Pith Number

pith:32ZBEPEM

pith:2016:32ZBEPEM7RRB6D22RQRTQA3MHO

not attested not anchored not stored refs pending

C*-envelopes and the Hao-Ng isomorphism for discrete groups

Elias G. Katsoulis

arxiv:1606.01513 v3 · 2016-06-05 · math.OA

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{32ZBEPEM7RRB6D22RQRTQA3MHO}

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	2026-05-18T01:09:29.401722Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

deb2123c8cfc621f0f5a8c2338036c3bb173c8d5740df74af2076fbc91839e7c

Aliases

arxiv: 1606.01513 · arxiv_version: 1606.01513v3 · doi: 10.48550/arxiv.1606.01513 · pith_short_12: 32ZBEPEM7RRB · pith_short_16: 32ZBEPEM7RRB6D22 · pith_short_8: 32ZBEPEM

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/32ZBEPEM7RRB6D22RQRTQA3MHO \
  | 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: deb2123c8cfc621f0f5a8c2338036c3bb173c8d5740df74af2076fbc91839e7c

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "ebd1fc7fb2ec7ab2fc32a81d67f8c25e6e55091d098de056b723f07a40b62c32",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.OA",
    "submitted_at": "2016-06-05T14:10:29Z",
    "title_canon_sha256": "367b15c7775a45ac8c8769f1e64f54a01df2fa2a8aeaac84dda65545ec04cc9e"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1606.01513",
    "kind": "arxiv",
    "version": 3
  }
}