Pith Number

pith:YIV7VBJO

pith:2010:YIV7VBJOPFYLUFZ7XZKFLC7XHJ

not attested not anchored not stored refs pending

Threefold extremal contractions of type IA

Shigefumi Mori, Yuri Prokhorov

arxiv:1004.4188 v1 · 2010-04-23 · 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{YIV7VBJOPFYLUFZ7XZKFLC7XHJ}

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	2026-05-18T04:18:46.274022Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

c22bfa852e7970ba173fbe54558bf73a465cd6d7d1217c44a6d6765c4fd7f169

Aliases

arxiv: 1004.4188 · arxiv_version: 1004.4188v1 · doi: 10.48550/arxiv.1004.4188 · pith_short_12: YIV7VBJOPFYL · pith_short_16: YIV7VBJOPFYLUFZ7 · pith_short_8: YIV7VBJO

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/YIV7VBJOPFYLUFZ7XZKFLC7XHJ \
  | 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: c22bfa852e7970ba173fbe54558bf73a465cd6d7d1217c44a6d6765c4fd7f169

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "0f73b24a96420f49e3420db3846be6ab7c4ada56996e403a1e6c770042020e50",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AG",
    "submitted_at": "2010-04-23T17:30:26Z",
    "title_canon_sha256": "07265d8e18b79bf881ef11bb45d63b194bbabf9c37b8af49a3fd623b55fb1ffa"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1004.4188",
    "kind": "arxiv",
    "version": 1
  }
}