Pith Number

pith:ULFD3GCX

pith:2025:ULFD3GCXZPFPGOYP4NABCU6FJW

not attested not anchored not stored refs pending

Every graph with no $K_7^{\vee}$-minor is $6$-colorable

Agnes Totschnig, Sergey Norin

arxiv:2507.03244 v1 · 2025-07-04 · 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{ULFD3GCXZPFPGOYP4NABCU6FJW}

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	2026-07-05T11:31:55.508342Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

a2ca3d9857cbcaf33b0fe3401153c54d9330cf097fb0a4ce8ee8d96313bef4f0

Aliases

arxiv: 2507.03244 · arxiv_version: 2507.03244v1 · doi: 10.48550/arxiv.2507.03244 · pith_short_12: ULFD3GCXZPFP · pith_short_16: ULFD3GCXZPFPGOYP · pith_short_8: ULFD3GCX

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/ULFD3GCXZPFPGOYP4NABCU6FJW \
  | 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: a2ca3d9857cbcaf33b0fe3401153c54d9330cf097fb0a4ce8ee8d96313bef4f0

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "03b5202464d02b5d7c2132a1f9a9891d74f67b3941f7f815b44829abc33b53c3",
    "cross_cats_sorted": [],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2025-07-04T01:34:26Z",
    "title_canon_sha256": "476ccf90f18457057c0a3e43c4668774fca646d4b8da0d6b9bedf91c8b2b8805"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2507.03244",
    "kind": "arxiv",
    "version": 1
  }
}