Pith Number

pith:V4QPUG6S

pith:2026:V4QPUG6SO3FLVVZJEUSHNTV5MU

not attested not anchored not stored refs pending

3-Colouring Graphs Excluding a Fixed Minor

Hussein Houdrouge, Pat Morin, Vida Dujmovi\'c

arxiv:2607.02159 v1 · 2026-07-02 · 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{V4QPUG6SO3FLVVZJEUSHNTV5MU}

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	2026-07-03T01:17:43.643747Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

af20fa1bd276cabad729252476cebd650cf2b6fe30b1a6eff1083d23a5239890

Aliases

arxiv: 2607.02159 · arxiv_version: 2607.02159v1 · doi: 10.48550/arxiv.2607.02159 · pith_short_12: V4QPUG6SO3FL · pith_short_16: V4QPUG6SO3FLVVZJ · pith_short_8: V4QPUG6S

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/V4QPUG6SO3FLVVZJEUSHNTV5MU \
  | 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: af20fa1bd276cabad729252476cebd650cf2b6fe30b1a6eff1083d23a5239890

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "20f1d717002be0a5c8dab931619ad593f6d71e1d1080dfd9ebb141684fcc061a",
    "cross_cats_sorted": [
      "cs.DM"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2026-07-02T13:33:20Z",
    "title_canon_sha256": "2a2a2e5b16962b42b75f4b1f4dc94c66947b473deb9ff43365fe4ff64e22aa91"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2607.02159",
    "kind": "arxiv",
    "version": 1
  }
}