Pith Number

pith:CFCCW5K5

pith:2012:CFCCW5K52KZ5V7PZGMQYNHRNRM

not attested not anchored not stored refs pending

The Minimal Model Program Revisited

Paolo Cascini, Vladimir Lazi\'c

arxiv:1202.0738 v1 · 2012-02-03 · math.AG

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{CFCCW5K52KZ5V7PZGMQYNHRNRM}

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	2026-05-17T23:48:48.123924Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

11442b755dd2b3dafdf93321869e2d8b3eceb41e55c61c867fc4ee533ae02a22

Aliases

arxiv: 1202.0738 · arxiv_version: 1202.0738v1 · doi: 10.48550/arxiv.1202.0738 · pith_short_12: CFCCW5K52KZ5 · pith_short_16: CFCCW5K52KZ5V7PZ · pith_short_8: CFCCW5K5

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/CFCCW5K52KZ5V7PZGMQYNHRNRM \
  | 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: 11442b755dd2b3dafdf93321869e2d8b3eceb41e55c61c867fc4ee533ae02a22

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "a45e610f8231ab7c25cf14c4f05b1cce7a86f68b9e0a8bd8fc0fcfe9801434ab",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AG",
    "submitted_at": "2012-02-03T15:35:08Z",
    "title_canon_sha256": "93f6007360b135b4e55762b650e11345b421afc0cb21d4cf3d7863622eb0226d"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1202.0738",
    "kind": "arxiv",
    "version": 1
  }
}