Pith Number

pith:SYGJ525Q

pith:2025:SYGJ525Q22V3GO5RWSXWGHCFDW

not attested not anchored not stored refs pending

The Crossed Product, Modular (Tomita) Dynamics and its Role in the Transition of Type $III$ to Type $II_{\infty}$ v.Neumann Algebras and Connections to Quantum Gravity

Manfred Requardt

arxiv:2507.01419 v1 · 2025-07-02 · gr-qc · hep-th · 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{SYGJ525Q22V3GO5RWSXWGHCFDW}

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	2026-07-05T11:30:48.489064Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

960c9eebb0d6abb33bb1b4af631c451db0b55a161a25d7a2c61cc371b3fb6545

Aliases

arxiv: 2507.01419 · arxiv_version: 2507.01419v1 · doi: 10.48550/arxiv.2507.01419 · pith_short_12: SYGJ525Q22V3 · pith_short_16: SYGJ525Q22V3GO5R · pith_short_8: SYGJ525Q

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/SYGJ525Q22V3GO5RWSXWGHCFDW \
  | 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: 960c9eebb0d6abb33bb1b4af631c451db0b55a161a25d7a2c61cc371b3fb6545

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "b754b887c787d2e3946264dce55ffe3a88aac754767e1780fc045ecaa78e215d",
    "cross_cats_sorted": [
      "hep-th",
      "math-ph",
      "math.MP"
    ],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "gr-qc",
    "submitted_at": "2025-07-02T07:18:23Z",
    "title_canon_sha256": "391da4f2809893536b1f2b60823021de80b7de723ce9dc1ee0fd4c48b06acf19"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2507.01419",
    "kind": "arxiv",
    "version": 1
  }
}