Pith Number

pith:ZTZDLVRR

pith:2015:ZTZDLVRRSGHWKLBDVK2W6HGQ5T

not attested not anchored not stored refs pending

Cycle lengths in finite groups and the size of the solvable radical

Alexander Bors

arxiv:1501.07172 v2 · 2015-01-28 · 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{ZTZDLVRRSGHWKLBDVK2W6HGQ5T}

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	2026-05-18T01:51:25.005511Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

ccf235d631918f652c23aab56f1cd0ecf96c9b546b147ddc640245ffa0a0d361

Aliases

arxiv: 1501.07172 · arxiv_version: 1501.07172v2 · doi: 10.48550/arxiv.1501.07172 · pith_short_12: ZTZDLVRRSGHW · pith_short_16: ZTZDLVRRSGHWKLBD · pith_short_8: ZTZDLVRR

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/ZTZDLVRRSGHWKLBDVK2W6HGQ5T \
  | 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: ccf235d631918f652c23aab56f1cd0ecf96c9b546b147ddc640245ffa0a0d361

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "dbb05f2cf32954cf10a8e89d021c7c7ce52ab49e76206880ad4f4d09fe6e88e5",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.GR",
    "submitted_at": "2015-01-28T16:16:21Z",
    "title_canon_sha256": "79b34b5d40b9f141c0bf78cb0b2383b47c96ec0daf3464abbcbca8b7db9e59e1"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1501.07172",
    "kind": "arxiv",
    "version": 2
  }
}