Pith Number

pith:GI5CYXZ7

pith:2011:GI5CYXZ7RKOGIDH7N2APDBZ5E2

not attested not anchored not stored refs pending

Existence of log canonical closures

Chenyang Xu, Christopher D. Hacon

arxiv:1105.1169 v3 · 2011-05-05 · 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{GI5CYXZ7RKOGIDH7N2APDBZ5E2}

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	2026-05-18T03:52:26.474752Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

323a2c5f3f8a9c640cff6e80f1873d26b327516c353d70a8526d07335821488f

Aliases

arxiv: 1105.1169 · arxiv_version: 1105.1169v3 · doi: 10.48550/arxiv.1105.1169 · pith_short_12: GI5CYXZ7RKOG · pith_short_16: GI5CYXZ7RKOGIDH7 · pith_short_8: GI5CYXZ7

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/GI5CYXZ7RKOGIDH7N2APDBZ5E2 \
  | 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: 323a2c5f3f8a9c640cff6e80f1873d26b327516c353d70a8526d07335821488f

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "ec90dde80070ca223b51ebec5fc2d0268d45379da3b693fee81d830669324ecc",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AG",
    "submitted_at": "2011-05-05T20:22:18Z",
    "title_canon_sha256": "331e5831261a3f93fb263252147f3d3ff2603a77523be1c5cc98c2f23c939c29"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1105.1169",
    "kind": "arxiv",
    "version": 3
  }
}