Pith Number

pith:P2U2WR4Y

pith:2016:P2U2WR4YMULVHB32DBDHDRPZJR

not attested not anchored not stored refs pending

Hopf images in locally compact quantum groups

Pawe{\l} J\'oziak, Pawe{\l} Kasprzak, Piotr M. So{\l}tan

arxiv:1611.06225 v2 · 2016-11-15 · math.OA · math.FA · math.QA

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{P2U2WR4YMULVHB32DBDHDRPZJR}

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	2026-05-18T00:41:12.719809Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

7ea9ab4798651753877a184671c5f94c6f8cc56d32dd62401f77785add8bdd23

Aliases

arxiv: 1611.06225 · arxiv_version: 1611.06225v2 · doi: 10.48550/arxiv.1611.06225 · pith_short_12: P2U2WR4YMULV · pith_short_16: P2U2WR4YMULVHB32 · pith_short_8: P2U2WR4Y

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/P2U2WR4YMULVHB32DBDHDRPZJR \
  | 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: 7ea9ab4798651753877a184671c5f94c6f8cc56d32dd62401f77785add8bdd23

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "6474d0aab70976dd162df8e66c3746691524bf480b89984759ebdca98d3ef9a2",
    "cross_cats_sorted": [
      "math.FA",
      "math.QA"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.OA",
    "submitted_at": "2016-11-15T22:00:51Z",
    "title_canon_sha256": "23b40005baa40cfd311070772e7bb8a038e7cf4e25c150123395a2653eab5be9"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1611.06225",
    "kind": "arxiv",
    "version": 2
  }
}