Pith Number

pith:AYNU5BTT

pith:2011:AYNU5BTTGNVOK6JSWZDWZ3M2UA

not attested not anchored not stored refs pending

Coloring $\Delta$-Critical Graphs With Small High Vertex Cliques

Landon Rabern

arxiv:1102.1023 v1 · 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{AYNU5BTTGNVOK6JSWZDWZ3M2UA}

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	2026-05-18T04:29:55.175559Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

061b4e8673336ae57932b6476ced9aa0134716a6c788dcbf868cd31cfe2717fb

Aliases

arxiv: 1102.1023 · arxiv_version: 1102.1023v1 · doi: 10.48550/arxiv.1102.1023 · pith_short_12: AYNU5BTTGNVO · pith_short_16: AYNU5BTTGNVOK6JS · pith_short_8: AYNU5BTT

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/AYNU5BTTGNVOK6JSWZDWZ3M2UA \
  | 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: 061b4e8673336ae57932b6476ced9aa0134716a6c788dcbf868cd31cfe2717fb

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "756ab4220ecf44bf140ceb10dc8c1adc1b7e4a6b034dd510db13c8d6a8719df8",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2011-02-04T21:48:30Z",
    "title_canon_sha256": "b3af2702bade2c355e90fd5bc49fb262dd0e4a93faa850eced6c6b6b49db2ba3"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1102.1023",
    "kind": "arxiv",
    "version": 1
  }
}