Pith Number

pith:NRMUNP2Q

pith:2010:NRMUNP2QSV4QQ2UU6LGPAVTTVV

not attested not anchored not stored refs pending

Lefschetz Fibrations on Compact Stein Manifolds

M. Firat Arikan, Selman Akbulut

arxiv:1003.2200 v5 · 2010-03-10 · math.GT · math.AG · math.SG

Open paper page JSON Open Graph Bundle Merged state Verified badge What is a Pith Number?

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{NRMUNP2QSV4QQ2UU6LGPAVTTVV}

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	2026-05-18T00:20:27.994339Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

6c5946bf509579086a94f2ccf05673ad665f411afb6872fa07e889d53a7b9b56

Aliases

arxiv: 1003.2200 · arxiv_version: 1003.2200v5 · doi: 10.48550/arxiv.1003.2200 · pith_short_12: NRMUNP2QSV4Q · pith_short_16: NRMUNP2QSV4QQ2UU · pith_short_8: NRMUNP2Q

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/NRMUNP2QSV4QQ2UU6LGPAVTTVV \
  | 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: 6c5946bf509579086a94f2ccf05673ad665f411afb6872fa07e889d53a7b9b56

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "15c504f19d60f40ffcdf6b4fc815d458d2b6359a2b29fcd5b84f9d224f255273",
    "cross_cats_sorted": [
      "math.AG",
      "math.SG"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.GT",
    "submitted_at": "2010-03-10T20:53:11Z",
    "title_canon_sha256": "54266b431fad7b834d28e6a8000920520dea2c0388334164907ac1bba8a1c8cc"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1003.2200",
    "kind": "arxiv",
    "version": 5
  }
}