Pith Number

pith:BM4GDHOZ

pith:2010:BM4GDHOZ6THNJYY4FA3BNF64Y6

not attested not anchored not stored refs pending

Triple crossing numbers of graphs

Hiroyuki Tanaka, Masakazu Teragaito

arxiv:1002.4231 v2 · 2010-02-23 · 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{BM4GDHOZ6THNJYY4FA3BNF64Y6}

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	2026-05-18T04:04:43.843534Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

0b38619dd9f4ced4e31c28361697dcc7a968275609757706e4ccb90cb45670ac

Aliases

arxiv: 1002.4231 · arxiv_version: 1002.4231v2 · doi: 10.48550/arxiv.1002.4231 · pith_short_12: BM4GDHOZ6THN · pith_short_16: BM4GDHOZ6THNJYY4 · pith_short_8: BM4GDHOZ

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/BM4GDHOZ6THNJYY4FA3BNF64Y6 \
  | 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: 0b38619dd9f4ced4e31c28361697dcc7a968275609757706e4ccb90cb45670ac

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "dacb46b9f82677051b4de31af03cc162668e0425df9266feab244b8e114413d1",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2010-02-23T01:08:01Z",
    "title_canon_sha256": "21bc5441f351f1a8ee95fcc5aaedcc2675801e47b32124e3cd0a373b46aafd3c"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1002.4231",
    "kind": "arxiv",
    "version": 2
  }
}