Pith Number

pith:LEIMW2PR

pith:2012:LEIMW2PRX3L3NHXY2TXB5RK5EP

not attested not anchored not stored refs pending

The Clique Density Theorem

Christian Reiher

arxiv:1212.2454 v2 · 2012-12-11 · 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{LEIMW2PRX3L3NHXY2TXB5RK5EP}

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	2026-05-18T01:01:36.378943Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

5910cb69f1bed7b69ef8d4ee1ec55d23e2f3d36304aa88b453c60248f7202113

Aliases

arxiv: 1212.2454 · arxiv_version: 1212.2454v2 · doi: 10.48550/arxiv.1212.2454 · pith_short_12: LEIMW2PRX3L3 · pith_short_16: LEIMW2PRX3L3NHXY · pith_short_8: LEIMW2PR

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/LEIMW2PRX3L3NHXY2TXB5RK5EP \
  | 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: 5910cb69f1bed7b69ef8d4ee1ec55d23e2f3d36304aa88b453c60248f7202113

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "d6e0de726759a84c840d5fd93ebb83beaf0f44c0201dd4422683c7a39a7629b9",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2012-12-11T16:14:44Z",
    "title_canon_sha256": "304e196e4638ca7899c62664d118db3196a8e8f9fc4799ecca42a1a1b70b07ac"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1212.2454",
    "kind": "arxiv",
    "version": 2
  }
}