Pith Number

pith:GBMCOZLV

pith:2013:GBMCOZLVCY35OFO4ZUFZLJKZMF

not attested not anchored not stored refs pending

On log minimal models and Zariski decompositions II

Caucher Birkar, Zhengyu Hu

arxiv:1302.4015 v1 · 2013-02-16 · 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{GBMCOZLVCY35OFO4ZUFZLJKZMF}

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	2026-05-18T03:33:24.563983Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

30582765751637d715dccd0b95a559616f6a71524efb67c1dc802d9d6a28f90d

Aliases

arxiv: 1302.4015 · arxiv_version: 1302.4015v1 · doi: 10.48550/arxiv.1302.4015 · pith_short_12: GBMCOZLVCY35 · pith_short_16: GBMCOZLVCY35OFO4 · pith_short_8: GBMCOZLV

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/GBMCOZLVCY35OFO4ZUFZLJKZMF \
  | 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: 30582765751637d715dccd0b95a559616f6a71524efb67c1dc802d9d6a28f90d

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "0cd1dfed1a982357d0a9eb8eb2fa6a64c7c2f660cdc0710bf54028b078d3b92d",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AG",
    "submitted_at": "2013-02-16T23:59:08Z",
    "title_canon_sha256": "5471b07ef9c5c4e96cbf42cd5ca175bded2cd5eab6121d632f2c55669049c588"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1302.4015",
    "kind": "arxiv",
    "version": 1
  }
}