Pith Number

pith:R6NZRD6U

pith:2013:R6NZRD6U3HZF5QJO3MXLTIJVTU

not attested not anchored not stored refs pending

Small clique number graphs with three trivial critical ideals

Carlos A. Alfaro, Carlos E. Valencia

arxiv:1311.5927 v1 · 2013-11-22 · math.CO · math.AC

Open paper page JSON Open Graph Bundle Merged state Verified badge What is a Pith Number?

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{R6NZRD6U3HZF5QJO3MXLTIJVTU}

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	2026-05-18T03:06:21.070907Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

8f9b988fd4d9f25ec12edb2eb9a1359d031681d0701977b369eca96bc03d4dd4

Aliases

arxiv: 1311.5927 · arxiv_version: 1311.5927v1 · doi: 10.48550/arxiv.1311.5927 · pith_short_12: R6NZRD6U3HZF · pith_short_16: R6NZRD6U3HZF5QJO · pith_short_8: R6NZRD6U

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/R6NZRD6U3HZF5QJO3MXLTIJVTU \
  | 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: 8f9b988fd4d9f25ec12edb2eb9a1359d031681d0701977b369eca96bc03d4dd4

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "8ae3a840f46c6a29fc70d8f6ef4f5737392666803d2e3c86676ed1c64926a5eb",
    "cross_cats_sorted": [
      "math.AC"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2013-11-22T23:03:40Z",
    "title_canon_sha256": "acd2047eacb286dec129479c22940ef8e9cb0cede807b348611ed142536ecd2e"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1311.5927",
    "kind": "arxiv",
    "version": 1
  }
}