Pith Number

pith:LCTOLYAI

pith:2009:LCTOLYAIVW6KTUZCVFW4JM4IMM

not attested not anchored not stored refs pending

Displacing Lagrangian toric fibers via probes

Dusa McDuff

arxiv:0904.1686 v4 · 2009-04-10 · math.SG · math.AG · math.CO

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{LCTOLYAIVW6KTUZCVFW4JM4IMM}

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	2026-05-18T04:17:03.571823Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

58a6e5e008adbca9d322a96dc4b3886304a8d9e2907d24e778a3fe9566cda0bb

Aliases

arxiv: 0904.1686 · arxiv_version: 0904.1686v4 · doi: 10.48550/arxiv.0904.1686 · pith_short_12: LCTOLYAIVW6K · pith_short_16: LCTOLYAIVW6KTUZC · pith_short_8: LCTOLYAI

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/LCTOLYAIVW6KTUZCVFW4JM4IMM \
  | 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: 58a6e5e008adbca9d322a96dc4b3886304a8d9e2907d24e778a3fe9566cda0bb

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "141657b8672b16c0b0ff08741c44a06f19c9256c97f5b8f8d5e3b004fca49843",
    "cross_cats_sorted": [
      "math.AG",
      "math.CO"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.SG",
    "submitted_at": "2009-04-10T13:19:32Z",
    "title_canon_sha256": "7446a9d3831dcd0e35f86339e49095a94a048e99a81953cd2269540c9d1c5b26"
  },
  "schema_version": "1.0",
  "source": {
    "id": "0904.1686",
    "kind": "arxiv",
    "version": 4
  }
}