Pith Number

pith:ULRH26B4

pith:2021:ULRH26B4NEYLZZN73L2FFZKYTD

not attested not anchored not stored refs pending

The tripartite-circle crossing number of graphs with two small partition classes

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

arxiv:2108.01032 v2 · 2021-08-02 · math.CO · cs.DM

Open paper page JSON Open Graph Bundle Merged state Verified badge What is a Pith Number?

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{ULRH26B4NEYLZZN73L2FFZKYTD}

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	2026-07-05T09:38:47.337333Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

a2e27d783c6930bce5bfdaf452e55898db3e4ea19a9439d76ee9c69c5533b0fb

Aliases

arxiv: 2108.01032 · arxiv_version: 2108.01032v2 · doi: 10.48550/arxiv.2108.01032 · pith_short_12: ULRH26B4NEYL · pith_short_16: ULRH26B4NEYLZZN7 · pith_short_8: ULRH26B4

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/ULRH26B4NEYLZZN73L2FFZKYTD \
  | 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: a2e27d783c6930bce5bfdaf452e55898db3e4ea19a9439d76ee9c69c5533b0fb

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "a46f57281832ad47e4d09ac1732bea2c3aaec4633c8b44298a8dd64dea76a223",
    "cross_cats_sorted": [
      "cs.DM"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2021-08-02T16:43:35Z",
    "title_canon_sha256": "56435bb0ef7db677ac9eda208255c5cec8c25f53e362a467b2d9ce038a16135a"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2108.01032",
    "kind": "arxiv",
    "version": 2
  }
}