Pith Number

pith:CWCD4WJL

pith:2010:CWCD4WJLSR7PIDCYHMQBUGSSC3

not attested not anchored not stored refs pending

The competition-common enemy graphs of digraphs satisfying Conditions $C(p)$ and $C'(p)$

Yoshio Sano

arxiv:1006.2631 v2 · 2010-06-14 · 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{CWCD4WJLSR7PIDCYHMQBUGSSC3}

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	2026-05-18T04:28:29.849480Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

15843e592b947ef40c583b201a1a5216c45d6b79d8c3431db4caeca9db77c8a7

Aliases

arxiv: 1006.2631 · arxiv_version: 1006.2631v2 · doi: 10.48550/arxiv.1006.2631 · pith_short_12: CWCD4WJLSR7P · pith_short_16: CWCD4WJLSR7PIDCY · pith_short_8: CWCD4WJL

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/CWCD4WJLSR7PIDCYHMQBUGSSC3 \
  | 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: 15843e592b947ef40c583b201a1a5216c45d6b79d8c3431db4caeca9db77c8a7

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "0307cd88ae11e1be74107ac456a25d542b6f1f959c62884c9c001159c7483a1e",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2010-06-14T08:25:46Z",
    "title_canon_sha256": "53c1de021088e97f75eb1bd57534c6a9bac5c76ea3230c71276e912b6cd0b65a"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1006.2631",
    "kind": "arxiv",
    "version": 2
  }
}