Pith Number

pith:BL25BQCE

pith:2009:BL25BQCEA5ZG2BTVVC26IRNI4W

not attested not anchored not stored refs pending

A simple mathematical proof of Boltzmann's equal a priori probability hypothesis

Debra J. Searles, Denis J. Evans, Stephen R. Williams

arxiv:0903.1480 v2 · 2009-03-09 · cond-mat.stat-mech

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{BL25BQCEA5ZG2BTVVC26IRNI4W}

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	2026-05-18T03:46:04.272311Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

0af5d0c04407726d0675a8b5e445a8e5a68ba87448bacf2028735ae541026572

Aliases

arxiv: 0903.1480 · arxiv_version: 0903.1480v2 · doi: 10.48550/arxiv.0903.1480 · pith_short_12: BL25BQCEA5ZG · pith_short_16: BL25BQCEA5ZG2BTV · pith_short_8: BL25BQCE

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/BL25BQCEA5ZG2BTVVC26IRNI4W \
  | 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: 0af5d0c04407726d0675a8b5e445a8e5a68ba87448bacf2028735ae541026572

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "37682eab319ab6de2e05fc3ff977dcc4bc29f092a99a7f2373a7e4cbe2b4a6d9",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "cond-mat.stat-mech",
    "submitted_at": "2009-03-09T05:10:20Z",
    "title_canon_sha256": "45e6f42a7107f8d0efe1027eb3773efcac58de240ae57c2826de60d017888df1"
  },
  "schema_version": "1.0",
  "source": {
    "id": "0903.1480",
    "kind": "arxiv",
    "version": 2
  }
}