Pith Number

pith:72RNLXNW

pith:2018:72RNLXNWC4OSPUJ5P6KUZ6G2DC

not attested not anchored not stored refs pending

From billiards to thermodynamic laws: I. Stochastic energy exchange model

Lingchen Bu, Yao Li

arxiv:1805.02133 v2 · 2018-05-06 · math.DS

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{72RNLXNWC4OSPUJ5P6KUZ6G2DC}

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	2026-05-18T00:07:23.476656Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

fea2d5ddb6171d27d13d7f954cf8da18a4ae144f93ff1367deaa84972c59e4dd

Aliases

arxiv: 1805.02133 · arxiv_version: 1805.02133v2 · doi: 10.48550/arxiv.1805.02133 · pith_short_12: 72RNLXNWC4OS · pith_short_16: 72RNLXNWC4OSPUJ5 · pith_short_8: 72RNLXNW

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/72RNLXNWC4OSPUJ5P6KUZ6G2DC \
  | 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: fea2d5ddb6171d27d13d7f954cf8da18a4ae144f93ff1367deaa84972c59e4dd

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "41b2386a72798cbd42a2939942c97a326f04a6cafa488132c806027639dc23dd",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.DS",
    "submitted_at": "2018-05-06T02:03:46Z",
    "title_canon_sha256": "55888c0d9612eaf877d05530bf9c5c62fd211b8e65670a7ebbd32bf0a445931b"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1805.02133",
    "kind": "arxiv",
    "version": 2
  }
}