Pith Number

pith:FQQSHWV3

pith:2012:FQQSHWV3D5ZWKCH4UARTNNL6BR

not attested not anchored not stored refs pending

Limit points in the range of the commuting probability function on finite groups

Peter Hegarty

arxiv:1207.0760 v1 · 2012-07-03 · math.GR

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{FQQSHWV3D5ZWKCH4UARTNNL6BR}

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	2026-05-18T03:51:49.149250Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

2c2123dabb1f736508fca02336b57e0c4ce79a27998a55f0f2b694e30fbcc1a5

Aliases

arxiv: 1207.0760 · arxiv_version: 1207.0760v1 · doi: 10.48550/arxiv.1207.0760 · pith_short_12: FQQSHWV3D5ZW · pith_short_16: FQQSHWV3D5ZWKCH4 · pith_short_8: FQQSHWV3

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/FQQSHWV3D5ZWKCH4UARTNNL6BR \
  | 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: 2c2123dabb1f736508fca02336b57e0c4ce79a27998a55f0f2b694e30fbcc1a5

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "0265c39ee615127ef16859fdf25cca2d00526a81113e090366fa4f19aabddf89",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.GR",
    "submitted_at": "2012-07-03T17:32:53Z",
    "title_canon_sha256": "00a299c8e26e3fa1930df2b3f5bda247dcf0fa147a61add586243cce99b34394"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1207.0760",
    "kind": "arxiv",
    "version": 1
  }
}