Pith Number

pith:Z3O5V2FS

pith:2014:Z3O5V2FSFYTNYTNKKCRONDARPN

not attested not anchored not stored refs pending

On the minimal number of singular fibers with non-compact Jacobians for families of curves over $\mathbb P^1$

Kang Zuo, Sheng-Li Tan, Wan-Yuan Xu, Xin Lu

arxiv:1409.6593 v1 · 2014-09-23 · 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{Z3O5V2FSFYTNYTNKKCRONDARPN}

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	2026-05-18T01:17:44.267607Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

cedddae8b22e26dc4daa50a2e68c117b6756767a8caa77e5178e9982e4717757

Aliases

arxiv: 1409.6593 · arxiv_version: 1409.6593v1 · doi: 10.48550/arxiv.1409.6593 · pith_short_12: Z3O5V2FSFYTN · pith_short_16: Z3O5V2FSFYTNYTNK · pith_short_8: Z3O5V2FS

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/Z3O5V2FSFYTNYTNKKCRONDARPN \
  | 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: cedddae8b22e26dc4daa50a2e68c117b6756767a8caa77e5178e9982e4717757

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "054e7698ce335f93543c2a30760b93c2382b782a1894256868b378745daf0b2c",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AG",
    "submitted_at": "2014-09-23T15:24:22Z",
    "title_canon_sha256": "e883b2c99ef1720296cc8e534d6426eb9c75dd882165cfb9318604150700dbc6"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1409.6593",
    "kind": "arxiv",
    "version": 1
  }
}