Pith Number

pith:PLXX7GDL

pith:2007:PLXX7GDL7WWJNTKKH42VVC7BCN

not attested not anchored not stored refs pending

Disproof of modularity of moduli space of CY 3-folds of double covers of P3 ramified along eight planes in general positions

Kang Zuo, Ralf Gerkmann, Sheng Mao

arxiv:0709.1051 v1 · 2007-09-07 · 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{PLXX7GDL7WWJNTKKH42VVC7BCN}

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	2026-07-04T15:04:05.349780Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

7aef7f986bfdac96cd4a3f355a8be1136637032f092df82ca62442a2504a23d0

Aliases

arxiv: 0709.1051 · arxiv_version: 0709.1051v1 · doi: 10.48550/arxiv.0709.1051 · pith_short_12: PLXX7GDL7WWJ · pith_short_16: PLXX7GDL7WWJNTKK · pith_short_8: PLXX7GDL

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/PLXX7GDL7WWJNTKKH42VVC7BCN \
  | 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: 7aef7f986bfdac96cd4a3f355a8be1136637032f092df82ca62442a2504a23d0

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "2cbc207b5d3622633a8c67ef008af2e9a05687baa18cafbc25bad0b53d875de4",
    "cross_cats_sorted": [],
    "license": "",
    "primary_cat": "math.AG",
    "submitted_at": "2007-09-07T11:29:05Z",
    "title_canon_sha256": "b87b94f58cd249f9ce213a254f2bf1c639a23670ddf684daa1865393f5719c84"
  },
  "schema_version": "1.0",
  "source": {
    "id": "0709.1051",
    "kind": "arxiv",
    "version": 1
  }
}