Pith Number

pith:VF4AS3WJ

pith:2019:VF4AS3WJW3PCFCMBOFGILD3Z3X

not attested not anchored not stored refs pending

Fujita-type freeness for quasi-log canonical threefolds

Haidong Liu

arxiv:1902.08581 v1 · 2019-02-21 · 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{VF4AS3WJW3PCFCMBOFGILD3Z3X}

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	2026-05-17T23:52:56.763626Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

a978096ec9b6de228981714c858f79ddf6e6a9660738712636840eb255ff2da3

Aliases

arxiv: 1902.08581 · arxiv_version: 1902.08581v1 · doi: 10.48550/arxiv.1902.08581 · pith_short_12: VF4AS3WJW3PC · pith_short_16: VF4AS3WJW3PCFCMB · pith_short_8: VF4AS3WJ

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/VF4AS3WJW3PCFCMBOFGILD3Z3X \
  | 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: a978096ec9b6de228981714c858f79ddf6e6a9660738712636840eb255ff2da3

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "b50774d653f56bcdcc474e3ee71de97ff8ed1ffdb71958694a4e3375090c009a",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AG",
    "submitted_at": "2019-02-21T07:22:45Z",
    "title_canon_sha256": "5bcbfff9d3f5c7c21d78cb5d1e01f2380acf69eb91ba25b5ffee8fa4ca94496c"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1902.08581",
    "kind": "arxiv",
    "version": 1
  }
}