Pith Number

pith:RULLNRG7

pith:2004:RULLNRG7KAD3BRPCXA2SFCE6XI

not attested not anchored not stored refs pending

A categorification for the chromatic polynomial

Laure Helme-Guizon, Yongwu Rong

arxiv:math/0412264 v2 · 2004-12-13 · 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{RULLNRG7KAD3BRPCXA2SFCE6XI}

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	2026-05-18T02:41:32.147363Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

8d16b6c4df5007b0c5e2b83522889eba2d2c8f3232810cf3d4662d2580320037

Aliases

arxiv: math/0412264 · arxiv_version: math/0412264v2 · doi: 10.48550/arxiv.math/0412264 · pith_short_12: RULLNRG7KAD3 · pith_short_16: RULLNRG7KAD3BRPC · pith_short_8: RULLNRG7

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/RULLNRG7KAD3BRPCXA2SFCE6XI \
  | 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: 8d16b6c4df5007b0c5e2b83522889eba2d2c8f3232810cf3d4662d2580320037

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "f3b44b414a1b74be230f3e5fab8448eecd99916d5da145fcdcfa68333faeec05",
    "cross_cats_sorted": [
      "math.GT"
    ],
    "license": "",
    "primary_cat": "math.CO",
    "submitted_at": "2004-12-13T20:41:47Z",
    "title_canon_sha256": "ab365b03d860f85e7711c00b2cda080a3609cd831ece47f30b537a41c744904a"
  },
  "schema_version": "1.0",
  "source": {
    "id": "math/0412264",
    "kind": "arxiv",
    "version": 2
  }
}