Pith Number

pith:QKDHKPCB

pith:2012:QKDHKPCBJBNK3HBGI4KVD6CDR4

not attested not anchored not stored refs pending

On Bounding the Diameter of the Commuting Graph of a Group

Aedan Pope, Michael Giudici

arxiv:1206.3731 v2 · 2012-06-17 · math.GR · math.CO

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{QKDHKPCBJBNK3HBGI4KVD6CDR4}

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	2026-05-18T03:53:16.886255Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

8286753c41485aad9c26471551f8438f3c0bda9787c207f1c6ff4b2eba67f75b

Aliases

arxiv: 1206.3731 · arxiv_version: 1206.3731v2 · doi: 10.48550/arxiv.1206.3731 · pith_short_12: QKDHKPCBJBNK · pith_short_16: QKDHKPCBJBNK3HBG · pith_short_8: QKDHKPCB

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/QKDHKPCBJBNK3HBGI4KVD6CDR4 \
  | 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: 8286753c41485aad9c26471551f8438f3c0bda9787c207f1c6ff4b2eba67f75b

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "87240d806dce863a11cbbf4d634c81094ad1c1a70408ae76295f639fc2af5ae6",
    "cross_cats_sorted": [
      "math.CO"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.GR",
    "submitted_at": "2012-06-17T07:40:10Z",
    "title_canon_sha256": "b1b29019c297d6a2216b9d304060e3e4d3abcc1b0d265fbfb1d83a02d45fe104"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1206.3731",
    "kind": "arxiv",
    "version": 2
  }
}