Pith Number

pith:CMVB5MYK

pith:2025:CMVB5MYKEOLL3ZAUH5RDHRIQ7E

not attested not anchored not stored refs pending

Frobenius liftable hypersurfaces

Jakub Witaszek, Supravat Sarkar, Tatsuro Kawakami

arxiv:2507.12198 v1 · 2025-07-16 · 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{CMVB5MYKEOLL3ZAUH5RDHRIQ7E}

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	2026-07-05T11:38:16.359263Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

132a1eb30a2396bde4143f6233c510f9169de3ec20937cf5b7f84025f08fc95b

Aliases

arxiv: 2507.12198 · arxiv_version: 2507.12198v1 · doi: 10.48550/arxiv.2507.12198 · pith_short_12: CMVB5MYKEOLL · pith_short_16: CMVB5MYKEOLL3ZAU · pith_short_8: CMVB5MYK

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/CMVB5MYKEOLL3ZAUH5RDHRIQ7E \
  | 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: 132a1eb30a2396bde4143f6233c510f9169de3ec20937cf5b7f84025f08fc95b

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "4aa49c7a126d0dd4c5601e8383aac1991d9f675305144ee95f27b9d5a940cadb",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AG",
    "submitted_at": "2025-07-16T12:54:21Z",
    "title_canon_sha256": "7d3aa160cbb197112edfaa2421b73b3356ad48cff8d1260b609901f5c9268ed5"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2507.12198",
    "kind": "arxiv",
    "version": 1
  }
}