Pith Number

pith:MCSDWHIJ

pith:2014:MCSDWHIJLH7JM2CGOLP6CEARDW

not attested not anchored not stored refs pending

Frattini and related subgroups of Mapping Class Groups

A. W. Reid, G. Masbaum

arxiv:1412.3366 v2 · 2014-12-10 · math.GT · 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{MCSDWHIJLH7JM2CGOLP6CEARDW}

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	2026-05-18T02:27:58.389143Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

60a43b1d0959fe96684672dfe110111da49978145fbd9b03c8d937fef9821bf0

Aliases

arxiv: 1412.3366 · arxiv_version: 1412.3366v2 · doi: 10.48550/arxiv.1412.3366 · pith_short_12: MCSDWHIJLH7J · pith_short_16: MCSDWHIJLH7JM2CG · pith_short_8: MCSDWHIJ

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/MCSDWHIJLH7JM2CGOLP6CEARDW \
  | 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: 60a43b1d0959fe96684672dfe110111da49978145fbd9b03c8d937fef9821bf0

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "1eac35ad083b39a6c3809f04e40ef4c7ea6bc3d780fa6f88e3df2b6ac0288aa4",
    "cross_cats_sorted": [
      "math.GR"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.GT",
    "submitted_at": "2014-12-10T16:54:03Z",
    "title_canon_sha256": "01f43c3623d2b64803a84bc8b153b907295930f0029d68533f7f9459df296ab1"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1412.3366",
    "kind": "arxiv",
    "version": 2
  }
}