Pith Number

pith:FYFXAPHV

pith:2026:FYFXAPHVLP5BVDVOXGYMBAXZE4

not attested not anchored not stored refs pending

A proof of Haemers' toughness conjecture

Gary Greaves, Haoran Zhu

arxiv:2605.15738 v1 · 2026-05-15 · 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{FYFXAPHVLP5BVDVOXGYMBAXZE4}

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	2026-05-20T00:01:15.567116Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

2e0b703cf55bfa1a8eaeb9b0c082f9273b66a5e54b5168c71258b5a85b5d7152

Aliases

arxiv: 2605.15738 · arxiv_version: 2605.15738v1 · doi: 10.48550/arxiv.2605.15738 · pith_short_12: FYFXAPHVLP5B · pith_short_16: FYFXAPHVLP5BVDVO · pith_short_8: FYFXAPHV

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/FYFXAPHVLP5BVDVOXGYMBAXZE4 \
  | 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: 2e0b703cf55bfa1a8eaeb9b0c082f9273b66a5e54b5168c71258b5a85b5d7152

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "f3cb946d86627a351bb188f4be91fd42e07033d706eca5bb686c3c351a61310b",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2026-05-15T08:48:06Z",
    "title_canon_sha256": "fd6b8ccbda46dbecde53b3ca677d7f2931390bb73728e865e33968fc87d2687e"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2605.15738",
    "kind": "arxiv",
    "version": 1
  }
}