Pith Number

pith:XWPC3Y3G

pith:2009:XWPC3Y3G5VVYJPSDPXE57QTV2P

not attested not anchored not stored refs pending

Fundamental theorems for the log minimal model program

Osamu Fujino

arxiv:0909.4445 v3 · 2009-09-24 · 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{XWPC3Y3G5VVYJPSDPXE57QTV2P}

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	2026-05-18T04:42:13.798483Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

bd9e2de366ed6b84be437dc9dfc275d3d6b0bba3a6335d2b7fd665979af88d16

Aliases

arxiv: 0909.4445 · arxiv_version: 0909.4445v3 · doi: 10.48550/arxiv.0909.4445 · pith_short_12: XWPC3Y3G5VVY · pith_short_16: XWPC3Y3G5VVYJPSD · pith_short_8: XWPC3Y3G

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/XWPC3Y3G5VVYJPSDPXE57QTV2P \
  | 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: bd9e2de366ed6b84be437dc9dfc275d3d6b0bba3a6335d2b7fd665979af88d16

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "c473d702316dcaedc4f5fd0439f891da289fefc25ce31794d1bca865db8ea5a4",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AG",
    "submitted_at": "2009-09-24T13:52:42Z",
    "title_canon_sha256": "2e426e2a2582e45b93eff4fae5cd0cabfadfe6f20693b2752b7f8d9859d4fa9d"
  },
  "schema_version": "1.0",
  "source": {
    "id": "0909.4445",
    "kind": "arxiv",
    "version": 3
  }
}