Pith Number

pith:AC6P6GJZ

pith:2013:AC6P6GJZCP4J7ZDFINTEOGZ7LH

not attested not anchored not stored refs pending

Tomita-Takesaki Modular Theory vs. Quantum Information Theory

Junde Wu, Lin Zhang

arxiv:1301.1836 v2 · 2013-01-09 · math-ph · math.MP · math.OA · quant-ph

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{AC6P6GJZCP4J7ZDFINTEOGZ7LH}

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	2026-05-18T01:11:05.426971Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

00bcff193913f89fe4654366471b3f59f334621c729e2b99fe5789d6b5ebf129

Aliases

arxiv: 1301.1836 · arxiv_version: 1301.1836v2 · doi: 10.48550/arxiv.1301.1836 · pith_short_12: AC6P6GJZCP4J · pith_short_16: AC6P6GJZCP4J7ZDF · pith_short_8: AC6P6GJZ

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/AC6P6GJZCP4J7ZDFINTEOGZ7LH \
  | 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: 00bcff193913f89fe4654366471b3f59f334621c729e2b99fe5789d6b5ebf129

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "286cc50d374fbb18c7c92bed87dd2c3198056408fe586a082bf8c7fa77af57d5",
    "cross_cats_sorted": [
      "math.MP",
      "math.OA",
      "quant-ph"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math-ph",
    "submitted_at": "2013-01-09T12:58:01Z",
    "title_canon_sha256": "d839f180c96860fa28998f18537281280748f57cc19e81b27e399db8071cc5dc"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1301.1836",
    "kind": "arxiv",
    "version": 2
  }
}