Pith Number

pith:U5VYZK2M

pith:2009:U5VYZK2MU3ZBZCBTNDQKEC7FFL

not attested not anchored not stored refs pending

Painlev\'e Functions in Statistical Physics

Craig A. Tracy, Harold Widom

arxiv:0912.2362 v2 · 2009-12-14 · math.PR · math-ph · math.MP · nlin.SI

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{U5VYZK2MU3ZBZCBTNDQKEC7FFL}

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	2026-05-18T04:25:26.090207Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

a76b8cab4ca6f21c883368e0a20be52aeabd3ecb5bb85efb9df301f294e453fb

Aliases

arxiv: 0912.2362 · arxiv_version: 0912.2362v2 · doi: 10.48550/arxiv.0912.2362 · pith_short_12: U5VYZK2MU3ZB · pith_short_16: U5VYZK2MU3ZBZCBT · pith_short_8: U5VYZK2M

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/U5VYZK2MU3ZBZCBTNDQKEC7FFL \
  | 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: a76b8cab4ca6f21c883368e0a20be52aeabd3ecb5bb85efb9df301f294e453fb

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "ddb2952e2a4e2f46ecc65f989eafad6e9d4b0045917e818970168ad7c9721edc",
    "cross_cats_sorted": [
      "math-ph",
      "math.MP",
      "nlin.SI"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.PR",
    "submitted_at": "2009-12-14T17:19:40Z",
    "title_canon_sha256": "bef2f3e24352ee1bfc549b430df1a8401ae3b35c5b595ac38e86fef06689ff2a"
  },
  "schema_version": "1.0",
  "source": {
    "id": "0912.2362",
    "kind": "arxiv",
    "version": 2
  }
}