Pith Number

pith:CPHLMEOC

pith:2010:CPHLMEOCDHEBCSTBNNR4CYBJOF

not attested not anchored not stored refs pending

Extension theorems, Non-vanishing and the existence of good minimal models

Christopher D. Hacon, Jean-Pierre Demailly, Mihai Paun

arxiv:1012.0493 v2 · 2010-12-02 · math.AG · math.CV

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{CPHLMEOCDHEBCSTBNNR4CYBJOF}

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	2026-05-18T04:32:54.347012Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

13ceb611c219c8114a616b63c160297147a765da60a2aa0f7ac31d3191520491

Aliases

arxiv: 1012.0493 · arxiv_version: 1012.0493v2 · doi: 10.48550/arxiv.1012.0493 · pith_short_12: CPHLMEOCDHEB · pith_short_16: CPHLMEOCDHEBCSTB · pith_short_8: CPHLMEOC

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/CPHLMEOCDHEBCSTBNNR4CYBJOF \
  | 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: 13ceb611c219c8114a616b63c160297147a765da60a2aa0f7ac31d3191520491

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "bc5aaa24c1cf3894519943d7d63bc45d7c6b7c00c29d13ebe515ce99967cff95",
    "cross_cats_sorted": [
      "math.CV"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AG",
    "submitted_at": "2010-12-02T16:55:01Z",
    "title_canon_sha256": "1330ce7423210c1e54b07f11d01a16666d3cbf491adde9d6d266e204e120f90e"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1012.0493",
    "kind": "arxiv",
    "version": 2
  }
}