diff --git a/docs/RECON_NOVELTY_20260925.md b/docs/RECON_NOVELTY_20260925.md index 569fb1e36..5550d371a 100644 --- a/docs/RECON_NOVELTY_20260925.md +++ b/docs/RECON_NOVELTY_20260925.md @@ -13,3 +13,15 @@ Exact searches did not locate the P15 sharp factor 1/[3-log(3e-2)] in a matching This is a bounded web/arXiv/publisher reconnaissance, not a worldwide novelty certificate. Require a second independent literature audit before public "first" language. **Addendum 2026-09-27.** The nonauthor challenge requested in PR #114 located prior art the scoped search missed: Beliaev–Cammarota–Wigman (arXiv:1704.04943) and Azaïs–Delmas (arXiv:1911.02300) for the close-pair critical-point intensity; the fold normal form for the cubic gap; Chazal–Divol (arXiv:1802.10457) for near-diagonal density of expected diagrams; Bobrowski–Skraba (arXiv:2207.03926, arXiv:2406.05553) for random-persistence universality; and, for P15, Talagrand (STOC 2010) and Frankston–Kahn–Narayanan–Park (Ann. Math. 2021) alongside the two references already in the proof. The ledger records the narrowed deltas. Safe public wording, if DP-01's premise is later accepted, is "we derive …; to our knowledge …", never "first". + +## Addendum 2026-10-14 — distinguish universality statements + +The preceding paragraphs preserve the September 25/27 search record, not a current theorem-status inventory. + +[Heo, arXiv:2610.08257v1](https://arxiv.org/html/2610.08257v1), submitted 6 October 2026, is a preprint reporting different centered persistence-ratio limit laws for independent uniform samples in dimensions two and three, with the Čech filtration and homological degree one fixed (Theorem 1.1). It also excludes the proposed left-skewed Gumbel family (Corollary 1.4). These are attributed preprint results, not an independent verification of the complete proof here. + +[Bobrowski–Skraba, arXiv:2406.05553v3](https://arxiv.org/html/2406.05553v3), Section 2.2 and Theorems 3.1–3.2, concern a different universality statement: at fixed dimension, positive homological degree and filtration, the ratio limit is independent of the sampling density under their stated density and death-radius cutoff hypotheses. It may still depend on those fixed indices. A strong law of large numbers is not the stronger common-law conjecture across dimensions. + +Neither result directly proves or refutes the project's additive Gaussian H0 lifetime law. Point sampling and smooth random-field filtrations, ratio and additive-gap observables, and H1 and H0 must not be conflated. A common leading exponent does not establish a common full distribution. Keep the novelty comparison specific to the declared Gaussian H0 exponent, coefficient and elder-selection control; do not broaden it to all analytic near-diagonal persistence asymptotics. + +The [scoped reconnaissance report](https://github.com/d6g8k5htny-coder/main/issues/275#issuecomment-6177725462) records the primary sections inspected and coverage limits. This addendum is source-exposed OpenAI / GPT-6 Astra Pro literature maintenance, not a fresh worldwide-priority certificate or independent-human review. Scientific effect: NONE; the priority ledger, historical review states and theorem-acceptance predicates are unchanged.