Pith Number

pith:2GTQC4G4

pith:2012:2GTQC4G4OJRG2C5NJOWVB3P6LY

not attested not anchored not stored refs pending

Structure of crossed products by strictly proper actions on continuous-trace algebras

Dana P. Williams, Siegfried Echterhoff

arxiv:1208.4488 v1 · 2012-08-22 · 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{2GTQC4G4OJRG2C5NJOWVB3P6LY}

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	2026-05-18T03:48:14.145875Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

d1a70170dc72626d0bad4bad50edfe5e24bb5899a7b000d687c73148cb95daca

Aliases

arxiv: 1208.4488 · arxiv_version: 1208.4488v1 · doi: 10.48550/arxiv.1208.4488 · pith_short_12: 2GTQC4G4OJRG · pith_short_16: 2GTQC4G4OJRG2C5N · pith_short_8: 2GTQC4G4

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/2GTQC4G4OJRG2C5NJOWVB3P6LY \
  | 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: d1a70170dc72626d0bad4bad50edfe5e24bb5899a7b000d687c73148cb95daca

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "965765966b68cd6d273674b8a35efad66638360bb52f72f1c8dad55b6acfe130",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.OA",
    "submitted_at": "2012-08-22T12:49:36Z",
    "title_canon_sha256": "6bf04047b9ac4ad44733bbd539cb495de2fc6cf87a18860920f42eb5982ea6a1"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1208.4488",
    "kind": "arxiv",
    "version": 1
  }
}