Pith Number

pith:BO7JZCQI

pith:2017:BO7JZCQIQ2YMKL2X4DU7X2DFTT

not attested not anchored not stored refs pending

Virtually free finite-normal-subgroup-free groups are strongly verbally closed

Andrey M. Mazhuga, Anton A. Klyachko, Veronika Yu. Miroshnichenko

arxiv:1712.03406 v3 · 2017-12-09 · 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{BO7JZCQIQ2YMKL2X4DU7X2DFTT}

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	2026-05-18T00:12:32.584865Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

0bbe9c8a0886b0c52f57e0e9fbe8659cdd47abc0383046fb33d116cd8a369464

Aliases

arxiv: 1712.03406 · arxiv_version: 1712.03406v3 · doi: 10.48550/arxiv.1712.03406 · pith_short_12: BO7JZCQIQ2YM · pith_short_16: BO7JZCQIQ2YMKL2X · pith_short_8: BO7JZCQI

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/BO7JZCQIQ2YMKL2X4DU7X2DFTT \
  | 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: 0bbe9c8a0886b0c52f57e0e9fbe8659cdd47abc0383046fb33d116cd8a369464

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "ee2547d98f9743f2862f6a7e3773ed94619ce189167ea9d93e22d93181d9642c",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.GR",
    "submitted_at": "2017-12-09T16:03:12Z",
    "title_canon_sha256": "d09f4559acd7536e654a1c7010934bc877e08a6f79ec0dbbd8897b57280abd56"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1712.03406",
    "kind": "arxiv",
    "version": 3
  }
}