Pith Number

pith:4SRZBFDY

pith:2004:4SRZBFDYHV4I4N3YVNHXXYHU3Z

not attested not anchored not stored refs pending

Boltzmann entropy and the microcanonical ensemble

Jan Naudts

arxiv:cond-mat/0412683 v1 · 2004-12-24 · 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{4SRZBFDYHV4I4N3YVNHXXYHU3Z}

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	2026-05-18T01:39:57.118705Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

e4a39094783d788e3778ab4f7be0f4de4daf3d003f572bafccdef6853f057c82

Aliases

arxiv: cond-mat/0412683 · arxiv_version: cond-mat/0412683v1 · doi: 10.48550/arxiv.cond-mat/0412683 · pith_short_12: 4SRZBFDYHV4I · pith_short_16: 4SRZBFDYHV4I4N3Y · pith_short_8: 4SRZBFDY

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/4SRZBFDYHV4I4N3YVNHXXYHU3Z \
  | 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: e4a39094783d788e3778ab4f7be0f4de4daf3d003f572bafccdef6853f057c82

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "bb0f3fe08607e61d6ebd2124444fc38a1399c107b97dddd9b8a30ba6dfadb068",
    "cross_cats_sorted": [],
    "license": "",
    "primary_cat": "cond-mat.stat-mech",
    "submitted_at": "2004-12-24T16:52:24Z",
    "title_canon_sha256": "a88b36d613efb1a0b0761df3a692cb053080766663b554a5a8dc0b003ca40770"
  },
  "schema_version": "1.0",
  "source": {
    "id": "cond-mat/0412683",
    "kind": "arxiv",
    "version": 1
  }
}