Pith Number

pith:4Q7BF3P7

pith:2026:4Q7BF3P777UFIB7MVPLRKASYNX

not attested not anchored not stored refs pending

For edge-color-critical graphs, non-$r$-partite spectral extremal graphs are edge extremal

Jiadong Wu, Suil O

arxiv:2607.00561 v1 · 2026-07-01 · 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{4Q7BF3P777UFIB7MVPLRKASYNX}

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	2026-07-02T01:17:47.663403Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

e43e12edffffe85407ecabd71502586dd60caca460d95b46b8fa53e1cd877da5

Aliases

arxiv: 2607.00561 · arxiv_version: 2607.00561v1 · doi: 10.48550/arxiv.2607.00561 · pith_short_12: 4Q7BF3P777UF · pith_short_16: 4Q7BF3P777UFIB7M · pith_short_8: 4Q7BF3P7

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/4Q7BF3P777UFIB7MVPLRKASYNX \
  | 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: e43e12edffffe85407ecabd71502586dd60caca460d95b46b8fa53e1cd877da5

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "cfba0451ca2a201ba0696686ad15a297a96e2e8d5a99e1e4710a589c8448499e",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2026-07-01T07:50:55Z",
    "title_canon_sha256": "6bfbbc2932b8e2a14cd20e51c7aa35555e76710b279c4d63a133648bcf95ae78"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2607.00561",
    "kind": "arxiv",
    "version": 1
  }
}