Pith Number

pith:65JJCTIU

pith:2019:65JJCTIUMRDSXOBHBL5NXYLE2C

not attested not anchored not stored refs pending

The Frobenius structure theorem for affine log Calabi-Yau varieties containing a torus

Sean Keel, Tony Yue Yu

arxiv:1908.09861 v2 · 2019-08-26 · math.AG · math.RT · math.SG

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{65JJCTIUMRDSXOBHBL5NXYLE2C}

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	2026-07-05T03:49:36.537519Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

f752914d1464472bb8270afadbe164d08ccdd478dbdd93b678789538cb827ec1

Aliases

arxiv: 1908.09861 · arxiv_version: 1908.09861v2 · doi: 10.48550/arxiv.1908.09861 · pith_short_12: 65JJCTIUMRDS · pith_short_16: 65JJCTIUMRDSXOBH · pith_short_8: 65JJCTIU

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/65JJCTIUMRDSXOBHBL5NXYLE2C \
  | 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: f752914d1464472bb8270afadbe164d08ccdd478dbdd93b678789538cb827ec1

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "28974388aa22a91a4052ec2de7ad4c2f24163507e01c3de403d0da9d9b945cfa",
    "cross_cats_sorted": [
      "math.RT",
      "math.SG"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AG",
    "submitted_at": "2019-08-26T18:05:23Z",
    "title_canon_sha256": "03919a28c6b1d916877b5f5d0e12c745ebeff4543d4a647462636f8a843ac16d"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1908.09861",
    "kind": "arxiv",
    "version": 2
  }
}