Pith Number

pith:BWBPX7XX

pith:2017:BWBPX7XX4GBSUOCMTBPENTTEVP

not attested not anchored not stored refs pending

Equivalence of tensor products over a category of W*-algebras

Ryszard Pawe{\l} Kostecki, Tomasz Ignacy Tylec

arxiv:1712.07399 v1 · 2017-12-20 · math-ph · math.MP · 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{BWBPX7XX4GBSUOCMTBPENTTEVP}

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	2026-05-18T00:27:34.564509Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

0d82fbfef7e1832a384c985e46ce64abc0b83cae352b71e4b683ada5bdca0d34

Aliases

arxiv: 1712.07399 · arxiv_version: 1712.07399v1 · doi: 10.48550/arxiv.1712.07399 · pith_short_12: BWBPX7XX4GBS · pith_short_16: BWBPX7XX4GBSUOCM · pith_short_8: BWBPX7XX

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/BWBPX7XX4GBSUOCMTBPENTTEVP \
  | 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: 0d82fbfef7e1832a384c985e46ce64abc0b83cae352b71e4b683ada5bdca0d34

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "b823226b18f01db2b07f9726398aff502123e97a7777f8891e7a8c864a472f11",
    "cross_cats_sorted": [
      "math.MP",
      "math.OA"
    ],
    "license": "http://creativecommons.org/licenses/by-sa/4.0/",
    "primary_cat": "math-ph",
    "submitted_at": "2017-12-20T10:28:08Z",
    "title_canon_sha256": "a869d980de1838907556f705121e3dc29dee0f935fb4b9593580379dcbbbad24"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1712.07399",
    "kind": "arxiv",
    "version": 1
  }
}