Pith Number

pith:TZBWCKXB

pith:2005:TZBWCKXBIAWYDMLQ7PREUPPVO5

not attested not anchored not stored refs pending

The chromatic polynomial of fatgraphs and its categorification

Iain Moffatt, Martin Loebl

arxiv:math/0511557 v3 · 2005-11-22 · math.CO · math.GT

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{TZBWCKXBIAWYDMLQ7PREUPPVO5}

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	2026-05-18T04:01:11.893279Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

9e43612ae1402d81b170fbe24a3df5777c40b2d8212cbcce08241e482c7f02cb

Aliases

arxiv: math/0511557 · arxiv_version: math/0511557v3 · doi: 10.48550/arxiv.math/0511557 · pith_short_12: TZBWCKXBIAWY · pith_short_16: TZBWCKXBIAWYDMLQ · pith_short_8: TZBWCKXB

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/TZBWCKXBIAWYDMLQ7PREUPPVO5 \
  | 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: 9e43612ae1402d81b170fbe24a3df5777c40b2d8212cbcce08241e482c7f02cb

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "03c618ae8edbc0260a58fa0175873378a839d1ef1d7298042f79788d1a1bd9dd",
    "cross_cats_sorted": [
      "math.GT"
    ],
    "license": "",
    "primary_cat": "math.CO",
    "submitted_at": "2005-11-22T13:30:08Z",
    "title_canon_sha256": "988f7f3e9d4daa95e5e634b4f5d444bded47582a515f3b31d3823cdfd41f67a5"
  },
  "schema_version": "1.0",
  "source": {
    "id": "math/0511557",
    "kind": "arxiv",
    "version": 3
  }
}