Pith Number

pith:RE6WMPVP

pith:2000:RE6WMPVPM6DVYPTHGFH3G3LVFH

not attested not anchored not stored refs pending

Lefschetz fibrations on compact Stein surfaces

Burak Ozbagci, Selman Akbulut

arxiv:math/0012239 v4 · 2000-12-22 · math.GT · 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{RE6WMPVPM6DVYPTHGFH3G3LVFH}

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	2026-05-18T02:32:46.730652Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

893d663eaf67875c3e67314fb36d7529f3b32e277dd9224e3c63d1bb2ea3e50b

Aliases

arxiv: math/0012239 · arxiv_version: math/0012239v4 · doi: 10.48550/arxiv.math/0012239 · pith_short_12: RE6WMPVPM6DV · pith_short_16: RE6WMPVPM6DVYPTH · pith_short_8: RE6WMPVP

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/RE6WMPVPM6DVYPTHGFH3G3LVFH \
  | 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: 893d663eaf67875c3e67314fb36d7529f3b32e277dd9224e3c63d1bb2ea3e50b

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "983c0b97cfa0360fdf4ee3b0062f9886e47248bcc182ca72a1e2e862e9fd74e1",
    "cross_cats_sorted": [
      "math.AG"
    ],
    "license": "",
    "primary_cat": "math.GT",
    "submitted_at": "2000-12-22T17:46:27Z",
    "title_canon_sha256": "56c0170c2fd4767f7325c88bb861904745e00f04447dd0ac2fe27ce751db152a"
  },
  "schema_version": "1.0",
  "source": {
    "id": "math/0012239",
    "kind": "arxiv",
    "version": 4
  }
}