Pith Number

pith:2ETVNU3M

pith:2018:2ETVNU3MG2QO22AFKKQ62ZQWWU

not attested not anchored not stored refs pending

Toric Fano contractions associated to long extremal rays

Hiroshi Sato, Osamu Fujino

arxiv:1804.05302 v2 · 2018-04-15 · 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{2ETVNU3MG2QO22AFKKQ62ZQWWU}

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	2026-05-18T00:07:55.202217Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

d12756d36c36a0ed680552a1ed6616b52d001a34740b3a04f0a004012bc0a733

Aliases

arxiv: 1804.05302 · arxiv_version: 1804.05302v2 · doi: 10.48550/arxiv.1804.05302 · pith_short_12: 2ETVNU3MG2QO · pith_short_16: 2ETVNU3MG2QO22AF · pith_short_8: 2ETVNU3M

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/2ETVNU3MG2QO22AFKKQ62ZQWWU \
  | 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: d12756d36c36a0ed680552a1ed6616b52d001a34740b3a04f0a004012bc0a733

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "043bb13dc67d0fbf7fc0a5d5f9cd6fdc26e11e00c8cc08926e53b671bbc670ab",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AG",
    "submitted_at": "2018-04-15T03:59:01Z",
    "title_canon_sha256": "a0ead92aea24833f5df483b7232e8b63133d6b883cbaa7447e77bc7e3fe3b647"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1804.05302",
    "kind": "arxiv",
    "version": 2
  }
}