Pith Number

pith:WVKP2H32

pith:2026:WVKP2H32TQSFLMIST7RVOOOABM

not attested not anchored not stored refs pending

The excluded minors for $\mathsf{Z}_{3}$-gainable and regular biased graphs

Daryl Funk, Dillon Mayhew, Nick Brettell, Rutger Campbell

arxiv:2606.23826 v1 · 2026-06-22 · 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{WVKP2H32TQSFLMIST7RVOOOABM}

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	2026-06-24T00:14:27.994368Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

b554fd1f7a9c2455b1129fe35739c00b0c7e571cd7cf35ef6b8b042f0ba7c962

Aliases

arxiv: 2606.23826 · arxiv_version: 2606.23826v1 · doi: 10.48550/arxiv.2606.23826 · pith_short_12: WVKP2H32TQSF · pith_short_16: WVKP2H32TQSFLMIS · pith_short_8: WVKP2H32

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/WVKP2H32TQSFLMIST7RVOOOABM \
  | 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: b554fd1f7a9c2455b1129fe35739c00b0c7e571cd7cf35ef6b8b042f0ba7c962

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "79a78e2c72ed13b72a7175578976c8c1fc4c7e7b3d3dc5fe726b09a134e9a635",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2026-06-22T18:10:44Z",
    "title_canon_sha256": "ab48fb61d67a5047a78f2d47218c74eb60d5d04ad82686d1d0c43fec8e6f99de"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2606.23826",
    "kind": "arxiv",
    "version": 1
  }
}