Pith Number

pith:AQ3OXOO2

pith:2015:AQ3OXOO24NMBZXONRX5UNVEUQO

not attested not anchored not stored refs pending

Coloring graphs without fan vertex-minors and graphs without cycle pivot-minors

Ilkyoo Choi, O-joung Kwon, Sang-il Oum

arxiv:1512.03481 v1 · 2015-12-10 · 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{AQ3OXOO24NMBZXONRX5UNVEUQO}

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	2026-05-18T00:34:58.106037Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

0436ebb9dae3581cddcd8dfb46d49483900d9bb0ab60d7ee3f7eb72470917a32

Aliases

arxiv: 1512.03481 · arxiv_version: 1512.03481v1 · doi: 10.48550/arxiv.1512.03481 · pith_short_12: AQ3OXOO24NMB · pith_short_16: AQ3OXOO24NMBZXON · pith_short_8: AQ3OXOO2

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/AQ3OXOO24NMBZXONRX5UNVEUQO \
  | 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: 0436ebb9dae3581cddcd8dfb46d49483900d9bb0ab60d7ee3f7eb72470917a32

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "0eb9a86521f1997276539d5a0bcb2e93bb2754813eefa84033ba34b765dde0de",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2015-12-10T23:11:08Z",
    "title_canon_sha256": "16b5596753e9b645e08e01278e35f6e8b9152711ee55c6d2cb10453594268f26"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1512.03481",
    "kind": "arxiv",
    "version": 1
  }
}