Pith Number

pith:57OKCF66

pith:2012:57OKCF66Y4BZLZAZ5ZVO6K57YS

not attested not anchored not stored refs pending

Cohen-Macaulay Circulant Graphs

Adam Van Tuyl, Catriona Watt, Kevin N. Vander Meulen

arxiv:1210.8351 v1 · 2012-10-31 · 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{57OKCF66Y4BZLZAZ5ZVO6K57YS}

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	2026-05-18T03:41:55.295862Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

efdca117dec70395e419ee6aef2bbfc4bc49125533fc80f2746f82c1aec08c5a

Aliases

arxiv: 1210.8351 · arxiv_version: 1210.8351v1 · doi: 10.48550/arxiv.1210.8351 · pith_short_12: 57OKCF66Y4BZ · pith_short_16: 57OKCF66Y4BZLZAZ · pith_short_8: 57OKCF66

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/57OKCF66Y4BZLZAZ5ZVO6K57YS \
  | 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: efdca117dec70395e419ee6aef2bbfc4bc49125533fc80f2746f82c1aec08c5a

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "1d4dc78f5403fbab95c2e2addcced499bf1a1b9dd065adcc4725ac2570de38c9",
    "cross_cats_sorted": [
      "math.CO"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AC",
    "submitted_at": "2012-10-31T14:49:28Z",
    "title_canon_sha256": "ca87790fd5852bb75750d22d9330c9da8e4b26593fac275b0e6bf11e30770c45"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1210.8351",
    "kind": "arxiv",
    "version": 1
  }
}