Pith Number

pith:VRVDYEC6

pith:2003:VRVDYEC6ET2QQ33F6M6JVPS3Z3

not attested not anchored not stored refs pending

Introduction to the toric Mori theory

Hiroshi Sato, Osamu Fujino

arxiv:math/0307180 v2 · 2003-07-12 · 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{VRVDYEC6ET2QQ33F6M6JVPS3Z3}

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	2026-05-18T01:05:28.753966Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

ac6a3c105e24f5086f65f33c9abe5bcecfbb37a570bd7ca0fa1bddce01d0a365

Aliases

arxiv: math/0307180 · arxiv_version: math/0307180v2 · doi: 10.48550/arxiv.math/0307180 · pith_short_12: VRVDYEC6ET2Q · pith_short_16: VRVDYEC6ET2QQ33F · pith_short_8: VRVDYEC6

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/VRVDYEC6ET2QQ33F6M6JVPS3Z3 \
  | 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: ac6a3c105e24f5086f65f33c9abe5bcecfbb37a570bd7ca0fa1bddce01d0a365

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "39500f76966763d4cfa686e4f6a5081874a935eb579d71669524ce89038bf8b3",
    "cross_cats_sorted": [],
    "license": "",
    "primary_cat": "math.AG",
    "submitted_at": "2003-07-12T12:22:00Z",
    "title_canon_sha256": "da4718c14d1387623d1635b45957a8d6e1ac8d129b97aacd881c3e15d808e5f8"
  },
  "schema_version": "1.0",
  "source": {
    "id": "math/0307180",
    "kind": "arxiv",
    "version": 2
  }
}