Pith Number

pith:4XCNVQUR

pith:2019:4XCNVQURGGKMC2T4QFS5KNQNZB

not attested not anchored not stored refs pending

Bounding the tripartite-circle crossing number of complete tripartite graphs

Charles Camacho, Elizabeth Bailey Matson, Jennifer White, Linda Kleist, Marija Jeli\'c Milutinovi\'c, Rachel Kirsch, Silvia Fern\'andez-Merchant

arxiv:1910.06963 v2 · 2019-10-15 · 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{4XCNVQURGGKMC2T4QFS5KNQNZB}

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	2026-07-05T06:25:56.143080Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

e5c4dac2913194c16a7c8165d5360dc8540bc46c7675c23114993915384b3ca0

Aliases

arxiv: 1910.06963 · arxiv_version: 1910.06963v2 · doi: 10.48550/arxiv.1910.06963 · pith_short_12: 4XCNVQURGGKM · pith_short_16: 4XCNVQURGGKMC2T4 · pith_short_8: 4XCNVQUR

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/4XCNVQURGGKMC2T4QFS5KNQNZB \
  | 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: e5c4dac2913194c16a7c8165d5360dc8540bc46c7675c23114993915384b3ca0

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "fe7579644bfde060666327b7995c7a7141d8cb1ab5778b355fd78f0d043c6f48",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2019-10-15T17:59:55Z",
    "title_canon_sha256": "3262e4e6fb9cf44bb624265390f48f49792c15e68f0769e4b2bbf2f4421c6656"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1910.06963",
    "kind": "arxiv",
    "version": 2
  }
}