Pith Number

pith:XOQFX4EM

pith:2012:XOQFX4EMHDSUFS7Z46XDBKC5JY

not attested not anchored not stored refs pending

There is no upper bound for the diameter of the commuting graph of a finite group

Chris Parker, Michael Giudici

arxiv:1210.0348 v1 · 2012-10-01 · 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{XOQFX4EMHDSUFS7Z46XDBKC5JY}

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	2026-05-18T03:44:22.678580Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

bba05bf08c38e542cbf9e7ae30a85d4e03854df5991c1eb3cae3252cd5a82a75

Aliases

arxiv: 1210.0348 · arxiv_version: 1210.0348v1 · doi: 10.48550/arxiv.1210.0348 · pith_short_12: XOQFX4EMHDSU · pith_short_16: XOQFX4EMHDSUFS7Z · pith_short_8: XOQFX4EM

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/XOQFX4EMHDSUFS7Z46XDBKC5JY \
  | 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: bba05bf08c38e542cbf9e7ae30a85d4e03854df5991c1eb3cae3252cd5a82a75

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "f980d178c4b4e9264b98fc808074cc0d85d45f2c2326fd73371e3144674e9ad4",
    "cross_cats_sorted": [
      "math.CO"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.GR",
    "submitted_at": "2012-10-01T11:04:56Z",
    "title_canon_sha256": "fbe7dc1f8c8eb8998b1693e8556d08014a0d7a3fa470a1bcb9bf73889e02d0fd"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1210.0348",
    "kind": "arxiv",
    "version": 1
  }
}