Pith Number

pith:WPRR5RR3

pith:2019:WPRR5RR353MLAHHHLLUGV77DUY

not attested not anchored not stored refs pending

On minimal model theory for log abundant lc pairs

Kenta Hashizume, Zhengyu Hu

arxiv:1906.00769 v4 · 2019-06-03 · 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{WPRR5RR353MLAHHHLLUGV77DUY}

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

Abundance for uniruled pairs which are not rationally connected

Receipt and verification

First computed	2026-07-05T00:00:15.606137Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

b3e31ec63beed8b01ce75ae86affe3a62cb7753ce9049e2aacb30d586f5fd199

Aliases

arxiv: 1906.00769 · arxiv_version: 1906.00769v4 · doi: 10.48550/arxiv.1906.00769 · pith_short_12: WPRR5RR353ML · pith_short_16: WPRR5RR353MLAHHH · pith_short_8: WPRR5RR3

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/WPRR5RR353MLAHHHLLUGV77DUY \
  | 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: b3e31ec63beed8b01ce75ae86affe3a62cb7753ce9049e2aacb30d586f5fd199

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "013607f80db3a2c21516b7cbc14012a67a5a90f0ef47c23123c6315ad17c000f",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AG",
    "submitted_at": "2019-06-03T13:03:18Z",
    "title_canon_sha256": "f3e14f4dd1cbb7a6b2ef0994884fb7e02694717fa531ef219e024568538a7b61"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1906.00769",
    "kind": "arxiv",
    "version": 4
  }
}