Pith Number

pith:ZCLECI4P

pith:2015:ZCLECI4PTGLSIU5PONMO2BIQZH

not attested not anchored not stored refs pending

Ranks of subgroups in boundedly generated groups

Mark Shusterman

arxiv:1510.05904 v1 · 2015-10-20 · 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{ZCLECI4PTGLSIU5PONMO2BIQZH}

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	2026-05-18T00:45:08.553788Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

c89641238f99972453af7358ed0510c9df7414bf3e9be488ce9d7fa4d1d12638

Aliases

arxiv: 1510.05904 · arxiv_version: 1510.05904v1 · doi: 10.48550/arxiv.1510.05904 · pith_short_12: ZCLECI4PTGLS · pith_short_16: ZCLECI4PTGLSIU5P · pith_short_8: ZCLECI4P

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/ZCLECI4PTGLSIU5PONMO2BIQZH \
  | 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: c89641238f99972453af7358ed0510c9df7414bf3e9be488ce9d7fa4d1d12638

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "6217d63cc7a093b7f9cc840d3433da0e842c0154c1d2e68c405214cdfb43d3da",
    "cross_cats_sorted": [
      "math.CO"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.GR",
    "submitted_at": "2015-10-20T14:07:19Z",
    "title_canon_sha256": "cf20b41ab9aca74db651f852265eaa6c56e9d4ce0398ea132572290c526bc640"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1510.05904",
    "kind": "arxiv",
    "version": 1
  }
}