Pith Number

pith:D5UWX77O

pith:2025:D5UWX77OVC64WUJ2CDI575ELP5

not attested not anchored not stored refs pending

$P$-trivial MMP, Zariski decompositions and minimal models for generalised pairs

Zhengyu Hu

arxiv:2501.07551 v1 · 2025-01-13 · 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{D5UWX77OVC64WUJ2CDI575ELP5}

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

On the minimal model theory for generalized pairs of relative log numerical dimension zero

Receipt and verification

First computed	2026-07-05T10:00:30.036359Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

1f696bffeea8bdcb513a10d1dff48b7f739ee363fe78c8e5d94dc1781819bf30

Aliases

arxiv: 2501.07551 · arxiv_version: 2501.07551v1 · doi: 10.48550/arxiv.2501.07551 · pith_short_12: D5UWX77OVC64 · pith_short_16: D5UWX77OVC64WUJ2 · pith_short_8: D5UWX77O

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/D5UWX77OVC64WUJ2CDI575ELP5 \
  | 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: 1f696bffeea8bdcb513a10d1dff48b7f739ee363fe78c8e5d94dc1781819bf30

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "85ef417dbe881629743d41f30ae9798aa95bb90698a930a3b8d7113a8ce4a591",
    "cross_cats_sorted": [],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "math.AG",
    "submitted_at": "2025-01-13T18:36:42Z",
    "title_canon_sha256": "2cde677a8dd66a16369f24c331deef77a320cfc7cb32baba68175b0001f4c156"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2501.07551",
    "kind": "arxiv",
    "version": 1
  }
}