Pith Number

pith:ZVPGAPW4

pith:2015:ZVPGAPW4EFOW2SYASR5WUNU6DZ

not attested not anchored not stored refs pending

Crossed Products of Operator Algebras

Christopher Ramsey, Elias Katsoulis

arxiv:1512.08162 v5 · 2015-12-27 · 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{ZVPGAPW4EFOW2SYASR5WUNU6DZ}

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	2026-05-18T00:00:22.883109Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

cd5e603edc215d6d4b00947b6a369e1e44c76ac1927e76b941cc8e42f170c1ed

Aliases

arxiv: 1512.08162 · arxiv_version: 1512.08162v5 · doi: 10.48550/arxiv.1512.08162 · pith_short_12: ZVPGAPW4EFOW · pith_short_16: ZVPGAPW4EFOW2SYA · pith_short_8: ZVPGAPW4

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/ZVPGAPW4EFOW2SYASR5WUNU6DZ \
  | 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: cd5e603edc215d6d4b00947b6a369e1e44c76ac1927e76b941cc8e42f170c1ed

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "b8e00724691c403894590aef7298827caa3ae93796ca64f01f64a439785f323c",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.OA",
    "submitted_at": "2015-12-27T01:24:05Z",
    "title_canon_sha256": "9b4cf72dff7e75ec68403bb06b81e77db9490e93c69d6b8e01d9ab21b179f246"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1512.08162",
    "kind": "arxiv",
    "version": 5
  }
}