Pith Number

pith:XJK2ZIY6

pith:2019:XJK2ZIY6QLZR44TFEAR5CUSUWC

not attested not anchored not stored refs pending

ACC for minimal log discrepancies of exceptional singularities

Jihao Liu, Jingjun Han, V. V. Shokurov

arxiv:1903.04338 v2 · 2019-03-11 · 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{XJK2ZIY6QLZR44TFEAR5CUSUWC}

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

Discreteness of volumes of divisors on Calabi-Yau type varieties

Receipt and verification

First computed	2026-07-05T00:45:50.629953Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

ba55aca31e82f31e72652023d15254b0a95c2005dc43e935d45c44586563a2a4

Aliases

arxiv: 1903.04338 · arxiv_version: 1903.04338v2 · doi: 10.48550/arxiv.1903.04338 · pith_short_12: XJK2ZIY6QLZR · pith_short_16: XJK2ZIY6QLZR44TF · pith_short_8: XJK2ZIY6

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/XJK2ZIY6QLZR44TFEAR5CUSUWC \
  | 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: ba55aca31e82f31e72652023d15254b0a95c2005dc43e935d45c44586563a2a4

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "6fa18b1560eb15d8b174cd1a23142309d121df929512aa0c8ac48c238232a44b",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AG",
    "submitted_at": "2019-03-11T14:49:11Z",
    "title_canon_sha256": "84e40e8989b7db9f9f43466a9e3e18779a3a4b25dfd68e5abc8b8db161e34d13"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1903.04338",
    "kind": "arxiv",
    "version": 2
  }
}