Pith Number

pith:4BDEB62C

pith:2012:4BDEB62CRUUPJTTE6OYDLNJK2M

not attested not anchored not stored refs pending

Crossed products of C*-algebras for singular actions

Hendrik Grundling, Karl-Hermann Neeb

arxiv:1210.3409 v2 · 2012-10-12 · math.OA · math-ph · math.MP

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{4BDEB62CRUUPJTTE6OYDLNJK2M}

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	2026-05-18T03:43:17.602737Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

e04640fb428d28f4ce64f3b035b52ad305335a9ac2fc25d4ded43ddae65a4794

Aliases

arxiv: 1210.3409 · arxiv_version: 1210.3409v2 · doi: 10.48550/arxiv.1210.3409 · pith_short_12: 4BDEB62CRUUP · pith_short_16: 4BDEB62CRUUPJTTE · pith_short_8: 4BDEB62C

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/4BDEB62CRUUPJTTE6OYDLNJK2M \
  | 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: e04640fb428d28f4ce64f3b035b52ad305335a9ac2fc25d4ded43ddae65a4794

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "af1057c89808f1c5323e677135d31749660afe8b347eb8676363c07a4e92c83e",
    "cross_cats_sorted": [
      "math-ph",
      "math.MP"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.OA",
    "submitted_at": "2012-10-12T01:18:05Z",
    "title_canon_sha256": "45989f430ee0d95ec49e2d037c1897b85e0f1f5754349f25ac0114a7c164ed2b"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1210.3409",
    "kind": "arxiv",
    "version": 2
  }
}