Pith Number

pith:PID2B6U4

pith:2012:PID2B6U4O7QIFK464EQZXCCCAP

not attested not anchored not stored refs pending

Geometric dimension of groups for the family of virtually cyclic subgroups

Dieter Degrijse, Nansen Petrosyan

arxiv:1204.3482 v2 · 2012-04-16 · math.GR · math.AT

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{PID2B6U4O7QIFK464EQZXCCCAP}

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	2026-05-18T03:54:15.807930Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

7a07a0fa9c77e082ab9ee1219b884203c8d5d43eb8cae764dcd85be98ed75a6e

Aliases

arxiv: 1204.3482 · arxiv_version: 1204.3482v2 · doi: 10.48550/arxiv.1204.3482 · pith_short_12: PID2B6U4O7QI · pith_short_16: PID2B6U4O7QIFK46 · pith_short_8: PID2B6U4

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/PID2B6U4O7QIFK464EQZXCCCAP \
  | 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: 7a07a0fa9c77e082ab9ee1219b884203c8d5d43eb8cae764dcd85be98ed75a6e

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "d5ae03b5c6762fdcdce8109dc567e14225e1840cd5450ad71289c8296ef7488f",
    "cross_cats_sorted": [
      "math.AT"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.GR",
    "submitted_at": "2012-04-16T13:49:07Z",
    "title_canon_sha256": "2331c130636219b41580e02e3b608e9d87106d4f128e1911bc5a43131753bb05"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1204.3482",
    "kind": "arxiv",
    "version": 2
  }
}