Pith Number

pith:2JMI4SRE

pith:2010:2JMI4SREX3TQJKDRJ4CGVH5G3R

not attested not anchored not stored refs pending

Crossed products and the Mackey-Rieffel-Green machine

Siegfried Echterhoff

arxiv:1006.4975 v4 · 2010-06-25 · math.OA · math.DS

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{2JMI4SREX3TQJKDRJ4CGVH5G3R}

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	2026-05-18T00:42:33.794871Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

d2588e4a24bee704a8714f046a9fa6dc7ef0dbf22d8c17ac02f3e652a1f8cc8c

Aliases

arxiv: 1006.4975 · arxiv_version: 1006.4975v4 · doi: 10.48550/arxiv.1006.4975 · pith_short_12: 2JMI4SREX3TQ · pith_short_16: 2JMI4SREX3TQJKDR · pith_short_8: 2JMI4SRE

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/2JMI4SREX3TQJKDRJ4CGVH5G3R \
  | 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: d2588e4a24bee704a8714f046a9fa6dc7ef0dbf22d8c17ac02f3e652a1f8cc8c

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "8b578e06f6f9ef2d655dabf62fccf2ff27b3242230cf9c424e3d02ccd6235a5a",
    "cross_cats_sorted": [
      "math.DS"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.OA",
    "submitted_at": "2010-06-25T12:19:27Z",
    "title_canon_sha256": "cf6a758391156ec7fcfda4dd016be4f36bd2a68a3a64a4080116f35598d66825"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1006.4975",
    "kind": "arxiv",
    "version": 4
  }
}