anthropics / anthropics/formal-math

Unconditional simple-on-critical-line proportion for ζ raised to 0.6728005676 (kernel-checked) — see PR #17

Ouverte
#25 0 commentaires 0 réactions 0 personnes assignées Voir sur GitHub
Langage dominant
Lean
Étoiles
239
Forks
46
Merge moyen
1 j 19 h
PR mergées (30 j)
7

Description

PR: https://github.com/anthropics/formal-math/pull/17

This work extends the `zeta23/` project beyond the paper's Montgomery–Taylor endpoint
(0.672500703679) with fully formal, unconditional improvements of the proportion of
zeta zeros that are simple and on the critical line:

| A | bound | certificate |
|---|---|---|
| 1/80 | 0.672755620655 | 2,969 kernel-replayed modules |
| 51/4000 | 0.6727837118 | 8,953 |
| 257/20000 | 0.6727949489 | 30,153 |
| **129/10000** | **0.6728005676** | 56,924 |

- Method: a positive spectral penalty from six translates of the MT kernel, fed into the
zero-count ledger; the only numerical input per target is a 5D affine inequality
`A ≤ E₆(g) + B₆·Σg`, proved by `decide +kernel` replay of an exact rational
branch-and-bound certificate over a Lean-checked envelope of the kernel.
- Also included: the `Union` (simple-or-on-line) and `LineDecimal` (certified decimal
enclosure of the MT constant) comparator topics — 24 new Mathlib-only trusted statements
in total, all in the Palomar template layout.
- Every audited declaration depends only on `propext`, `Classical.choice`, `Quot.sound`;
no `native_decide`, floating point, or external oracle. Audits, independent exact
replays and build logs are in `zeta23/AUDIT.md` and `zeta23/certificates/sextuple/`.
- The method is near its ceiling: any catalog gives at most ≈ 0.6728111 with this kernel
(analysis in `zeta23/certificates/sextuple/a1290/`).

Note: the certificate chains are ≈100k kernel modules (≈430 CPU-hours), so CI cannot
rebuild them on a hosted runner; the committed logs are the record of those builds.

Guide de contribution

Aucun guide de contribution indexé pour ce dépôt

Évaluation

Cette issue n'a pas encore été évaluée.

Recevez les nouvelles issues par e-mail

Un résumé court des issues GitHub adaptées aux débutants.