Pith Number

pith:BBDACMUI

pith:2026:BBDACMUI5JQ5IPNIA7JSJEUJCX

not attested not anchored not stored refs pending

Fluctuations of the Sherrington--Kirkpatrick free energy at critical temperature

Brice Huang, Hang Du

arxiv:2607.02172 v1 · 2026-07-02 · math.PR · cond-mat.dis-nn · 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{BBDACMUI5JQ5IPNIA7JSJEUJCX}

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.

Receipt and verification

First computed	2026-07-03T01:17:43.977255Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

0846013288ea61d43da807d324928915fb5ce395790848328c41d11a08f2e485

Aliases

arxiv: 2607.02172 · arxiv_version: 2607.02172v1 · doi: 10.48550/arxiv.2607.02172 · pith_short_12: BBDACMUI5JQ5 · pith_short_16: BBDACMUI5JQ5IPNI · pith_short_8: BBDACMUI

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/BBDACMUI5JQ5IPNIA7JSJEUJCX \
  | 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: 0846013288ea61d43da807d324928915fb5ce395790848328c41d11a08f2e485

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "bfa9e67865ca326cdecdeff772ce9f30a2f7de08da9d3d5e4d1c182f56277c31",
    "cross_cats_sorted": [
      "cond-mat.dis-nn",
      "math-ph",
      "math.MP"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.PR",
    "submitted_at": "2026-07-02T13:44:13Z",
    "title_canon_sha256": "6028b209f3644e7570819b44450a316c2965958d9def915fa4bf55a8bffe9089"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2607.02172",
    "kind": "arxiv",
    "version": 1
  }
}