Pith Number

pith:GZQPEOSE

pith:2013:GZQPEOSEC2OXZCPHQVDFKMLZJ6

not attested not anchored not stored refs pending

Subnormal subgroups in free groups, their growth and cogrowth

Alexander Olshanskii

arxiv:1312.0129 v2 · 2013-11-30 · 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{GZQPEOSEC2OXZCPHQVDFKMLZJ6}

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	2026-05-18T02:46:31.115606Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

3660f23a44169d7c89e785465531794fb96ce8b2167942a62c1d1a3b3d6802bc

Aliases

arxiv: 1312.0129 · arxiv_version: 1312.0129v2 · doi: 10.48550/arxiv.1312.0129 · pith_short_12: GZQPEOSEC2OX · pith_short_16: GZQPEOSEC2OXZCPH · pith_short_8: GZQPEOSE

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/GZQPEOSEC2OXZCPHQVDFKMLZJ6 \
  | 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: 3660f23a44169d7c89e785465531794fb96ce8b2167942a62c1d1a3b3d6802bc

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "b2e4cd30c08aff17ed94fb1e2833730078431dd7ec26b4e45de1f31f0e912f71",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.GR",
    "submitted_at": "2013-11-30T17:29:54Z",
    "title_canon_sha256": "bf631711a1a4b16c736f82952724f60185f4b48f6856c6c9860baddf1709a182"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1312.0129",
    "kind": "arxiv",
    "version": 2
  }
}