Pith Number

pith:WB7B6WEX

pith:2016:WB7B6WEX3TRGMHEMYIIRBGEZIM

not attested not anchored not stored refs pending

Free subgroup numbers modulo prime powers: the non-periodic case

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

arxiv:1602.08723 v1 · 2016-02-28 · 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{WB7B6WEX3TRGMHEMYIIRBGEZIM}

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	2026-05-18T00:35:09.516773Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

b07e1f5897dce2661c8cc211109899430bf03f7a7a206c3351b5b8b93bb4e33c

Aliases

arxiv: 1602.08723 · arxiv_version: 1602.08723v1 · doi: 10.48550/arxiv.1602.08723 · pith_short_12: WB7B6WEX3TRG · pith_short_16: WB7B6WEX3TRGMHEM · pith_short_8: WB7B6WEX

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/WB7B6WEX3TRGMHEMYIIRBGEZIM \
  | 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: b07e1f5897dce2661c8cc211109899430bf03f7a7a206c3351b5b8b93bb4e33c

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "adccaf267342b35edd80662f3625e9b6a762bc3c4741b059df8842d7463f59ee",
    "cross_cats_sorted": [
      "math.CO"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.GR",
    "submitted_at": "2016-02-28T14:35:44Z",
    "title_canon_sha256": "e03299b2f485c1af287c593d741a52e7258cecd59093332e95ed158b093fb415"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1602.08723",
    "kind": "arxiv",
    "version": 1
  }
}