Pith Number

pith:VAPDOPS5

pith:2012:VAPDOPS5UBGDL5VSH7EGSBD6H2

not attested not anchored not stored refs pending

A Proof of a Conjecture of Ohba

Bruce A. Reed, Hehui Wu, Jonathan A. Noel

arxiv:1211.1999 v2 · 2012-11-08 · math.CO · cs.DM

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{VAPDOPS5UBGDL5VSH7EGSBD6H2}

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	2026-05-18T03:00:14.819910Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

a81e373e5da04c35f6b23fc869047e3e8dbd04bfef8538247771748fe761b922

Aliases

arxiv: 1211.1999 · arxiv_version: 1211.1999v2 · doi: 10.48550/arxiv.1211.1999 · pith_short_12: VAPDOPS5UBGD · pith_short_16: VAPDOPS5UBGDL5VS · pith_short_8: VAPDOPS5

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/VAPDOPS5UBGDL5VSH7EGSBD6H2 \
  | 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: a81e373e5da04c35f6b23fc869047e3e8dbd04bfef8538247771748fe761b922

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "c80a4b015ad9c1da8d5ee602e88f659060ec09c0dafbba89cc70ffe1d4de16c4",
    "cross_cats_sorted": [
      "cs.DM"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2012-11-08T21:48:33Z",
    "title_canon_sha256": "0c422351526dda5fb7b4fab38f77ce12914d77beec7320258c12c118597bb99c"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1211.1999",
    "kind": "arxiv",
    "version": 2
  }
}