Pith Number

pith:24NLOSB4

pith:2014:24NLOSB4XVSDUMPVPHQVDY5IME

not attested not anchored not stored refs pending

Periodicity of free subgroup numbers modulo prime powers

Christian Krattenthaler (Universit\"at Wien), Thomas W. M\"uller (Queen Mary, University of London)

arxiv:1404.1258 v1 · 2014-04-04 · math.GR · math.CO

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{24NLOSB4XVSDUMPVPHQVDY5IME}

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	2026-05-18T01:21:20.014781Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

d71ab7483cbd643a31f579e151e3a86121b79e63983f7ab0b143ac66a1231dc0

Aliases

arxiv: 1404.1258 · arxiv_version: 1404.1258v1 · doi: 10.48550/arxiv.1404.1258 · pith_short_12: 24NLOSB4XVSD · pith_short_16: 24NLOSB4XVSDUMPV · pith_short_8: 24NLOSB4

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/24NLOSB4XVSDUMPVPHQVDY5IME \
  | 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: d71ab7483cbd643a31f579e151e3a86121b79e63983f7ab0b143ac66a1231dc0

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "332c5c6d84bd8b24c689b2399f1a52557910d9366660e32083d4f65e14c1a333",
    "cross_cats_sorted": [
      "math.CO"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.GR",
    "submitted_at": "2014-04-04T14:12:59Z",
    "title_canon_sha256": "a4d19e929a7f154d89efd034f8f8914dccf937cdf3860eed96ab5773eb32986f"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1404.1258",
    "kind": "arxiv",
    "version": 1
  }
}