Pith Number

pith:TMXYYTV4

pith:2015:TMXYYTV4P7WPNGIYPJWC3L72DA

not attested not anchored not stored refs pending

Variants of theorems of Baer and Hall on finite-by-hypercentral groups

Carlo Casolo, Silvana Rinauro, Ulderico Dardano

arxiv:1505.06762 v1 · 2015-05-25 · 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{TMXYYTV4P7WPNGIYPJWC3L72DA}

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	2026-05-18T02:03:31.913665Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

9b2f8c4ebc7fecf699187a6c2daffa18043ecd595bf4d11cd20bb4d27c529732

Aliases

arxiv: 1505.06762 · arxiv_version: 1505.06762v1 · doi: 10.48550/arxiv.1505.06762 · pith_short_12: TMXYYTV4P7WP · pith_short_16: TMXYYTV4P7WPNGIY · pith_short_8: TMXYYTV4

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/TMXYYTV4P7WPNGIYPJWC3L72DA \
  | 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: 9b2f8c4ebc7fecf699187a6c2daffa18043ecd595bf4d11cd20bb4d27c529732

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "7e7ac3e2bfd701d889d2ece2c08ba36987ea7499cf95174108c2b918cf329d9a",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.GR",
    "submitted_at": "2015-05-25T21:34:05Z",
    "title_canon_sha256": "4e20d1cc9847bdd24b4a132d259f66535a491fe24f28c02e5cbe2ca4981036d8"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1505.06762",
    "kind": "arxiv",
    "version": 1
  }
}