Pith Number

pith:QFEVOLWA

pith:2014:QFEVOLWAINQBSTXMV4STTLPGUJ

not attested not anchored not stored refs pending

A Brooks-type result for sparse critical graphs

Alexandr Kostochka, Matthew Yancey

arxiv:1408.0846 v3 · 2014-08-05 · 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{QFEVOLWAINQBSTXMV4STTLPGUJ}

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	2026-05-18T00:47:21.397230Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

8149572ec04360194eecaf2539ade6a262d3ab0a78c17dcdb6e4f3ae901a2111

Aliases

arxiv: 1408.0846 · arxiv_version: 1408.0846v3 · doi: 10.48550/arxiv.1408.0846 · pith_short_12: QFEVOLWAINQB · pith_short_16: QFEVOLWAINQBSTXM · pith_short_8: QFEVOLWA

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/QFEVOLWAINQBSTXMV4STTLPGUJ \
  | 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: 8149572ec04360194eecaf2539ade6a262d3ab0a78c17dcdb6e4f3ae901a2111

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "08786b2be273950be6f7992bb80e4f1d882d3a35ded92099913c48f7814150ce",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2014-08-05T01:12:33Z",
    "title_canon_sha256": "0ae42fda998a487c77f1b48e3c49acb049556cc6ab05edaf554e60781c79f59d"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1408.0846",
    "kind": "arxiv",
    "version": 3
  }
}