Pith Number

pith:7XSPZWOM

pith:2009:7XSPZWOMA4OCNVNLTFP7FMLZKH

not attested not anchored not stored refs pending

Finiteness theorems for the Picard objects of an algebraic stack

Sylvain Brochard

arxiv:0904.1166 v3 · 2009-04-07 · 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{7XSPZWOMA4OCNVNLTFP7FMLZKH}

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	2026-05-18T04:06:17.897681Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

fde4fcd9cc071c26d5ab995ff2b17951dc033dc925a9884bb1c7e4cbb0f9ce01

Aliases

arxiv: 0904.1166 · arxiv_version: 0904.1166v3 · doi: 10.48550/arxiv.0904.1166 · pith_short_12: 7XSPZWOMA4OC · pith_short_16: 7XSPZWOMA4OCNVNL · pith_short_8: 7XSPZWOM

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/7XSPZWOMA4OCNVNLTFP7FMLZKH \
  | 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: fde4fcd9cc071c26d5ab995ff2b17951dc033dc925a9884bb1c7e4cbb0f9ce01

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "8dc8db6a1b6ea4c469f49f95f0cfc354319dd84d7d022711a9d931463bca25c5",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AG",
    "submitted_at": "2009-04-07T15:20:13Z",
    "title_canon_sha256": "23a171286407ece05bd53e7d651b643ee2bdb351b9275551e44df6839682c17c"
  },
  "schema_version": "1.0",
  "source": {
    "id": "0904.1166",
    "kind": "arxiv",
    "version": 3
  }
}