Pith Number

pith:Y3LPVZKB

pith:2017:Y3LPVZKB2RUANT5JHBU7JDVXEB

not attested not anchored not stored refs pending

Crossed products of operator algebras: applications of Takai duality

Christopher Ramsey, Elias Katsoulis

arxiv:1705.08729 v4 · 2017-05-24 · 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{Y3LPVZKB2RUANT5JHBU7JDVXEB}

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	2026-05-18T00:32:30.879335Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

c6d6fae541d46806cfa93869f48eb720454c8796c3730c8f786a4714b0b8e560

Aliases

arxiv: 1705.08729 · arxiv_version: 1705.08729v4 · doi: 10.48550/arxiv.1705.08729 · pith_short_12: Y3LPVZKB2RUA · pith_short_16: Y3LPVZKB2RUANT5J · pith_short_8: Y3LPVZKB

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/Y3LPVZKB2RUANT5JHBU7JDVXEB \
  | 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: c6d6fae541d46806cfa93869f48eb720454c8796c3730c8f786a4714b0b8e560

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "853322117a07bf17edf06c63ac9d9aca7403dd48126892cef866a867eb0fd63d",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.OA",
    "submitted_at": "2017-05-24T12:44:02Z",
    "title_canon_sha256": "aa95ae9bd4a36376e9926e0719bc4a021ba3458c1a8599df1218e6b0d62217ce"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1705.08729",
    "kind": "arxiv",
    "version": 4
  }
}