Pith Number

pith:3W7C5WV5

pith:2012:3W7C5WV5T4XSHPRHKYH6LMQTKB

not attested not anchored not stored refs pending

An analytic family of representations for the mapping class group of punctured surfaces

Bruno Martelli, Francesco Costantino

arxiv:1210.2666 v1 · 2012-10-09 · math.GT · math.QA · math.RT

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{3W7C5WV5T4XSHPRHKYH6LMQTKB}

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	2026-05-18T02:38:17.611827Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

ddbe2edabd9f2f23be27560fe5b213505d39ae2ed273e7babb06a4b66f9bd871

Aliases

arxiv: 1210.2666 · arxiv_version: 1210.2666v1 · doi: 10.48550/arxiv.1210.2666 · pith_short_12: 3W7C5WV5T4XS · pith_short_16: 3W7C5WV5T4XSHPRH · pith_short_8: 3W7C5WV5

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/3W7C5WV5T4XSHPRHKYH6LMQTKB \
  | 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: ddbe2edabd9f2f23be27560fe5b213505d39ae2ed273e7babb06a4b66f9bd871

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "1af9da0f99c28ec1eb4444b7fa8596231d603601fb6d93f9556d98b3b3d7fc23",
    "cross_cats_sorted": [
      "math.QA",
      "math.RT"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.GT",
    "submitted_at": "2012-10-09T17:05:04Z",
    "title_canon_sha256": "9c0af4b2f9801820758dffc1118571012cd19e5527fcefec4ff0c99799c4f917"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1210.2666",
    "kind": "arxiv",
    "version": 1
  }
}