Pith Number

pith:IA6ZL5DE

pith:2015:IA6ZL5DEZTNOSA2UNYI7E73WWO

not attested not anchored not stored refs pending

Disjoint cycles of different lengths in graphs and digraphs

Ararat Harutyunyan, Binlong Li, Julien Bensmail, Ngoc Khang Le, Nicolas Lichiardopol

arxiv:1510.06667 v2 · 2015-10-22 · 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{IA6ZL5DEZTNOSA2UNYI7E73WWO}

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	2026-05-18T01:23:11.885809Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

403d95f464ccdae903546e11f27f76b398a63bb0323af85e95c080a2ac0fff42

Aliases

arxiv: 1510.06667 · arxiv_version: 1510.06667v2 · doi: 10.48550/arxiv.1510.06667 · pith_short_12: IA6ZL5DEZTNO · pith_short_16: IA6ZL5DEZTNOSA2U · pith_short_8: IA6ZL5DE

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/IA6ZL5DEZTNOSA2UNYI7E73WWO \
  | 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: 403d95f464ccdae903546e11f27f76b398a63bb0323af85e95c080a2ac0fff42

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "e959bdc01e15f474568312d4e78fc5b2a6b06f6c802a10dc96413a71608887e5",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2015-10-22T15:58:51Z",
    "title_canon_sha256": "74e2f04a8fb85eaf30956660dc783022cd7ea7af8bbfc6ec896be05baf2bf45a"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1510.06667",
    "kind": "arxiv",
    "version": 2
  }
}