Pith Number

pith:M2N4L64J

pith:2012:M2N4L64J6WWVUNPVXMG3Z67JUX

not attested not anchored not stored refs pending

Sporadic simple groups and quotient singularities

Constantin Shramov, Ivan Cheltsov

arxiv:1207.2227 v2 · 2012-07-10 · math.AG · math.GR

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{M2N4L64J6WWVUNPVXMG3Z67JUX}

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	2026-05-18T01:56:26.106052Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

669bc5fb89f5ad5a35f5bb0dbcfbe9a5f210398b3af29fcd2c48f8e585e1f1dd

Aliases

arxiv: 1207.2227 · arxiv_version: 1207.2227v2 · doi: 10.48550/arxiv.1207.2227 · pith_short_12: M2N4L64J6WWV · pith_short_16: M2N4L64J6WWVUNPV · pith_short_8: M2N4L64J

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/M2N4L64J6WWVUNPVXMG3Z67JUX \
  | 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: 669bc5fb89f5ad5a35f5bb0dbcfbe9a5f210398b3af29fcd2c48f8e585e1f1dd

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "d9d894bf2f386cf8241b66236403283cd75c93bd1deefc935b6d1d278539dbeb",
    "cross_cats_sorted": [
      "math.GR"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AG",
    "submitted_at": "2012-07-10T06:13:52Z",
    "title_canon_sha256": "2fda21d31f516fab9adcb0818461908562b48d9482dfa6aabdfd863381c67f6a"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1207.2227",
    "kind": "arxiv",
    "version": 2
  }
}