Pith Number

pith:NZD7PTB3

pith:2010:NZD7PTB3TZBAMI4FK22AMMOBBZ

not attested not anchored not stored refs pending

Group rings whose group of units is hyperbolic

V. Bovdi

arxiv:1009.2568 v1 · 2010-09-14 · math.GR · math.RA · math.RT

Open paper page JSON Open Graph Bundle Merged state Verified badge What is a Pith Number?

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{NZD7PTB3TZBAMI4FK22AMMOBBZ}

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	2026-05-18T04:40:56.786243Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

6e47f7cc3b9e4206238556b40631c10e6835586ff43daa0c195659d690205790

Aliases

arxiv: 1009.2568 · arxiv_version: 1009.2568v1 · doi: 10.48550/arxiv.1009.2568 · pith_short_12: NZD7PTB3TZBA · pith_short_16: NZD7PTB3TZBAMI4F · pith_short_8: NZD7PTB3

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/NZD7PTB3TZBAMI4FK22AMMOBBZ \
  | 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: 6e47f7cc3b9e4206238556b40631c10e6835586ff43daa0c195659d690205790

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "e9725051cd2255d7d7937dc58c202aab6987d309061aac77f1d200d78886fc85",
    "cross_cats_sorted": [
      "math.RA",
      "math.RT"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.GR",
    "submitted_at": "2010-09-14T04:50:51Z",
    "title_canon_sha256": "f52ae56ecc74646605035da64607310528f58e3e04dc1eff2786b510b900274a"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1009.2568",
    "kind": "arxiv",
    "version": 1
  }
}