Pith Number

pith:E7OCKU3E

pith:2026:E7OCKU3E3IVHNZBQZCIZVXIHDO

not attested not anchored not stored refs pending

Quasi-$F$-singularities and singularities in birational geometry

Shou Yoshikawa, Shunsuke Takagi, Tatsuro Kawakami

arxiv:2606.31666 v1 · 2026-06-30 · math.AG · math.AC

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{E7OCKU3E3IVHNZBQZCIZVXIHDO}

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	2026-07-01T01:18:11.052510Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

27dc255364da2a76e430c8919add071b9d030634d984db50301a5ea6cba5f5bd

Aliases

arxiv: 2606.31666 · arxiv_version: 2606.31666v1 · doi: 10.48550/arxiv.2606.31666 · pith_short_12: E7OCKU3E3IVH · pith_short_16: E7OCKU3E3IVHNZBQ · pith_short_8: E7OCKU3E

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/E7OCKU3E3IVHNZBQZCIZVXIHDO \
  | 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: 27dc255364da2a76e430c8919add071b9d030634d984db50301a5ea6cba5f5bd

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "cccd914d2d3893db4a64fe00f24476b1268a7971eef4a521d55d1c493dfd3613",
    "cross_cats_sorted": [
      "math.AC"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AG",
    "submitted_at": "2026-06-30T13:46:05Z",
    "title_canon_sha256": "97058296f100024dbbe8b74152d110e0b4f3d4dc6d909427709521c70ae6329e"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2606.31666",
    "kind": "arxiv",
    "version": 1
  }
}