Pith Number

pith:76H3E7OZ

pith:2010:76H3E7OZAYBVCFDZFCZQMFYMR2

not attested not anchored not stored refs pending

Lagrangian spheres, symplectic surfaces and the symplectic mapping class group

Tian-Jun Li, WeiWei Wu

arxiv:1012.4146 v2 · 2010-12-19 · 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{76H3E7OZAYBVCFDZFCZQMFYMR2}

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	2026-05-18T01:22:29.147598Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

ff8fb27dd9060351147928b306170c8ea5dccbe95236c627ecfe420bad534e55

Aliases

arxiv: 1012.4146 · arxiv_version: 1012.4146v2 · doi: 10.48550/arxiv.1012.4146 · pith_short_12: 76H3E7OZAYBV · pith_short_16: 76H3E7OZAYBVCFDZ · pith_short_8: 76H3E7OZ

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/76H3E7OZAYBVCFDZFCZQMFYMR2 \
  | 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: ff8fb27dd9060351147928b306170c8ea5dccbe95236c627ecfe420bad534e55

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "8828f75926520c725155ccd5b258166f652d6f40e31d0d045cb1aa709f7ed837",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.SG",
    "submitted_at": "2010-12-19T05:18:12Z",
    "title_canon_sha256": "90d8a752cbad8700a5295da7fec9a43c5b703a2aebb49c0ecc1011c4c7915a5d"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1012.4146",
    "kind": "arxiv",
    "version": 2
  }
}