Pith Number

pith:25P76EK5

pith:2010:25P76EK5Q2NQIGSAL3FIOFLKVS

not attested not anchored not stored refs pending

An H-theorem for the Brownian motion on the hyperbolic plane

C. Vignat, P.W. Lamberti

arxiv:1009.3232 v3 · 2010-09-16 · 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{25P76EK5Q2NQIGSAL3FIOFLKVS}

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	2026-05-18T04:31:52.218558Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

d75fff115d869b041a405eca87156aacb118a1dc09928953355e83d94f45e8be

Aliases

arxiv: 1009.3232 · arxiv_version: 1009.3232v3 · doi: 10.48550/arxiv.1009.3232 · pith_short_12: 25P76EK5Q2NQ · pith_short_16: 25P76EK5Q2NQIGSA · pith_short_8: 25P76EK5

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/25P76EK5Q2NQIGSAL3FIOFLKVS \
  | 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: d75fff115d869b041a405eca87156aacb118a1dc09928953355e83d94f45e8be

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "13c9580a03e4ec9fb91df73abf4393ccd34ea52265ce446c6de5151405be65dc",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "cond-mat.stat-mech",
    "submitted_at": "2010-09-16T18:03:32Z",
    "title_canon_sha256": "79e5b2c3a5b5c5b09f8c77c403c404c0e508c157ce7e08691b2258068e3a43f3"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1009.3232",
    "kind": "arxiv",
    "version": 3
  }
}