Pith Number

pith:FSNPMT75

pith:2011:FSNPMT75U44CZNKNPKQZIVVO77

not attested not anchored not stored refs pending

On the edge connectivity of direct products with dense graphs

Wei Wang, Zhidan Yan

arxiv:1102.5181 v1 · 2011-02-25 · 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{FSNPMT75U44CZNKNPKQZIVVO77}

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	2026-05-18T04:27:56.117083Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

2c9af64ffda7382cb54d7aa19456aeffd2e1d2f32cd907d297fab0bfd248c866

Aliases

arxiv: 1102.5181 · arxiv_version: 1102.5181v1 · doi: 10.48550/arxiv.1102.5181 · pith_short_12: FSNPMT75U44C · pith_short_16: FSNPMT75U44CZNKN · pith_short_8: FSNPMT75

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/FSNPMT75U44CZNKNPKQZIVVO77 \
  | 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: 2c9af64ffda7382cb54d7aa19456aeffd2e1d2f32cd907d297fab0bfd248c866

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "4599381528a03fd0726abddd11661327493c076aaa66aa9c399f70d5468e6132",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2011-02-25T07:58:03Z",
    "title_canon_sha256": "d74603c797c90ea3b7f3b33127a0a54e5c9b5269ea2f5f44b8d0f3ba5c44eac3"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1102.5181",
    "kind": "arxiv",
    "version": 1
  }
}