Pith Number

pith:TCE4MF3U

pith:2018:TCE4MF3UFBMOM4PIIK7JCAJ6YH

not attested not anchored not stored refs pending

Nonvanishing for threefolds in characteristic $p>5$

Chenyang Xu, Lei Zhang

arxiv:1801.03192 v3 · 2018-01-09 · 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{TCE4MF3UFBMOM4PIIK7JCAJ6YH}

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 threefolds in positive characteristic when $\nu=2$

Receipt and verification

First computed	2026-05-17T23:44:59.873459Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

9889c617742858e671e842be91013ec1c7e5540022027d95a4c889a36cf62d72

Aliases

arxiv: 1801.03192 · arxiv_version: 1801.03192v3 · doi: 10.48550/arxiv.1801.03192 · pith_short_12: TCE4MF3UFBMO · pith_short_16: TCE4MF3UFBMOM4PI · pith_short_8: TCE4MF3U

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/TCE4MF3UFBMOM4PIIK7JCAJ6YH \
  | 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: 9889c617742858e671e842be91013ec1c7e5540022027d95a4c889a36cf62d72

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "3aedf26b8fc53056e9c92251be06c7258e8e466cedf919a8d69720a83592f678",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AG",
    "submitted_at": "2018-01-09T23:50:19Z",
    "title_canon_sha256": "afe03103190cfa9e20d6d9e12cc37f33582de5c9d10d17271b57ca903cd55d03"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1801.03192",
    "kind": "arxiv",
    "version": 3
  }
}