Pith Number

pith:VSU5ZQAB

pith:1996:VSU5ZQAB6XQIVTPVA4MS6IE3BE

not attested not anchored not stored refs pending

A Galois Correspondence for Compact Groups of Automorphisms of von Neumann Algebras with a Generalization to Kac Algebras

Masaki Izumi, Roberto Longo, Sorin Popa

arxiv:funct-an/9604004 v2 · 1996-04-05 · funct-an · 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{VSU5ZQAB6XQIVTPVA4MS6IE3BE}

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	2026-07-04T15:07:44.573822Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

aca9dcc001f5e08acdf507192f209b09064212dfc3f4933242ca0272b8257331

Aliases

arxiv: funct-an/9604004 · arxiv_version: funct-an/9604004v2 · doi: 10.48550/arxiv.funct-an/9604004 · pith_short_12: VSU5ZQAB6XQI · pith_short_16: VSU5ZQAB6XQIVTPV · pith_short_8: VSU5ZQAB

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/VSU5ZQAB6XQIVTPVA4MS6IE3BE \
  | 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: aca9dcc001f5e08acdf507192f209b09064212dfc3f4933242ca0272b8257331

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "67f7e8a093e7bf9428c26d43efdb91afdd0d89c271e8a9c0501517dd7d2f1a1b",
    "cross_cats_sorted": [
      "math.OA"
    ],
    "license": "",
    "primary_cat": "funct-an",
    "submitted_at": "1996-04-05T13:08:41Z",
    "title_canon_sha256": "b72ff30209d8176e975999ce56e5496d9dec94922774b93fd1af4de6a48e71cd"
  },
  "schema_version": "1.0",
  "source": {
    "id": "funct-an/9604004",
    "kind": "arxiv",
    "version": 2
  }
}