Pith Number

pith:TO2GPTG7

pith:2013:TO2GPTG7VILXOA7CCT36LJZJNM

not attested not anchored not stored refs pending

Zappa-Sz\'ep products of semigroups and their C*-algebras

David Robertson, Jacqui Ramagge, Michael F. Whittaker, Nathan Brownlowe

arxiv:1309.0300 v2 · 2013-09-02 · math.OA · 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{TO2GPTG7VILXOA7CCT36LJZJNM}

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	2026-05-18T02:56:51.870326Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

9bb467ccdfaa177703e214f7e5a7296b1b253758588cfd9a22354efb359f6894

Aliases

arxiv: 1309.0300 · arxiv_version: 1309.0300v2 · doi: 10.48550/arxiv.1309.0300 · pith_short_12: TO2GPTG7VILX · pith_short_16: TO2GPTG7VILXOA7C · pith_short_8: TO2GPTG7

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/TO2GPTG7VILXOA7CCT36LJZJNM \
  | 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: 9bb467ccdfaa177703e214f7e5a7296b1b253758588cfd9a22354efb359f6894

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "0d0b8fe84bf4a48ce636f913425e9dfeb625e392098efc499f4078eb50eb412e",
    "cross_cats_sorted": [
      "math.GR"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.OA",
    "submitted_at": "2013-09-02T04:55:48Z",
    "title_canon_sha256": "67abed15f0958f90030bf1f2e36b81eeee68bbd7649b0da4310b458088ccf40a"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1309.0300",
    "kind": "arxiv",
    "version": 2
  }
}