Pith Number

pith:WDOHXNNZ

pith:2012:WDOHXNNZZ2GKL62FSONACP7IBH

not attested not anchored not stored refs pending

3-Factor-criticality of vertex-transitive graphs

Heping Zhang, Wuyang Sun

arxiv:1212.3940 v1 · 2012-12-17 · 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{WDOHXNNZZ2GKL62FSONACP7IBH}

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	2026-05-18T03:38:21.980745Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

b0dc7bb5b9ce8ca5fb45939a013fe809e7bb79a70f9cf5b4dcb2a18a37c74fef

Aliases

arxiv: 1212.3940 · arxiv_version: 1212.3940v1 · doi: 10.48550/arxiv.1212.3940 · pith_short_12: WDOHXNNZZ2GK · pith_short_16: WDOHXNNZZ2GKL62F · pith_short_8: WDOHXNNZ

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/WDOHXNNZZ2GKL62FSONACP7IBH \
  | 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: b0dc7bb5b9ce8ca5fb45939a013fe809e7bb79a70f9cf5b4dcb2a18a37c74fef

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "737d18c8351f62596edef8ae71bb63767dde599c42bc87774f113554db45d359",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2012-12-17T09:17:37Z",
    "title_canon_sha256": "3ce89b18c70ec8ff2d403e8eb9945b38dd4de1659b20cdacb723292357f345ee"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1212.3940",
    "kind": "arxiv",
    "version": 1
  }
}