Pith Number

pith:GHJIIWMM

pith:2013:GHJIIWMMHMXO24KXPBVRT3F3TO

not attested not anchored not stored refs pending

Entropy, Pressure and Duality for Gibbs plans in Ergodic Transport

A. O. Lopes, J. K. Mengue, J. Mohr, R. R. Souza

arxiv:1308.6514 v3 · 2013-08-29 · math.DS · cond-mat.stat-mech · math-ph · math.MP · math.OC · math.PR

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{GHJIIWMMHMXO24KXPBVRT3F3TO}

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	2026-05-17T23:53:01.813047Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

31d284598c3b2eed7157786b19ecbb9bb9521a4db4247a57a82f3e2eb685d2ca

Aliases

arxiv: 1308.6514 · arxiv_version: 1308.6514v3 · doi: 10.48550/arxiv.1308.6514 · pith_short_12: GHJIIWMMHMXO · pith_short_16: GHJIIWMMHMXO24KX · pith_short_8: GHJIIWMM

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/GHJIIWMMHMXO24KXPBVRT3F3TO \
  | 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: 31d284598c3b2eed7157786b19ecbb9bb9521a4db4247a57a82f3e2eb685d2ca

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "497e9a3def7a3ef5f581bd735230b807de16715c0a3ea1434df0056134659907",
    "cross_cats_sorted": [
      "cond-mat.stat-mech",
      "math-ph",
      "math.MP",
      "math.OC",
      "math.PR"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.DS",
    "submitted_at": "2013-08-29T16:35:26Z",
    "title_canon_sha256": "9185b84b04f49cbf3179926fc617d5e8e5572c64da2717be1df72837c89e8281"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1308.6514",
    "kind": "arxiv",
    "version": 3
  }
}