Pith Number

pith:4EGJA7AR

pith:2012:4EGJA7ARIECRQEIL4PCN3N3ZOO

not attested not anchored not stored refs pending

Markovian loop clusters on graphs

Sophie Lemaire (LM-Orsay), Yves Le Jan (LM-Orsay)

arxiv:1211.0300 v3 · 2012-11-01 · 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{4EGJA7ARIECRQEIL4PCN3N3ZOO}

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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.

Cited by

1 paper in Pith

Loop clusters on complete graphs

Receipt and verification

First computed	2026-05-18T03:27:54.426567Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

e10c907c11410518110be3c4ddb779738a406e163a938cb6b5a24181e5c60b15

Aliases

arxiv: 1211.0300 · arxiv_version: 1211.0300v3 · doi: 10.48550/arxiv.1211.0300 · pith_short_12: 4EGJA7ARIECR · pith_short_16: 4EGJA7ARIECRQEIL · pith_short_8: 4EGJA7AR

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/4EGJA7ARIECRQEIL4PCN3N3ZOO \
  | 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: e10c907c11410518110be3c4ddb779738a406e163a938cb6b5a24181e5c60b15

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "732c9b03b825470861b7535e5e2594882157366a63059d07facacca6cdf51b96",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.PR",
    "submitted_at": "2012-11-01T20:25:56Z",
    "title_canon_sha256": "659a2129b187f9ce59c94948eecd61a7a9c82cea86621d4b87a1be3909eb482c"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1211.0300",
    "kind": "arxiv",
    "version": 3
  }
}