Pith Number

pith:PR2LHU5B

pith:2014:PR2LHU5BMPNPK3CIBQPXUPJODW

not attested not anchored not stored refs pending

Existence of Lefschetz fibrations on Stein and Weinstein domains

Emmanuel Giroux, John Pardon

arxiv:1411.6176 v3 · 2014-11-22 · math.SG · math.CV

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{PR2LHU5BMPNPK3CIBQPXUPJODW}

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	2026-05-18T00:47:51.463749Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

7c74b3d3a163daf56c480c1f7a3d2e1dbd731c8ae1ba5e070bf791367aad8e10

Aliases

arxiv: 1411.6176 · arxiv_version: 1411.6176v3 · doi: 10.48550/arxiv.1411.6176 · pith_short_12: PR2LHU5BMPNP · pith_short_16: PR2LHU5BMPNPK3CI · pith_short_8: PR2LHU5B

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/PR2LHU5BMPNPK3CIBQPXUPJODW \
  | 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: 7c74b3d3a163daf56c480c1f7a3d2e1dbd731c8ae1ba5e070bf791367aad8e10

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "59b1b87baae76fa4ba4c2a3a1d557dbcea22e58ed8da65325254d991fffa8aee",
    "cross_cats_sorted": [
      "math.CV"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.SG",
    "submitted_at": "2014-11-22T22:34:47Z",
    "title_canon_sha256": "d3290f4d57bdf1e466a08b80620bcda75cb35f748a4a68d046f32357ee6aab6a"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1411.6176",
    "kind": "arxiv",
    "version": 3
  }
}