Pith Number

pith:K4LFV47R

pith:2015:K4LFV47RZH72ZWWLCZMSAPLLNC

not attested not anchored not stored refs pending

Tutte relations, TQFT, and planarity of cubic graphs

Ian Agol, Vyacheslav Krushkal

arxiv:1512.07339 v1 · 2015-12-23 · math.CO · math.QA

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{K4LFV47RZH72ZWWLCZMSAPLLNC}

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	2026-05-18T01:23:49.976302Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

57165af3f1c9ffacdacb1659203d6b689510d08ab3f54c430635c37b24fb2841

Aliases

arxiv: 1512.07339 · arxiv_version: 1512.07339v1 · doi: 10.48550/arxiv.1512.07339 · pith_short_12: K4LFV47RZH72 · pith_short_16: K4LFV47RZH72ZWWL · pith_short_8: K4LFV47R

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/K4LFV47RZH72ZWWLCZMSAPLLNC \
  | 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: 57165af3f1c9ffacdacb1659203d6b689510d08ab3f54c430635c37b24fb2841

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "8a6bf1a3c2a953ddc7423381c9e655e11c72d57eb41cd8eabc4c885199046324",
    "cross_cats_sorted": [
      "math.QA"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2015-12-23T02:38:35Z",
    "title_canon_sha256": "27bfc5acfad584a306b599b0cf43f263293ac5d2884d81780c22907f5ea8fdcf"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1512.07339",
    "kind": "arxiv",
    "version": 1
  }
}