Pith Number

pith:POINM4R3

pith:2010:POINM4R3HEZK4KZ4XHNQXFAPF5

not attested not anchored not stored refs pending

On subgroup conjugacy separability in the class of virtually free groups

Fritz Grunewald, Oleg Bogopolski

arxiv:1012.5122 v1 · 2010-12-22 · 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{POINM4R3HEZK4KZ4XHNQXFAPF5}

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	2026-05-18T04:32:35.772483Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

7b90d6723b3932ae2b3cb9db0b940f2f697f0c3d122f633b7f310a056ce34221

Aliases

arxiv: 1012.5122 · arxiv_version: 1012.5122v1 · doi: 10.48550/arxiv.1012.5122 · pith_short_12: POINM4R3HEZK · pith_short_16: POINM4R3HEZK4KZ4 · pith_short_8: POINM4R3

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/POINM4R3HEZK4KZ4XHNQXFAPF5 \
  | 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: 7b90d6723b3932ae2b3cb9db0b940f2f697f0c3d122f633b7f310a056ce34221

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "bc1aa208dd484038251d0f554e156015f827cf6d396459ae2f7319bb6bb871fb",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.GR",
    "submitted_at": "2010-12-22T23:43:08Z",
    "title_canon_sha256": "0d46781aa82bad8717a9161d8c34408e5c2a2fa87e7b08474b7bd4d32bbeb1bf"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1012.5122",
    "kind": "arxiv",
    "version": 1
  }
}