Pith Number

pith:KSOFEU3E

pith:2009:KSOFEU3EZMIOAFWLWRFVTNPSED

not attested not anchored not stored refs pending

Fukaya A_\infty structures associated to Lefschetz fibrations. I

Paul Seidel

arxiv:0912.3932 v3 · 2009-12-19 · 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{KSOFEU3EZMIOAFWLWRFVTNPSED}

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	2026-05-18T01:21:14.315473Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

549c525364cb10e016cbb44b59b5f220d09ab53806319dcbac897eed2fc56616

Aliases

arxiv: 0912.3932 · arxiv_version: 0912.3932v3 · doi: 10.48550/arxiv.0912.3932 · pith_short_12: KSOFEU3EZMIO · pith_short_16: KSOFEU3EZMIOAFWL · pith_short_8: KSOFEU3E

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/KSOFEU3EZMIOAFWLWRFVTNPSED \
  | 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: 549c525364cb10e016cbb44b59b5f220d09ab53806319dcbac897eed2fc56616

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "c371ed4fb97140503f3b776086303be11fbf5b7d4a5d8b71ebc3894d737705ea",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.SG",
    "submitted_at": "2009-12-19T20:29:30Z",
    "title_canon_sha256": "bf883def38d0fd903b1afedf01d42345855a01b0e2b7051b4c4dc96ffe87f294"
  },
  "schema_version": "1.0",
  "source": {
    "id": "0912.3932",
    "kind": "arxiv",
    "version": 3
  }
}