Pith Number

pith:4QI4ZDLL

pith:2013:4QI4ZDLLJDW5K7LADDVDIOAP72

not attested not anchored not stored refs pending

The subadditivity of the Kodaira Dimension for Fibrations of Relative Dimension One in Positive Characteristics

Lei Zhang, Yifei Chen

arxiv:1305.6024 v1 · 2013-05-26 · 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{4QI4ZDLLJDW5K7LADDVDIOAP72}

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

Pseudo-effectivity of the relative canonical divisor and uniruledness in positive characteristic

Receipt and verification

First computed	2026-05-18T03:24:53.133025Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

e411cc8d6b48edd57d6018ea34380ffe9d6a575478ba17963ccf52bfe7520254

Aliases

arxiv: 1305.6024 · arxiv_version: 1305.6024v1 · doi: 10.48550/arxiv.1305.6024 · pith_short_12: 4QI4ZDLLJDW5 · pith_short_16: 4QI4ZDLLJDW5K7LA · pith_short_8: 4QI4ZDLL

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/4QI4ZDLLJDW5K7LADDVDIOAP72 \
  | 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: e411cc8d6b48edd57d6018ea34380ffe9d6a575478ba17963ccf52bfe7520254

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "38a77bd06491411d5e66c4ef51497e6d624037cc02dd2ffe7d8108e0439134e3",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AG",
    "submitted_at": "2013-05-26T14:07:31Z",
    "title_canon_sha256": "fc0cd3a012e00287b18c4c8731278eea8b92c90ce4645815264aee67132a3e4e"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1305.6024",
    "kind": "arxiv",
    "version": 1
  }
}