Pith Number

pith:R5VXJ6LF

pith:2012:R5VXJ6LFYMH6AOAN2PBDMYKPNT

not attested not anchored not stored refs pending

Can connected commuting graphs of finite groups have arbitrarily large diameter ?

Dmitry Zhelezov, Peter Hegarty

arxiv:1204.5456 v3 · 2012-04-24 · math.GR · math.PR

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{R5VXJ6LFYMH6AOAN2PBDMYKPNT}

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	2026-05-18T03:46:47.218204Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

8f6b74f965c30fe0380dd3c236614f6cce9aa90af665592085c085530c8d8147

Aliases

arxiv: 1204.5456 · arxiv_version: 1204.5456v3 · doi: 10.48550/arxiv.1204.5456 · pith_short_12: R5VXJ6LFYMH6 · pith_short_16: R5VXJ6LFYMH6AOAN · pith_short_8: R5VXJ6LF

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/R5VXJ6LFYMH6AOAN2PBDMYKPNT \
  | 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: 8f6b74f965c30fe0380dd3c236614f6cce9aa90af665592085c085530c8d8147

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "5c3965c780700fc545333a03f72f8efd97abafda9a203e4278a6d3db4977fa39",
    "cross_cats_sorted": [
      "math.PR"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.GR",
    "submitted_at": "2012-04-24T18:29:21Z",
    "title_canon_sha256": "4f6f56c1d4e9f98d03fa2cc69ac371d3f2a32a33794201fb21ef5e52f5cc9ad3"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1204.5456",
    "kind": "arxiv",
    "version": 3
  }
}