Pith Number

pith:2NBNCJJL

pith:2026:2NBNCJJLWSPHTEBN5IPQIMASNO

not attested not anchored not stored refs pending

Potential Hessian Ascent III: Sampling the Sherrington--Kirkpatrick Model at Beta < 1/2

Ewan Davies, Holden Lee, Jonathan Shi, Juspreet Singh Sandhu

Polynomial-time algorithm samples the Sherrington-Kirkpatrick Gibbs measure with negligible TVD error for all β < 1/2.

arxiv:2605.03718 v2 · 2026-05-05 · math.PR · cs.DS · math-ph · math.MP

Open paper page JSON Open Graph Bundle Merged state Verified badge What is a Pith Number?

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{2NBNCJJLWSPHTEBN5IPQIMASNO}

Prints a linked badge after your title and injects PDF metadata. Compiles on arXiv. Learn more · Embed verified badge

Record completeness

1 Bitcoin timestamp

2 Internet Archive

3 Author claim open · sign in to claim

4 Citations open

5 Replications open

✓ Portable graph bundle live · download bundle · merged state

The bundle contains the canonical record plus signed events. A mirror can host it anywhere and recompute the same current state with the deterministic merge algorithm.

Claims

C1strongest claim

We give a polynomial-time algorithm to sample from the Gibbs measure of the Sherrington--Kirkpatrick model with negligible total-variation distance (TVD) error up to inverse temperature β < 1/2.

C2weakest assumption

The restricted log-Sobolev inequality holds on the time-T localized distribution and the free-probability argument controlling the diagonal sub-algebra of the Hessian yields an O(1) KL bound for the finite-time Hessian-ascent process at all β < 1/2.

C3one line summary

A polynomial-time algorithm samples the SK model Gibbs measure with o(1) TVD error for β < 1/2 by combining potential Hessian ascent, stochastic localization, Jarzynski equality, and Glauber dynamics.

Receipt and verification

First computed	2026-05-20T02:05:44.253416Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

d342d1252bb49e79902dea1f0430126bb9edf14fb52bd7fdf915e7366c291764

Aliases

arxiv: 2605.03718 · arxiv_version: 2605.03718v2 · doi: 10.48550/arxiv.2605.03718 · pith_short_12: 2NBNCJJLWSPH · pith_short_16: 2NBNCJJLWSPHTEBN · pith_short_8: 2NBNCJJL

Agent API

Resolver JSON Graph JSON Events JSON Schema Signing key

Verify this Pith Number yourself

curl -sH 'Accept: application/ld+json' https://pith.science/pith/2NBNCJJLWSPHTEBN5IPQIMASNO \
  | jq -c '.canonical_record' \
  | python3 -c "import sys,json,hashlib; b=json.dumps(json.loads(sys.stdin.read()), sort_keys=True, separators=(',',':'), ensure_ascii=False).encode(); print(hashlib.sha256(b).hexdigest())"
# expect: d342d1252bb49e79902dea1f0430126bb9edf14fb52bd7fdf915e7366c291764

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "8e17a02d519a3baa883e2afe602629654c1f4414847f3bd14d702eae9bfa873a",
    "cross_cats_sorted": [
      "cs.DS",
      "math-ph",
      "math.MP"
    ],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "math.PR",
    "submitted_at": "2026-05-05T13:06:26Z",
    "title_canon_sha256": "19673e75fed137168a88d89d0b53272939e80aed2f258487ab61670f4b441da6"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2605.03718",
    "kind": "arxiv",
    "version": 2
  }
}