Pith Number

pith:6JCU7MTZ

pith:2013:6JCU7MTZYDDOZLB3RJKDBIA4WU

not attested not anchored not stored refs pending

Non-vanishing of Betti numbers of edge ideals and complete bipartite subgraphs

Kyouko Kimura

arxiv:1306.1333 v3 · 2013-06-06 · math.AC · 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{6JCU7MTZYDDOZLB3RJKDBIA4WU}

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	2026-05-18T02:38:44.597952Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

f2454fb279c0c6ecac3b8a5430a01cb5030ce0d59c98331942aeeb02df30a70a

Aliases

arxiv: 1306.1333 · arxiv_version: 1306.1333v3 · doi: 10.48550/arxiv.1306.1333 · pith_short_12: 6JCU7MTZYDDO · pith_short_16: 6JCU7MTZYDDOZLB3 · pith_short_8: 6JCU7MTZ

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/6JCU7MTZYDDOZLB3RJKDBIA4WU \
  | 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: f2454fb279c0c6ecac3b8a5430a01cb5030ce0d59c98331942aeeb02df30a70a

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "9320bc003eef7d0861e206b13b58841d2d5f2eeef6092217373d91702b5ab493",
    "cross_cats_sorted": [
      "math.CO"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AC",
    "submitted_at": "2013-06-06T08:14:08Z",
    "title_canon_sha256": "fe86f444a699b8bb8cf417c2a444ca1d119aa3f713aa207959be98b59967daff"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1306.1333",
    "kind": "arxiv",
    "version": 3
  }
}