Pith Number

pith:DDXL3BOG

pith:1999:DDXL3BOGWLLLQMQAR5CMBKBXKB

not attested not anchored not stored refs pending

A GIT proof of W{\l}odarczyk's weighted factorization theorem

Sean Keel, Yi Hu

arxiv:math/9904146 v1 · 1999-04-26 · 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{DDXL3BOGWLLLQMQAR5CMBKBXKB}

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	2026-07-04T14:41:07.873529Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

18eebd85c6b2d6b832008f44c0a837507ae4914b922753d2209ff0f273aae2bf

Aliases

arxiv: math/9904146 · arxiv_version: math/9904146v1 · doi: 10.48550/arxiv.math/9904146 · pith_short_12: DDXL3BOGWLLL · pith_short_16: DDXL3BOGWLLLQMQA · pith_short_8: DDXL3BOG

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/DDXL3BOGWLLLQMQAR5CMBKBXKB \
  | 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: 18eebd85c6b2d6b832008f44c0a837507ae4914b922753d2209ff0f273aae2bf

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "6f7723486e8426050021a910484ba7c10e67d56c88596ad2242bab0a676ff2e6",
    "cross_cats_sorted": [],
    "license": "",
    "primary_cat": "math.AG",
    "submitted_at": "1999-04-26T15:16:43Z",
    "title_canon_sha256": "6d9fe122a9751278413edce85b09881bf01f0083c9122fe8922f4b24425bbc7d"
  },
  "schema_version": "1.0",
  "source": {
    "id": "math/9904146",
    "kind": "arxiv",
    "version": 1
  }
}