Pith Number

pith:MU3ONQW2

pith:2009:MU3ONQW2XGDG3L2WKZA43NVGSO

not attested not anchored not stored refs pending

Exotic symplectic manifolds from Lefschetz fibrations

Maksim Maydanskiy

arxiv:0906.2224 v2 · 2009-06-11 · 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{MU3ONQW2XGDG3L2WKZA43NVGSO}

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	2026-05-18T03:41:56.812836Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

6536e6c2dab9866daf565641cdb6a693892ec3882a5148b756ea299253597e11

Aliases

arxiv: 0906.2224 · arxiv_version: 0906.2224v2 · doi: 10.48550/arxiv.0906.2224 · pith_short_12: MU3ONQW2XGDG · pith_short_16: MU3ONQW2XGDG3L2W · pith_short_8: MU3ONQW2

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/MU3ONQW2XGDG3L2WKZA43NVGSO \
  | 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: 6536e6c2dab9866daf565641cdb6a693892ec3882a5148b756ea299253597e11

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "27afb09973857ed53f18fabcf48e7a2a3dabc4adb73c68beab8f2d5d13d8d115",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.SG",
    "submitted_at": "2009-06-11T22:41:59Z",
    "title_canon_sha256": "3efefa418c2db48e40e78ef2a8821e155ffea3469e2afae213117f3bb4d558fc"
  },
  "schema_version": "1.0",
  "source": {
    "id": "0906.2224",
    "kind": "arxiv",
    "version": 2
  }
}