Pith Number

pith:WNQP3A2X

pith:2016:WNQP3A2XAINLOD3NA4WFF23U7M

not attested not anchored not stored refs pending

Tutte polynomials and random-cluster models in Bernoulli cell complexes

Tomoyuki Shirai, Yasuaki Hiraoka

arxiv:1602.04561 v1 · 2016-02-15 · math.PR · math.AT · math.CO

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{WNQP3A2XAINLOD3NA4WFF23U7M}

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	2026-05-18T01:20:49.666405Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

b360fd8357021ab70f6d072c52eb74fb264c16897a3e5a1ae686ecc150e15243

Aliases

arxiv: 1602.04561 · arxiv_version: 1602.04561v1 · doi: 10.48550/arxiv.1602.04561 · pith_short_12: WNQP3A2XAINL · pith_short_16: WNQP3A2XAINLOD3N · pith_short_8: WNQP3A2X

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/WNQP3A2XAINLOD3NA4WFF23U7M \
  | 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: b360fd8357021ab70f6d072c52eb74fb264c16897a3e5a1ae686ecc150e15243

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "8fb6fe284a936360a1e87c899db68494acb94a89fec679bfa68f577c898cf9c3",
    "cross_cats_sorted": [
      "math.AT",
      "math.CO"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.PR",
    "submitted_at": "2016-02-15T05:08:11Z",
    "title_canon_sha256": "7553b21e030e64fa72b643cb2e02e631a619de8e4e43d062e81537ef60089675"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1602.04561",
    "kind": "arxiv",
    "version": 1
  }
}