Pith Number

pith:QOK2BUYW

pith:2006:QOK2BUYWP4MUZGQCIUHRJ4SF2S

not attested not anchored not stored refs pending

Markov loops, determinants and Gaussian fields

Yves Le Jan (LM-Orsay)

arxiv:math/0612112 v4 · 2006-12-05 · 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{QOK2BUYWP4MUZGQCIUHRJ4SF2S}

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.

Cited by

1 paper in Pith

Loop clusters on complete graphs

Receipt and verification

First computed	2026-07-04T15:03:59.648242Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

8395a0d3167f194c9a02450f14f245d4b8cb09e4c5a8eaa0f356abd3a7274ea2

Aliases

arxiv: math/0612112 · arxiv_version: math/0612112v4 · doi: 10.48550/arxiv.math/0612112 · pith_short_12: QOK2BUYWP4MU · pith_short_16: QOK2BUYWP4MUZGQC · pith_short_8: QOK2BUYW

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/QOK2BUYWP4MUZGQCIUHRJ4SF2S \
  | 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: 8395a0d3167f194c9a02450f14f245d4b8cb09e4c5a8eaa0f356abd3a7274ea2

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "533f5a0a897f0a440d8493a08b8946d4f4a4a80ed08174424af10d227d86f468",
    "cross_cats_sorted": [],
    "license": "",
    "primary_cat": "math.PR",
    "submitted_at": "2006-12-05T05:45:55Z",
    "title_canon_sha256": "920aaea56cd2a1b96efdf37a024d78e64f5776b595640353e02bbe7170109b79"
  },
  "schema_version": "1.0",
  "source": {
    "id": "math/0612112",
    "kind": "arxiv",
    "version": 4
  }
}