Pith Number

pith:P6572CWL

pith:2015:P6572CWLOVGVNZCSU3KVKA2X2M

not attested not anchored not stored refs pending

Parameters for minimal unsatisfiability: Smarandache primitive numbers and full clauses

Oliver Kullmann, Xishun Zhao

arxiv:1505.02318 v2 · 2015-05-09 · cs.DM · cs.LO · 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{P6572CWLOVGVNZCSU3KVKA2X2M}

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	2026-05-18T01:37:10.803529Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

7fbbfd0acb754d56e452a6d5550357d30f92b8bab33cc592c21c815aa3f9bd94

Aliases

arxiv: 1505.02318 · arxiv_version: 1505.02318v2 · doi: 10.48550/arxiv.1505.02318 · pith_short_12: P6572CWLOVGV · pith_short_16: P6572CWLOVGVNZCS · pith_short_8: P6572CWL

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/P6572CWLOVGVNZCSU3KVKA2X2M \
  | 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: 7fbbfd0acb754d56e452a6d5550357d30f92b8bab33cc592c21c815aa3f9bd94

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "49663f2a63f7d03354979a5d8ca97025523570b1208506628ac3440c35242855",
    "cross_cats_sorted": [
      "cs.LO",
      "math.CO"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "cs.DM",
    "submitted_at": "2015-05-09T21:10:15Z",
    "title_canon_sha256": "5815dc4295e9b5fecef2697cc94b981355ffb700401622478e081ef1e2f6dfcb"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1505.02318",
    "kind": "arxiv",
    "version": 2
  }
}