Pith Number

pith:4YAXUB7N

pith:2014:4YAXUB7N6AXG5QHP2XR6JJD3UC

not attested not anchored not stored refs pending

Biregular graphs with three eigenvalues

Alexander L. Gavrilyuk, Gary R. W. Greaves, Jack H. Koolen, Xi-Ming Cheng

arxiv:1412.6971 v2 · 2014-12-22 · 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{4YAXUB7N6AXG5QHP2XR6JJD3UC}

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	2026-05-18T01:15:58.912402Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

e6017a07edf02e6ec0efd5e3e4a47ba08f8b0d700df831d43e09203fe2a86362

Aliases

arxiv: 1412.6971 · arxiv_version: 1412.6971v2 · doi: 10.48550/arxiv.1412.6971 · pith_short_12: 4YAXUB7N6AXG · pith_short_16: 4YAXUB7N6AXG5QHP · pith_short_8: 4YAXUB7N

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/4YAXUB7N6AXG5QHP2XR6JJD3UC \
  | 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: e6017a07edf02e6ec0efd5e3e4a47ba08f8b0d700df831d43e09203fe2a86362

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "a75f5894c37681fde84d0629bf7027ff7faa41882909b6f7d25abf4db14aad80",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2014-12-22T13:16:58Z",
    "title_canon_sha256": "ddfc8fee8d9cc36d94bdbc973e443cadcae6d9002acf8ff66c5b68f007fbad53"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1412.6971",
    "kind": "arxiv",
    "version": 2
  }
}