Pith Number

pith:2YPNP4XL

pith:2012:2YPNP4XLTQEL4VKCSQIGZ6W4ZY

not attested not anchored not stored refs pending

P1-bundles over projective manifolds of Picard number one each of which admit another smooth morphism of relative dimension one

Kiwamu Watanabe

arxiv:1201.3558 v3 · 2012-01-17 · 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{2YPNP4XLTQEL4VKCSQIGZ6W4ZY}

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	2026-05-18T03:37:08.892723Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

d61ed7f2eb9c08be554294106cfadcce0262c6a71e2cccc4142fc16386d4747e

Aliases

arxiv: 1201.3558 · arxiv_version: 1201.3558v3 · doi: 10.48550/arxiv.1201.3558 · pith_short_12: 2YPNP4XLTQEL · pith_short_16: 2YPNP4XLTQEL4VKC · pith_short_8: 2YPNP4XL

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/2YPNP4XLTQEL4VKCSQIGZ6W4ZY \
  | 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: d61ed7f2eb9c08be554294106cfadcce0262c6a71e2cccc4142fc16386d4747e

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "14e8ef33a368d70d37e403dd5d0eae19d9be22302943208fa4a9e2e20b50da56",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AG",
    "submitted_at": "2012-01-17T16:53:35Z",
    "title_canon_sha256": "b4bb0f185f23ea672f06afb230da982b693d36eecec929b6bd688ce1573077a8"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1201.3558",
    "kind": "arxiv",
    "version": 3
  }
}