Pith Number

pith:YFAB4XBN

pith:2013:YFAB4XBNFT34WZDRA3FNDAS3XH

not attested not anchored not stored refs pending

Complete multipartite graphs are determined by their distance spectra

Xiao-Dong Zhang, Ya-Lei Jin

arxiv:1307.5931 v1 · 2013-07-23 · 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{YFAB4XBNFT34WZDRA3FNDAS3XH}

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	2026-05-18T03:17:45.754940Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

c1401e5c2d2cf7cb647106cad1825bb9f02fe02c3d9805359ccbc6fc971f6ef9

Aliases

arxiv: 1307.5931 · arxiv_version: 1307.5931v1 · doi: 10.48550/arxiv.1307.5931 · pith_short_12: YFAB4XBNFT34 · pith_short_16: YFAB4XBNFT34WZDR · pith_short_8: YFAB4XBN

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/YFAB4XBNFT34WZDRA3FNDAS3XH \
  | 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: c1401e5c2d2cf7cb647106cad1825bb9f02fe02c3d9805359ccbc6fc971f6ef9

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "e64a259a73500b897b369d99d3819d7cefc8ec44b1ca095abb162aafe5b6cd79",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2013-07-23T03:08:26Z",
    "title_canon_sha256": "e8df6b64f9c5d4cefc5f4b1b31b813b5198826a85f0a3781f212a464e05afee3"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1307.5931",
    "kind": "arxiv",
    "version": 1
  }
}