Pith Number

pith:WQGDZNIZ

pith:2010:WQGDZNIZ2TCJXDLSGZFBNH7UJW

not attested not anchored not stored refs pending

A converse to the Andreotti-Grauert theorem

Jean-Pierre Demailly (IF)

arxiv:1011.3635 v2 · 2010-11-16 · 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{WQGDZNIZ2TCJXDLSGZFBNH7UJW}

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	2026-05-18T04:32:54.363648Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

b40c3cb519d4c49b8d72364a169ff44da22ac195589683b72d23cea72f3dabe1

Aliases

arxiv: 1011.3635 · arxiv_version: 1011.3635v2 · doi: 10.48550/arxiv.1011.3635 · pith_short_12: WQGDZNIZ2TCJ · pith_short_16: WQGDZNIZ2TCJXDLS · pith_short_8: WQGDZNIZ

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/WQGDZNIZ2TCJXDLSGZFBNH7UJW \
  | 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: b40c3cb519d4c49b8d72364a169ff44da22ac195589683b72d23cea72f3dabe1

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "e145b6164e6126bdcb21c636fdcbbe1b43fb7875fdbd6266e66f68dcf54f63d4",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AG",
    "submitted_at": "2010-11-16T10:09:52Z",
    "title_canon_sha256": "c6efab5dd42a8dc85483d56b1ef161486bd424dc88f474ec559877dd58301e7b"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1011.3635",
    "kind": "arxiv",
    "version": 2
  }
}