Pith Number

pith:GLZKH7YB

pith:2006:GLZKH7YBA3TQOGUJVIUY4BVYVO

not attested not anchored not stored refs pending

How to Observe Quantum Fields and Recover Them from Observational Data? -- Takesaki Duality as a Micro-Macro Duality --

Izumi Ojima, Mitsuharu Takeori

arxiv:math-ph/0604054 v1 · 2006-04-23 · 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{GLZKH7YBA3TQOGUJVIUY4BVYVO}

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.

Cited by

1 paper in Pith

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

Receipt and verification

First computed	2026-07-04T14:54:33.046045Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

32f2a3ff0106e7071a89aa298e06b8ab8ba71cb781f4f756f19b073c483755fa

Aliases

arxiv: math-ph/0604054 · arxiv_version: math-ph/0604054v1 · doi: 10.48550/arxiv.math-ph/0604054 · pith_short_12: GLZKH7YBA3TQ · pith_short_16: GLZKH7YBA3TQOGUJ · pith_short_8: GLZKH7YB

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/GLZKH7YBA3TQOGUJVIUY4BVYVO \
  | 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: 32f2a3ff0106e7071a89aa298e06b8ab8ba71cb781f4f756f19b073c483755fa

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "96498c55d7e3876b2b5e348bf49fdb4fb8000d1de5b07edf627ff2dfe718260d",
    "cross_cats_sorted": [
      "math.MP"
    ],
    "license": "",
    "primary_cat": "math-ph",
    "submitted_at": "2006-04-23T12:41:53Z",
    "title_canon_sha256": "690fe0b4e0eb79fe2ce7941c737ac939cbef7f0a78050e0c834b329ed0435cab"
  },
  "schema_version": "1.0",
  "source": {
    "id": "math-ph/0604054",
    "kind": "arxiv",
    "version": 1
  }
}