Pith Number

pith:WOR56MAK

pith:2021:WOR56MAKQR74BAFQZXXHYYKBE4

not attested not anchored not stored refs pending

Global Frobenius Liftability II: Surfaces and Fano Threefolds

Jakub Witaszek, Maciej Zdanowicz, Piotr Achinger

arxiv:2102.02788 v1 · 2021-02-04 · 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{WOR56MAKQR74BAFQZXXHYYKBE4}

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.

Cited by

1 paper in Pith

Images of toric variety and amplified endomorphism of weak Fano threefolds

Receipt and verification

First computed	2026-07-05T02:12:51.542267Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

b3a3df300a847fc080b0cdee7c61412721d5b6e5ea378d43d43ac7ff7695b660

Aliases

arxiv: 2102.02788 · arxiv_version: 2102.02788v1 · doi: 10.48550/arxiv.2102.02788 · pith_short_12: WOR56MAKQR74 · pith_short_16: WOR56MAKQR74BAFQ · pith_short_8: WOR56MAK

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/WOR56MAKQR74BAFQZXXHYYKBE4 \
  | 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: b3a3df300a847fc080b0cdee7c61412721d5b6e5ea378d43d43ac7ff7695b660

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "58e6094c3f7525d830d28002151fe3720e1f4b13f29bfd71c07eb7edf3ced388",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AG",
    "submitted_at": "2021-02-04T18:13:43Z",
    "title_canon_sha256": "35492ec78ae615ec928ba04c29871a20744b3d648855d065cb4b3b899de4c41b"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2102.02788",
    "kind": "arxiv",
    "version": 1
  }
}