Pith Number

pith:6Y4O7XY2

pith:2003:6Y4O7XY2MF4GOXBTFTYZ345UDJ

not attested not anchored not stored refs pending

Convergence to equilibrium for finite Markov processes, with application to the Random Energy Model

Marseille), Marseille) Pierre PICCO (CPT, Pierre MATHIEU (LATP

arxiv:math/0307148 v1 · 2003-07-10 · math.PR · math-ph · math.MP

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{6Y4O7XY2MF4GOXBTFTYZ345UDJ}

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	2026-05-18T01:38:28.945915Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

f638efdf1a6178675c332cf19df3b41a49ee9db52df3c83b8268f0292306874c

Aliases

arxiv: math/0307148 · arxiv_version: math/0307148v1 · doi: 10.48550/arxiv.math/0307148 · pith_short_12: 6Y4O7XY2MF4G · pith_short_16: 6Y4O7XY2MF4GOXBT · pith_short_8: 6Y4O7XY2

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/6Y4O7XY2MF4GOXBTFTYZ345UDJ \
  | 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: f638efdf1a6178675c332cf19df3b41a49ee9db52df3c83b8268f0292306874c

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "c9f023aefa3d69d85d8cd09ab619495b3f35155a8045fe4fc42e27010de2f5b7",
    "cross_cats_sorted": [
      "math-ph",
      "math.MP"
    ],
    "license": "",
    "primary_cat": "math.PR",
    "submitted_at": "2003-07-10T15:12:44Z",
    "title_canon_sha256": "066509d8f49b5d4c6e8fb08ef953eacb2393a7cc980393b7ad54a79bccbb038b"
  },
  "schema_version": "1.0",
  "source": {
    "id": "math/0307148",
    "kind": "arxiv",
    "version": 1
  }
}