Pith Number

pith:TTV4JXQS

pith:2013:TTV4JXQSCK2EO6INLOY6ROZA3D

not attested not anchored not stored refs pending

The $(k,\ell)$-rainbow index for complete bipartite and multipartite graphs

Jiangli Song, Qingqiong Cai, Xueliang Li

arxiv:1310.2783 v2 · 2013-10-10 · 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{TTV4JXQSCK2EO6INLOY6ROZA3D}

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	2026-05-18T03:10:02.945912Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

9cebc4de1212b447790d5bb1e8bb20d8e96ac58484dabb63230bb74ae87972a7

Aliases

arxiv: 1310.2783 · arxiv_version: 1310.2783v2 · doi: 10.48550/arxiv.1310.2783 · pith_short_12: TTV4JXQSCK2E · pith_short_16: TTV4JXQSCK2EO6IN · pith_short_8: TTV4JXQS

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/TTV4JXQSCK2EO6INLOY6ROZA3D \
  | 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: 9cebc4de1212b447790d5bb1e8bb20d8e96ac58484dabb63230bb74ae87972a7

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "20c2abb738123f285c4dedcc8ebfd20eee92c435b88e6e45687d99753b63d0cc",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2013-10-10T12:10:45Z",
    "title_canon_sha256": "d8598dce2a6b85bc0e3f2aa040aa852e94950b2c174abd4e9e132b6a01690548"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1310.2783",
    "kind": "arxiv",
    "version": 2
  }
}