Pith Number

pith:KONMFOUJ

pith:2012:KONMFOUJGTA4LIA3MXKBARQNCA

not attested not anchored not stored refs pending

Some Categorical Representations of the Modular Group

Benjamin Cooper

arxiv:1209.2358 v4 · 2012-09-11 · math.QA · 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{KONMFOUJGTA4LIA3MXKBARQNCA}

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	2026-05-18T02:32:22.736276Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

539ac2ba8934c1c5a01b65d410460d102bb2226d56a10dea056667c3a084da6e

Aliases

arxiv: 1209.2358 · arxiv_version: 1209.2358v4 · doi: 10.48550/arxiv.1209.2358 · pith_short_12: KONMFOUJGTA4 · pith_short_16: KONMFOUJGTA4LIA3 · pith_short_8: KONMFOUJ

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/KONMFOUJGTA4LIA3MXKBARQNCA \
  | 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: 539ac2ba8934c1c5a01b65d410460d102bb2226d56a10dea056667c3a084da6e

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "0e51b041a929970b9cfd6f8169a00610c2f87f68b031925fa905d3e53ba6461e",
    "cross_cats_sorted": [
      "math.GT"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.QA",
    "submitted_at": "2012-09-11T16:09:25Z",
    "title_canon_sha256": "1782672be2c28e3426cc1085774cb7e0e9a000edf2e046b7469f1643d79229e3"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1209.2358",
    "kind": "arxiv",
    "version": 4
  }
}