Pith Number

pith:ZPS3QAGP

pith:2010:ZPS3QAGPX5B73OXWV2ECOIE22X

not attested not anchored not stored refs pending

Equivalence between Extendibility and Factor-Criticality

Dingjun Lou, Tao Wang, Zan-Bo Zhang

arxiv:1011.3381 v1 · 2010-11-15 · 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{ZPS3QAGPX5B73OXWV2ECOIE22X}

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	2026-05-18T04:35:56.016968Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

cbe5b800cfbf43fdbaf6ae8827209ad5d19672bd4acf26a10e3f98488f9f6b20

Aliases

arxiv: 1011.3381 · arxiv_version: 1011.3381v1 · doi: 10.48550/arxiv.1011.3381 · pith_short_12: ZPS3QAGPX5B7 · pith_short_16: ZPS3QAGPX5B73OXW · pith_short_8: ZPS3QAGP

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/ZPS3QAGPX5B73OXWV2ECOIE22X \
  | 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: cbe5b800cfbf43fdbaf6ae8827209ad5d19672bd4acf26a10e3f98488f9f6b20

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "4749358a8359630c9901f089d8ab3b9c5c74093e217256b4ff70c461a353e72e",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2010-11-15T13:47:01Z",
    "title_canon_sha256": "e94bb11a79ef88c7d8bde09f09271b11f8537c838e5ddfa7b1ad9e48da540e63"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1011.3381",
    "kind": "arxiv",
    "version": 1
  }
}