Pith Number

pith:WPKOKPVD

pith:2007:WPKOKPVD5KIUUTPQWFWFPAQXPB

not attested not anchored not stored refs pending

A class function on the mapping class group of an orientable surface and the Meyer cocycle

Masatoshi Sato

arxiv:0712.4060 v1 · 2007-12-25 · math.GT

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{WPKOKPVD5KIUUTPQWFWFPAQXPB}

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	2026-05-18T01:22:31.139247Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

b3d4e53ea3ea914a4df0b16c5782177857f357b8587de6deea8bf684d2868b65

Aliases

arxiv: 0712.4060 · arxiv_version: 0712.4060v1 · doi: 10.48550/arxiv.0712.4060 · pith_short_12: WPKOKPVD5KIU · pith_short_16: WPKOKPVD5KIUUTPQ · pith_short_8: WPKOKPVD

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/WPKOKPVD5KIUUTPQWFWFPAQXPB \
  | 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: b3d4e53ea3ea914a4df0b16c5782177857f357b8587de6deea8bf684d2868b65

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "d3253c2b202ebe34b7714f1f10c57f107f2459efa0306bf92f54b02dff6a9e4c",
    "cross_cats_sorted": [],
    "license": "",
    "primary_cat": "math.GT",
    "submitted_at": "2007-12-25T11:32:14Z",
    "title_canon_sha256": "669c27aa64fef2a38b7a7a6fd6265a58c0ad55e783d302575b9e978dbf478885"
  },
  "schema_version": "1.0",
  "source": {
    "id": "0712.4060",
    "kind": "arxiv",
    "version": 1
  }
}