [cv(T2, a) for a in U]) + m1 = sum(cv(T1, U[k]) * x[k] for k in range(3)) + m2 = sum(cv(T2, U[k]) * x[k] for k in range(3)) + S11 = cv(T1, T1) - sum(cv(T1, U[k]) * y1[k] for k in range(3)) + S22 = cv(T2, T2) - sum(cv(T2, U[k]) * y2[k] for k in range(3)) + S12 = cv(T1, T2) - sum(cv(T1, U[k]) * y2[k] for k in range(3)) + q = sum(u[k] * x[k] for k in range(3)) + pU = math.exp(-float(q) / 2) / math.sqrt((2 * math.pi) ** 3 * float(det3(CUU))) + return pU * jac / float(t) ** 4 * E_negpos(float(m1), float(m2), float(S11), float(S12), float(S22)) + + +def f(h, jac, t0=1.5): + a, b = math.log(h / t0 ** 3), math.log(4.0) + tot = 0.0 + for x, w in zip(KX, KW): + k = math.exp(a + (b - a) * (x + 1) / 2) + t = (h / k) ** (1 / 3) + tot += w * (b - a) / 2 * k * (1 / 3) * h ** (1 / 3) * k ** (-4 / 3) * g(t, h, jac) + return tot + + +def main(): + ap = argparse.ArgumentParser() + ap.add_argument('--mutant', default=None) + args = ap.parse_args() + if args.mutant is not None and args.mutant not in ('M1', 'M2'): + sys.stderr.write('unknown mutant label\n') + return 2 + # R1: spectral moments of exp(-t^2/2) and tau^2, exactly: lambda_{2j} = (2j-1)!! + lam = {2 * j: F(math.prod(range(1, 2 * j, 2))) for j in (1, 2, 3)} + tau2 = lam[6] - lam[4] ** 2 / lam[2] + r1 = lam[2] == 1 and lam[4] == 3 and lam[6] == 15 and tau2 == 6 + tau2_used = 5.0 if args.mutant == 'M1' else float(tau2) + C = math.gamma(7 / 6) * 72 ** (-1 / 6) * (2 * math.pi) ** -0.5 * tau2_used ** (2 / 3) / float(lam[4]) + numax = math.sqrt(float(lam[4]) / float(lam[2])) / (2 * math.pi) + pred = C * numax + jac = 1.0 if args.mutant == 'M2' else 12.0 + ratios = {} + for e in range(2, 11): + h = 10.0 ** (-e) + ratios[e] = h ** (1 / 3) * f(h, jac) / pred + small = all(abs(ratios[e] - 1) <= 5e-5 for e in (8, 9, 10)) + mono = all(abs(ratios[e + 1] - 1) < abs(ratios[e] - 1) for e in range(3, 9)) + r2 = small and mono + out = {'object': 'CL-LIT-CLASSICAL-NEIGHBORS-20261001-v1.1 d1 Rice check', 'scientific_effect': 'NONE', + 'mutant': args.mutant, 'passed': bool(r1 and r2), + 'checks': {'R1_spectral_moments': {'passed': r1, 'info': {'lambda2': '1', 'lambda4': '3', 'lambda6': '15', 'tau2': str(tau2)}}, + 'R2_two_point_rice_ratio': {'passed': r2, 'info': { + 'C': float('%.9g' % C), 'nu_max': float('%.9g' % numax), 'C_nu_max': float('%.9g' % pred), + 'ratio_h^(1/3)f(h)/(C nu_max)': {('1e-%d' % e): float('%.7f' % ratios[e]) for e in ratios}}}}} + sys.stdout.write(json.dumps(out, indent=1, sort_keys=True) + '\n') + return 0 if out['passed'] else 1 + + +if __name__ == '__main__': + sys.exit(main()) From 37e5adc3cd2647d14b6b353637686be91416add6 Mon Sep 17 00:00:00 2001 From: Claude Date: Sun, 4 Oct 2026 04:43:40 +0000 Subject: [PATCH 3/4] Literature addendum v1.2: name the copies read (Codex INT-210-01/02) 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 Claude-Session: https://claude.ai/code/session_01NMeKEismAyeqgdB4sy2NJU --- .../ADDENDUM.md | 9 ++++--- .../PROTOCOL.json | 27 ++++++++++++++++--- .../SOURCE_FILES.json | 13 ++++----- 3 files changed, 36 insertions(+), 13 deletions(-) diff --git a/reviews/literature_classical_neighbors_20261001/ADDENDUM.md b/reviews/literature_classical_neighbors_20261001/ADDENDUM.md index fc0a84dcf..6c42b8a6b 100644 --- a/reviews/literature_classical_neighbors_20261001/ADDENDUM.md +++ b/reviews/literature_classical_neighbors_20261001/ADDENDUM.md @@ -1,6 +1,6 @@ # Literature addendum — the classical 1-D neighbours read in full; forward citations — 2026-10-01 -**Object:** CL-LIT-CLASSICAL-NEIGHBORS-20261001-v1.1 (v1 → v1.1 after Codex review of v1, comments 4151188790–4151188834: hypotheses for the `d = 1` law; the `[P]` source identified; the machine-readable verdict qualified; the provenance made exact; the NumPy simulation replaced by a deterministic standard-library Rice check, `d1_rice_check.py`). **Author:** Anthropic Claude (claude.ai session +**Object:** CL-LIT-CLASSICAL-NEIGHBORS-20261001-v1.2 (v1.1 → v1.2, 4 October 2026, after Codex's bounded source readback 5976264613, AMEND INT-210-01 and INT-210-02, and its follow-up 5976466598: the copy of Cartwright–Longuet-Higgins 1956 is named, with the printed page of each quotation, and so is a copy of Longuet-Higgins 1957; the verdict sentence of the PR body is bounded to the protocol; nothing else changes. v1 → v1.1 after Codex review of v1, comments 4151188790–4151188834: hypotheses for the `d = 1` law; the `[P]` source identified; the machine-readable verdict qualified; the provenance made exact; the NumPy simulation replaced by a deterministic standard-library Rice check, `d1_rice_check.py`). **Author:** Anthropic Claude (claude.ai session `session_01NMeKEismAyeqgdB4sy2NJU`; the searches and full-text reads were run by a clean-context Claude subagent of that session, the d = 1 computation and its deterministic check by the session). **Scientific effect:** NONE. **No priority or novelty claim follows from this memo.** It extends CL-LIT-RECON-LIFETIME-20260929-v1.1 @@ -28,7 +28,7 @@ as extracted (OCR or PDF text); verify against the printed pages before citing. | Source | Access | Relevant content | Prior art for the exponent? | |---|---|---|---| | S. O. Rice, *Mathematical analysis of random noise*, Bell Syst. Tech. J. 23(3) 282–332 (1944), doi:10.1002/j.1538-7305.1944.tb00874.x; 24(1) 46–156 (1945), doi:10.1002/j.1538-7305.1945.tb00453.x | full (archive.org OCR, items `bstj23-3-282`, `bstj24-1-46`) | §3.6 (pp. 71–75) gives only the height density of a single maximum: "the probability that a maximum selected at random from the universe of maxima will lie in I, I+dI" (3.6-9). The string "minim" does not occur in either OCR text. §3.4 (pp. 57–58): "The problem of determining the distribution function for the distance between two successive zeros seems to be quite difficult and apparently nobody has as yet given a satisfactory solution" — small-spacing results there concern zeros and separations, not heights. | no | -| D. E. Cartwright, M. S. Longuet-Higgins, *The statistical distribution of the maxima of a random function*, Proc. R. Soc. Lond. A 237, 212–232 (1956), doi:10.1098/rspa.1956.0173 | full (IFREMER copy) | §8 "Crest-to-trough wave heights" (pp. 229–231): "The statistical distribution of an is more difficult to obtain theoretically than that of Xn for general values of ε." "From figure 8 it will be seen that the records with the two broad spectra deviate especially from the Rayleigh distribution for low values of the wave amplitude, having relatively more waves in that range." §9: "The theoretical distribution of crest-to-trough heights is known only for a narrow spectrum (ε = 0), when it is a Rayleigh distribution." The excess of small waves is reported from data, with no exponent. | no | +| D. E. Cartwright, M. S. Longuet-Higgins, *The statistical distribution of the maxima of a random function*, Proc. R. Soc. Lond. A 237, 212–232 (1956), doi:10.1098/rspa.1956.0173 | full (IFREMER copy, `https://data-ww3.ifremer.fr/BIB/Cartwright_Longuet-Higgins_PRSLA1956.pdf`; v1.2 names it and re-checked the three quotations there through text extraction) | §8 "Crest-to-trough wave heights" (pp. 229–231): "The statistical distribution of an is more difficult to obtain theoretically than that of Xn for general values of ε." (p. 229) "From figure 8 it will be seen that the records with the two broad spectra deviate especially from the Rayleigh distribution for low values of the wave amplitude, having relatively more waves in that range." (p. 230) §9 "Conclusions" (p. 231): "The theoretical distribution of crest-to-trough heights is known only for a narrow spectrum (ε = 0), when it is a Rayleigh distribution." The excess of small waves is reported from data, with no exponent. | no | | G. Lindgren, *Gaussian integrals and Rice series in crossing distributions — to compute the distribution of maxima and other features of Gaussian processes*, Statist. Sci. 34(1) 100–128 (2019), doi:10.1214/18-STS662 | full (Project Euclid PDF) | Eq. (18): "f_T(t) × P(X^max ≤ x1, X^min ≤ x2 \| T = t) = (1/ν^max) E[1(t,x1,x2) X''(0)^− X''(t)^+ \| X'(0) = X'(t) = 0] f_{X'(0),X'(t)}(0,0)", with "1(t,x1,x2) = 1(X'(s) < 0, 0 < s < t, and X(0) ≤ x1 and X(t) ≤ x2)"; "Integrating over x1 − x2 = h one then obtains the joint amplitude, X^max − X^min = H, and period, T, distribution." Evaluated numerically (WAFO) only. | not stated (implicit, §3) | | I. Rychlik, P. Johannesson, M. R. Leadbetter, *Modelling and statistical analysis of ocean-wave data using transformed Gaussian processes*, Marine Structures 10, 13–47 (1997), doi:10.1016/S0951-8339(96)00017-2 | full | "This departure is due to the joint density of T, H having a peak for short waves with small amplitudes (see Fig. 13b) and hence, the numerical integration can have low accuracy for small amplitudes." Qualitative only. | no | | G. Lindgren, I. Rychlik, DTIC Technical Report 282 (1990; Int. Stat. Rev. 59, 1991) | read through text extraction, possibly truncated | "higher order approximations are smoother, in particular at the left, smaller end of the distribution." No power law. | no, as far as read | @@ -87,7 +87,10 @@ law of crest-to-trough heights, `f_H(h) ~ Ch^{−1/3}` with an explicit `C`; the - M. S. Longuet-Higgins, *The statistical analysis of a random, moving surface*, Phil. Trans. R. Soc. Lond. A 249, 321–387 (1957), doi:10.1098/rsta.1957.0002 — **partial** (the extraction stopped inside §2.4, about p. 348; §2.9 "The heights of - maxima" was not read). §2.4: "On a statistically uniform surface the average density of maxima per unit area plus the + maxima" was not read; v1.2: an IFREMER copy is at + `https://data-ww3.ifremer.fr/BIB/Longuet-Higgins_PTRSLA1957.pdf`, and a re-read of it through text + extraction on 4 October again stopped inside §2.4). + §2.4: "On a statistically uniform surface the average density of maxima per unit area plus the average density of minima is equal to the average density of saddle-points". Nothing about height differences between neighbouring critical points in the part read; the abstract's item (8) concerns narrow spectra ("when the spectrum is narrow, the probability distribution of the heights of maxima and minima…"). Not determinable for §2.9. diff --git a/reviews/literature_classical_neighbors_20261001/PROTOCOL.json b/reviews/literature_classical_neighbors_20261001/PROTOCOL.json index 9413b001c..71fbff93b 100644 --- a/reviews/literature_classical_neighbors_20261001/PROTOCOL.json +++ b/reviews/literature_classical_neighbors_20261001/PROTOCOL.json @@ -1,5 +1,5 @@ { - "object": "CL-LIT-CLASSICAL-NEIGHBORS-20261001-v1.1", + "object": "CL-LIT-CLASSICAL-NEIGHBORS-20261001-v1.2", "extends": { "object": "CL-LIT-RECON-LIFETIME-20260929-v1.1", "path": "reviews/literature_lifetime_law_recon_20260929/RECONNAISSANCE.md", @@ -59,13 +59,13 @@ ], "full_text_read": [ "Rice 1944/1945 (archive.org OCR)", - "Cartwright & Longuet-Higgins 1956 (IFREMER copy)", + "Cartwright & Longuet-Higgins 1956 (IFREMER copy https://data-ww3.ifremer.fr/BIB/Cartwright_Longuet-Higgins_PRSLA1956.pdf; v1.2 re-checked the three quotations, through text extraction, at printed pp. 229, 230 and 231)", "Lindgren 2019 Statist. Sci. (Project Euclid)", "Rychlik, Johannesson & Leadbetter 1997 (university copy)", "Lindgren & Rychlik DTIC TR 282 (text extraction, possibly truncated)" ], "partial": [ - "Longuet-Higgins 1957 (to section 2.4; section 2.9 unread)" + "Longuet-Higgins 1957 (to section 2.4; section 2.9 unread; an IFREMER copy is at https://data-ww3.ifremer.fr/BIB/Longuet-Higgins_PTRSLA1957.pdf, and a v1.2 re-read of it through text extraction again stopped inside section 2.4)" ], "not_accessible": [ "Lindgren & Rychlik 1982 Ocean Eng.", @@ -89,5 +89,24 @@ "status": "computation recorded for the attribution wording; not a reviewed theorem" }, "verdict": "no source located under this protocol states the small-gap exponent -1/3 (d = 1 or d >= 2) or a cusp-scale correction; Lindgren 2019 eq. (18) contains the d = 1 law implicitly (not expanded there); six works were inaccessible and three full-text/search tasks remain author-side (see not_accessible and still_author_side), so this is not a proof of novelty", - "scientific_effect": "NONE" + "scientific_effect": "NONE", + "v1_2": { + "after": "Codex bounded source readback 5976264613 (AMEND INT-210-01, INT-210-02) and follow-up 5976466598", + "changes": [ + "ADDENDUM section 2: the IFREMER copy of Cartwright & Longuet-Higgins 1956 is named, with printed pages 229, 230 and 231 for its three quotations (INT-210-02)", + "ADDENDUM section 4: an IFREMER copy of Longuet-Higgins 1957 is named; section 2.9 is still unread", + "PR body: the verdict sentence is bounded to the recorded protocol, and the Rice check reads \"downloaded OCR text\" (INT-210-01)" + ], + "independent_reads": [ + "Codex 5976264613: printed pages of Rice 1945 (sections 3.4, 3.6), Lindgren 2019 p. 119 eq. (18), Rychlik-Johannesson-Leadbetter 1997 p. 33, Lindgren-Rychlik TR 282 p. 31", + "Codex 5976466598: Cartwright & Longuet-Higgins 1956 sections 8-9 through the OCR transcript https://www.scribd.com/document/146911494/The-Statistical-Distribution-of-the-Maxima-of-a-Random-Function-by-Cartwright-and-Longuet-Higgins" + ], + "unchanged": [ + "the verdict", + "the d = 1 remark", + "d1_rice_check.py", + "D1_RICE.json", + "the workflow" + ] + } } diff --git a/reviews/literature_classical_neighbors_20261001/SOURCE_FILES.json b/reviews/literature_classical_neighbors_20261001/SOURCE_FILES.json index 842ef5c6d..51fe27d16 100644 --- a/reviews/literature_classical_neighbors_20261001/SOURCE_FILES.json +++ b/reviews/literature_classical_neighbors_20261001/SOURCE_FILES.json @@ -7,14 +7,14 @@ }, "files": [ { - "bytes": 13195, + "bytes": 13947, "path": "ADDENDUM.md", - "sha256": "f185d70d1e7f289163fd85a99bb9518da7cc3ead5da39db99e570ecde8b4f88e" + "sha256": "bbe1cec152580d4be926a0405aa9e90df075749b31bed48742e9ce316dffa046" }, { - "bytes": 6559, + "bytes": 8010, "path": "PROTOCOL.json", - "sha256": "891a437c03afbe95bbb2c8d276a48ce39f459d04ec777931a8ec80bca28ac338" + "sha256": "d21356f5c6a7c5717e821885bb49e2d3d7e4732ab5e3f357a42b4545a6e6044b" }, { "bytes": 7618, @@ -33,10 +33,11 @@ "M2" ], "novelty_claim": false, - "object": "CL-LIT-CLASSICAL-NEIGHBORS-20261001-v1.1", + "object": "CL-LIT-CLASSICAL-NEIGHBORS-20261001-v1.2", "replayed": [ "d1_rice_check.py" ], "scientific_effect": "NONE", - "session": "https://claude.ai/code/session_01NMeKEismAyeqgdB4sy2NJU" + "session": "https://claude.ai/code/session_01NMeKEismAyeqgdB4sy2NJU", + "v1_2_delivered_under": "Dylan Roy's standing instructions in session_01NMeKEismAyeqgdB4sy2NJU and his 2026-10-04 02:46 UTC instruction \"Merge if it's had a review and it will benefit the project\"; v1.2 answers Codex 5976264613 (INT-210-01, INT-210-02) and 5976466598" } From 213dd9eb8ba83de242516b10c999fbe56d17fd3f Mon Sep 17 00:00:00 2001 From: Claude Date: Sun, 4 Oct 2026 05:29:36 +0000 Subject: [PATCH 4/4] Literature addendum v1.3: section 3 status note (Theorem 1D, Math-#214) 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 1591ecee, 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 Claude-Session: https://claude.ai/code/session_01NMeKEismAyeqgdB4sy2NJU --- .../ADDENDUM.md | 27 +++++++++++++++++-- .../PROTOCOL.json | 16 +++++++++-- .../SOURCE_FILES.json | 19 +++++++++---- 3 files changed, 53 insertions(+), 9 deletions(-) diff --git a/reviews/literature_classical_neighbors_20261001/ADDENDUM.md b/reviews/literature_classical_neighbors_20261001/ADDENDUM.md index 6c42b8a6b..b289c7cd4 100644 --- a/reviews/literature_classical_neighbors_20261001/ADDENDUM.md +++ b/reviews/literature_classical_neighbors_20261001/ADDENDUM.md @@ -1,6 +1,6 @@ # Literature addendum — the classical 1-D neighbours read in full; forward citations — 2026-10-01 -**Object:** CL-LIT-CLASSICAL-NEIGHBORS-20261001-v1.2 (v1.1 → v1.2, 4 October 2026, after Codex's bounded source readback 5976264613, AMEND INT-210-01 and INT-210-02, and its follow-up 5976466598: the copy of Cartwright–Longuet-Higgins 1956 is named, with the printed page of each quotation, and so is a copy of Longuet-Higgins 1957; the verdict sentence of the PR body is bounded to the protocol; nothing else changes. v1 → v1.1 after Codex review of v1, comments 4151188790–4151188834: hypotheses for the `d = 1` law; the `[P]` source identified; the machine-readable verdict qualified; the provenance made exact; the NumPy simulation replaced by a deterministic standard-library Rice check, `d1_rice_check.py`). **Author:** Anthropic Claude (claude.ai session +**Object:** CL-LIT-CLASSICAL-NEIGHBORS-20261001-v1.3 (v1.2 → v1.3, 4 October 2026, a status note in §3: on the circle the `d = 1` law is now Theorem 1D of the merged Math-#214, whose proof also settles the check's regular-part assertion, and the persistence density's per-maximum constant is `2C`. v1.1 → v1.2, 4 October 2026, after Codex's bounded source readback 5976264613, AMEND INT-210-01 and INT-210-02, and its follow-up 5976466598: the copy of Cartwright–Longuet-Higgins 1956 is named, with the printed page of each quotation, and so is a copy of Longuet-Higgins 1957; the verdict sentence of the PR body is bounded to the protocol; nothing else changes. v1 → v1.1 after Codex review of v1, comments 4151188790–4151188834: hypotheses for the `d = 1` law; the `[P]` source identified; the machine-readable verdict qualified; the provenance made exact; the NumPy simulation replaced by a deterministic standard-library Rice check, `d1_rice_check.py`). **Author:** Anthropic Claude (claude.ai session `session_01NMeKEismAyeqgdB4sy2NJU`; the searches and full-text reads were run by a clean-context Claude subagent of that session, the d = 1 computation and its deterministic check by the session). **Scientific effect:** NONE. **No priority or novelty claim follows from this memo.** It extends CL-LIT-RECON-LIFETIME-20260929-v1.1 @@ -42,7 +42,7 @@ L. D. Lutes, Prob. Eng. Mech. 23, 254–266 (2008), doi:10.1016/j.probengmech.20 small amplitudes. OpenCitations lists 37, 65, 23, 10 and 3 citing works for Lindgren 1972, Lindgren–Rychlik 1982, Rychlik 1987, Lindgren–Broberg 2004 and Lutes 2008; no title suggests a small-amplitude asymptotic. -## 3. The `d = 1` analogue, made explicit (a remark for the attribution wording; not a theorem of this repository) +## 3. The `d = 1` analogue, made explicit (a remark for the attribution wording; on the circle, now Theorem 1D of Math-#214) **Source.** The contact computation of the parent `[P]` = `imports/lifetime_parent_20260925/UNIFORM_MATRIX_CAP_AND_LIFETIME.md` (blob `dfed3b8d`), (15.2), uses `d ≥ 2` only through the transverse block. That block is empty in `d = 1` (cone moment @@ -78,6 +78,29 @@ per decade, i.e. roughly as `h^{0.57}`, consistent with a relative correction of This checks the constant's arithmetic through the exact two-point Rice formula. It is not an independent proof of the law, since intermediate extrema are not excluded, which affects only the regular part. +**Status (v1.3, 4 October 2026).** On the circle `R/LZ`, under #214's hypothesis (H) (`ρ ∈ C^∞`, every Fourier +coefficient positive), this law is now a theorem of the repository. It is Theorem 1D of Math-#214 +(`frontiers/d1_third_order_law_20261001/PROOF.md`, blob `1591ecee`, merged at `e4ca2b3`), an author-side proof +candidate with OpenAI ACCEPT on all slices and a Grok Bot PASS. Per unit length it gives: +- the crest-to-trough density: `ν₊(h) = (C₀/2)h^{−1/3} + (I/2)h^{1/4} + B₂h^{1/3} + O(h^{1/2})`; +- the persistence lifetimes: `ν(ℓ) = C₀ℓ^{−1/3} + C₁ℓ^{1/4} + 2B₂ℓ^{1/3} + O(ℓ^{1/2})`. + +Per crest, #214 §0 gives `f_H(h) = 0.19971814h^{−1/3} − …` for the Gaussian kernel. That is the constant `C` above. + +Two readings follow. +- **The per-maximum constant.** The persistence density counts a fold pair in either orientation, so per maximum its + leading constant is `2C`. The sentence above, "the same constant should govern the elder (persistence) lifetimes", + holds per orientation. +- **The regular-part assertion** (Codex's scope limit, 5976264613) is part of #214's proof on the circle. + - On `(0, t_*]`, non-adjacency forces `K₅ ≥ ct^{−δ}` (Lemma 3.1), an `O(h^N)` event (§5). + - On `[t_*, t₀]`, the sign kernel `K₁^{sign}`, which is the check's integrand without the adjacency mark, is bounded. + This follows from Lemma 1.3: `G₁ ≤ m² + v₂`, with `(12/t⁴)m² ≍ α²/τ² ≤ C` and `(12/t⁴)v₂ = O(τ²)`. + - So the non-adjacent pairs add `O(1)`, a regular part that does not touch the `h^{−1/3}` constant the check tests. + #214 §6.2 sees the same `O(1)` numerically as the `rh^{−1/4}` term of `dev/h^{7/12}`. + - The check's covariance `e^{−t²/2}` lives on the line. #214 §6.4 claims nothing there, but its near-pair argument is + local, and it applies to the check's finite range `t ≤ 1.5` given the jet nondegeneracy of #214 Lemma 1.1. That + extension is author-side and is not claimed by #214. + So the exponent is implicit in exact classical formulas (Lindgren 2019, (18)), but on the evidence read it is not stated in print. **Suggested manuscript wording:** *"In dimension one the same contact computation gives the small-amplitude law of crest-to-trough heights, `f_H(h) ~ Ch^{−1/3}` with an explicit `C`; the exact joint law of adjacent extremes diff --git a/reviews/literature_classical_neighbors_20261001/PROTOCOL.json b/reviews/literature_classical_neighbors_20261001/PROTOCOL.json index 71fbff93b..6772ad061 100644 --- a/reviews/literature_classical_neighbors_20261001/PROTOCOL.json +++ b/reviews/literature_classical_neighbors_20261001/PROTOCOL.json @@ -1,5 +1,5 @@ { - "object": "CL-LIT-CLASSICAL-NEIGHBORS-20261001-v1.2", + "object": "CL-LIT-CLASSICAL-NEIGHBORS-20261001-v1.3", "extends": { "object": "CL-LIT-RECON-LIFETIME-20260929-v1.1", "path": "reviews/literature_lifetime_law_recon_20260929/RECONNAISSANCE.md", @@ -86,7 +86,7 @@ "source": "imports/lifetime_parent_20260925/UNIFORM_MATRIX_CAP_AND_LIFETIME.md (git blob dfed3b8d318a3ab1950957f393307733a4bef3f2), (15.2), specialized to d = 1", "value_gaussian_covariance": "0.199718135", "check": "d1_rice_check.py (stdlib, deterministic two-point Rice evaluation; D1_RICE.json): h^(1/3) f(h)/(C nu_max) -> 1 (0.9999983 at h = 1e-9)", - "status": "computation recorded for the attribution wording; not a reviewed theorem" + "status": "computation recorded for the attribution wording; v1.3: on the circle under (H) the law is Theorem 1D of the merged Math-#214 (PROOF.md blob 1591ecee, merge e4ca2b3; OpenAI ACCEPT all slices + Grok Bot PASS), with two further terms; per maximum the persistence density leading constant is 2C; the line is not covered by #214" }, "verdict": "no source located under this protocol states the small-gap exponent -1/3 (d = 1 or d >= 2) or a cusp-scale correction; Lindgren 2019 eq. (18) contains the d = 1 law implicitly (not expanded there); six works were inaccessible and three full-text/search tasks remain author-side (see not_accessible and still_author_side), so this is not a proof of novelty", "scientific_effect": "NONE", @@ -108,5 +108,17 @@ "D1_RICE.json", "the workflow" ] + }, + "v1_3": { + "change": "ADDENDUM section 3: title and a status paragraph; no change to the verdict, the d = 1 computation, the check or its output", + "cited_merged": { + "path": "frontiers/d1_third_order_law_20261001/PROOF.md", + "git_blob": "1591ecee3c82c8b42cb3220189ea0a4ce4bf195f", + "sha256": "a1b5e6ecc97341ad72d74973c69c0f94304b22c559ab0187310ef2bd73455804", + "bytes": 46313, + "merged_at": "e4ca2b3 (Math-#214)", + "used": "Theorem 1D (1D.1)-(1D.2); section 0 constants; Lemma 1.3; Lemma 3.1; section 5; Remarks 6.2 and 6.4" + }, + "regular_part_assertion": "on the circle: part of #214 proof (Lemma 3.1 on (0, t_*], bounded sign kernel on [t_*, t0] from Lemma 1.3); for the check covariance on the line: the same local argument, author-side" } } diff --git a/reviews/literature_classical_neighbors_20261001/SOURCE_FILES.json b/reviews/literature_classical_neighbors_20261001/SOURCE_FILES.json index 51fe27d16..9dc1f4a65 100644 --- a/reviews/literature_classical_neighbors_20261001/SOURCE_FILES.json +++ b/reviews/literature_classical_neighbors_20261001/SOURCE_FILES.json @@ -1,5 +1,14 @@ { "author": "Anthropic Claude", + "cited_merged": [ + { + "bytes": 46313, + "git_blob": "1591ecee3c82c8b42cb3220189ea0a4ce4bf195f", + "path": "frontiers/d1_third_order_law_20261001/PROOF.md", + "role": "Theorem 1D (Math-#214, merged e4ca2b3), cited in ADDENDUM section 3 (v1.3)", + "sha256": "a1b5e6ecc97341ad72d74973c69c0f94304b22c559ab0187310ef2bd73455804" + } + ], "delivered_under": "explicit owner instructions of Dylan Roy in claude.ai session session_01NMeKEismAyeqgdB4sy2NJU, given after OWNER_STOP (2026-09-27): 2026-09-30 \"Continue to Work on closing as many mathematical items as possible while working with and supporting the other models in the GitHub\" and the same session's \"Continue\" (2026-09-30 18:02 local), with the standing statement \"Any request or permissions are preapproved in advance by me Dylan Roy\" and the push authorization \"PRs only, never self-merge\"; OWNER_STOP.md (addressed to Cursor agents) left untouched; no self-merge", "extends": { "git_blob": "003b98794f02fd5c1cd45ed263bf2818b556e6ab", @@ -7,14 +16,14 @@ }, "files": [ { - "bytes": 13947, + "bytes": 16207, "path": "ADDENDUM.md", - "sha256": "bbe1cec152580d4be926a0405aa9e90df075749b31bed48742e9ce316dffa046" + "sha256": "5e3903ad05b0566a1e999b0e69b309a4165578705d687f4a3021d22ebd1e1e42" }, { - "bytes": 8010, + "bytes": 9025, "path": "PROTOCOL.json", - "sha256": "d21356f5c6a7c5717e821885bb49e2d3d7e4732ab5e3f357a42b4545a6e6044b" + "sha256": "a265bb4718e830f088811633883591d0ba9c9fb5c1b4730ba4d5c1b6580dbc27" }, { "bytes": 7618, @@ -33,7 +42,7 @@ "M2" ], "novelty_claim": false, - "object": "CL-LIT-CLASSICAL-NEIGHBORS-20261001-v1.2", + "object": "CL-LIT-CLASSICAL-NEIGHBORS-20261001-v1.3", "replayed": [ "d1_rice_check.py" ],