Pith Number

pith:YZEPFFGD

pith:2007:YZEPFFGDHPCTIM3EMIOVPNM3JL

not attested not anchored not stored refs pending

Lefschetz fibrations, intersection numbers, and representations of the framed braid group

Alexandru Oancea, Dietmar A. Salamon, Gwenael Massuyeau

arxiv:0708.2051 v5 · 2007-08-15 · math.GT · 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{YZEPFFGDHPCTIM3EMIOVPNM3JL}

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	2026-05-18T03:03:33.245798Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

c648f294c33bc5343364621d57b59b4af2a4919b188dbc56db9c3950b5cb1979

Aliases

arxiv: 0708.2051 · arxiv_version: 0708.2051v5 · doi: 10.48550/arxiv.0708.2051 · pith_short_12: YZEPFFGDHPCT · pith_short_16: YZEPFFGDHPCTIM3E · pith_short_8: YZEPFFGD

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/YZEPFFGDHPCTIM3EMIOVPNM3JL \
  | 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: c648f294c33bc5343364621d57b59b4af2a4919b188dbc56db9c3950b5cb1979

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "cf6761a444a65c798637ebfc9901bdb377cf5ea477d0e7b17eb025d049f0dec9",
    "cross_cats_sorted": [
      "math.SG"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.GT",
    "submitted_at": "2007-08-15T13:52:08Z",
    "title_canon_sha256": "97f3733e4faa49ce4df8f64c400c0444eb84df0511ae4f6df0bcd0dda22da870"
  },
  "schema_version": "1.0",
  "source": {
    "id": "0708.2051",
    "kind": "arxiv",
    "version": 5
  }
}