Pith Number

pith:LWYYPQZZ

pith:2009:LWYYPQZZJGZSVJJAHPWRRQGDY4

not attested not anchored not stored refs pending

On the local quotient structure of Artin stacks

Jarod Alper

arxiv:0904.2050 v4 · 2009-04-14 · 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{LWYYPQZZJGZSVJJAHPWRRQGDY4}

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	2026-05-18T00:28:27.894586Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

5db187c33949b32aa5203bed18c0c3c73156817f30e7885989022d65df06d4bd

Aliases

arxiv: 0904.2050 · arxiv_version: 0904.2050v4 · doi: 10.48550/arxiv.0904.2050 · pith_short_12: LWYYPQZZJGZS · pith_short_16: LWYYPQZZJGZSVJJA · pith_short_8: LWYYPQZZ

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/LWYYPQZZJGZSVJJAHPWRRQGDY4 \
  | 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: 5db187c33949b32aa5203bed18c0c3c73156817f30e7885989022d65df06d4bd

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "9d922719c881765f1f622049593727d0a07a4ff8c118ec02783332aa51f6b4b9",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AG",
    "submitted_at": "2009-04-14T05:33:18Z",
    "title_canon_sha256": "5109fc30e8db32aca092b23b02a629b44de4c755aae5ac2684333e7b6233968e"
  },
  "schema_version": "1.0",
  "source": {
    "id": "0904.2050",
    "kind": "arxiv",
    "version": 4
  }
}