Pith Number

pith:BLPNRIUZ

pith:2011:BLPNRIUZX54Y7N6WRC4XW6GEO4

not attested not anchored not stored refs pending

Adequate Subgroups II

Robert Guralnick

arxiv:1112.4561 v1 · 2011-12-20 · math.RT · math.GR · math.NT

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{BLPNRIUZX54Y7N6WRC4XW6GEO4}

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	2026-05-18T04:05:58.522838Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

0aded8a299bf798fb7d688b97b78c4773b72ef0efa67f448a61b6ee16afe1b9b

Aliases

arxiv: 1112.4561 · arxiv_version: 1112.4561v1 · doi: 10.48550/arxiv.1112.4561 · pith_short_12: BLPNRIUZX54Y · pith_short_16: BLPNRIUZX54Y7N6W · pith_short_8: BLPNRIUZ

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/BLPNRIUZX54Y7N6WRC4XW6GEO4 \
  | 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: 0aded8a299bf798fb7d688b97b78c4773b72ef0efa67f448a61b6ee16afe1b9b

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "eaf5d99fa71dc9fa3886c4ee11d87e7ef27f060a48433e1e6fa9ee342f405ed5",
    "cross_cats_sorted": [
      "math.GR",
      "math.NT"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.RT",
    "submitted_at": "2011-12-20T04:01:22Z",
    "title_canon_sha256": "09b8324aa9106a869eb1bdc482ec0cdb2499d5d72f23b5eabcf0a71db799fcb4"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1112.4561",
    "kind": "arxiv",
    "version": 1
  }
}