Pith Number

pith:HZSMCLOH

pith:2011:HZSMCLOHBTOFEOTWTCYE7G766I

not attested not anchored not stored refs pending

An improvement on Brooks' Theorem

Landon Rabern

arxiv:1102.1021 v2 · 2011-02-04 · 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{HZSMCLOHBTOFEOTWTCYE7G766I}

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	2026-05-18T04:16:02.052261Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

3e64c12dc70cdc523a7698b04f9bfef217fdfd40e2d21ef6d9901dfe56c6baa0

Aliases

arxiv: 1102.1021 · arxiv_version: 1102.1021v2 · doi: 10.48550/arxiv.1102.1021 · pith_short_12: HZSMCLOHBTOF · pith_short_16: HZSMCLOHBTOFEOTW · pith_short_8: HZSMCLOH

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/HZSMCLOHBTOFEOTWTCYE7G766I \
  | 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: 3e64c12dc70cdc523a7698b04f9bfef217fdfd40e2d21ef6d9901dfe56c6baa0

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "c2c51f37d875f442f62b4e3e2ba05691c706e47fa5b99bdff0f4dbe60f2dc09d",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2011-02-04T21:43:04Z",
    "title_canon_sha256": "299babf29beac087f020f0bc1dc55962bd494c75a7c726408840cce84f471a9a"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1102.1021",
    "kind": "arxiv",
    "version": 2
  }
}