Pith Number

pith:2A32AFHN

pith:2013:2A32AFHNOVKZGY5KE5NKAKEGX2

not attested not anchored not stored refs pending

On the crossing number of some complete multipartite graphs

Pak Tung Ho

arxiv:1310.4381 v1 · 2013-10-16 · 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{2A32AFHNOVKZGY5KE5NKAKEGX2}

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	2026-05-18T03:10:23.014336Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

d037a014ed75559363aa275aa02886beaef7dc83965dd7c68697f03638ef0716

Aliases

arxiv: 1310.4381 · arxiv_version: 1310.4381v1 · doi: 10.48550/arxiv.1310.4381 · pith_short_12: 2A32AFHNOVKZ · pith_short_16: 2A32AFHNOVKZGY5K · pith_short_8: 2A32AFHN

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/2A32AFHNOVKZGY5KE5NKAKEGX2 \
  | 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: d037a014ed75559363aa275aa02886beaef7dc83965dd7c68697f03638ef0716

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "a45085fa9868291f6f6465fda779cddb87ab01505055ced462e8e5c6f197b5dd",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2013-10-16T13:59:14Z",
    "title_canon_sha256": "6f9edcd767179d9ae4c61d8fe6b14d30b618bdad83e9c127576b19421b4cf06d"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1310.4381",
    "kind": "arxiv",
    "version": 1
  }
}