Pith Number

pith:OL6P4ZZX

pith:2007:OL6P4ZZXBMZTRXDYJ7YGL74VHB

not attested not anchored not stored refs pending

On the equivalence of the microcanonical and the canonical ensembles: a geometrical approach

Jaime Sanudo, Ricardo Lopez-Ruiz, Xavier Calbet

arxiv:0708.1866 v3 · 2007-08-14 · nlin.CD · cond-mat.stat-mech · stat.ME

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{OL6P4ZZXBMZTRXDYJ7YGL74VHB}

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	2026-05-18T04:09:14.978646Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

72fcfe67370b3338dc784ff065ff953840dc5c0f65a5abe1b65965ec0f959c09

Aliases

arxiv: 0708.1866 · arxiv_version: 0708.1866v3 · doi: 10.48550/arxiv.0708.1866 · pith_short_12: OL6P4ZZXBMZT · pith_short_16: OL6P4ZZXBMZTRXDY · pith_short_8: OL6P4ZZX

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/OL6P4ZZXBMZTRXDYJ7YGL74VHB \
  | 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: 72fcfe67370b3338dc784ff065ff953840dc5c0f65a5abe1b65965ec0f959c09

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "f60d757b6aaddc130f6102e5be9a837e10cce8821cdb24fef8f29f07178999ba",
    "cross_cats_sorted": [
      "cond-mat.stat-mech",
      "stat.ME"
    ],
    "license": "",
    "primary_cat": "nlin.CD",
    "submitted_at": "2007-08-14T11:39:45Z",
    "title_canon_sha256": "599825b4a9749a612cb9a11d92ca73e2ebad6db32ad9fa39cfac05c90b3af43d"
  },
  "schema_version": "1.0",
  "source": {
    "id": "0708.1866",
    "kind": "arxiv",
    "version": 3
  }
}