Pith Number

pith:66A2IWOG

pith:2005:66A2IWOGZURC5LWX2BOW2PSIMC

not attested not anchored not stored refs pending

Operator spaces and Araki-Woods factors --A quantum probabilistic approach--

Marius Junge

arxiv:math/0504255 v3 · 2005-04-12 · math.OA · math.FA

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{66A2IWOGZURC5LWX2BOW2PSIMC}

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	2026-07-04T14:50:12.559113Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

f781a459c6cd222eaed7d05d6d3e4860aa8cd7a2dda9be10676e237338296f53

Aliases

arxiv: math/0504255 · arxiv_version: math/0504255v3 · doi: 10.48550/arxiv.math/0504255 · pith_short_12: 66A2IWOGZURC · pith_short_16: 66A2IWOGZURC5LWX · pith_short_8: 66A2IWOG

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/66A2IWOGZURC5LWX2BOW2PSIMC \
  | 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: f781a459c6cd222eaed7d05d6d3e4860aa8cd7a2dda9be10676e237338296f53

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "1811b182d264382bd0b0323ac3e8be97704f99be981fc911fe551dc06a37831a",
    "cross_cats_sorted": [
      "math.FA"
    ],
    "license": "",
    "primary_cat": "math.OA",
    "submitted_at": "2005-04-12T21:08:49Z",
    "title_canon_sha256": "a7d9c53c5991f4f3bf13cc11cf3069fceab06f1b30a7360aa8e9205a77581e9d"
  },
  "schema_version": "1.0",
  "source": {
    "id": "math/0504255",
    "kind": "arxiv",
    "version": 3
  }
}