Pith Number

pith:UII6EEYY

pith:2011:UII6EEYYWJ5YWKTVR6F5MW6HGM

not attested not anchored not stored refs pending

A lower bound for the Graver complexity of the incidence matrix of a complete bipartite graph

Akimichi Takemura, Taisei Kudo

arxiv:1102.4674 v1 · 2011-02-23 · math.ST · stat.TH

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{UII6EEYYWJ5YWKTVR6F5MW6HGM}

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	2026-05-18T03:29:38.723463Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

a211e21318b27b8b2a758f8bd65bc7333c53e19240e666a3c6c6316433dfcb03

Aliases

arxiv: 1102.4674 · arxiv_version: 1102.4674v1 · doi: 10.48550/arxiv.1102.4674 · pith_short_12: UII6EEYYWJ5Y · pith_short_16: UII6EEYYWJ5YWKTV · pith_short_8: UII6EEYY

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/UII6EEYYWJ5YWKTVR6F5MW6HGM \
  | 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: a211e21318b27b8b2a758f8bd65bc7333c53e19240e666a3c6c6316433dfcb03

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "ceacae049aa6cfd8191ff8ac4009834b51dbe6d7a665896e913ce1ab66615a04",
    "cross_cats_sorted": [
      "stat.TH"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.ST",
    "submitted_at": "2011-02-23T07:11:18Z",
    "title_canon_sha256": "33d6954438917b34670c666ad8614177afca2c75a82fee06f4d92c29e0a82cad"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1102.4674",
    "kind": "arxiv",
    "version": 1
  }
}