Pith Number

pith:UCCUCW4Z

pith:2026:UCCUCW4Z6RVBUTVCKDUY57IFJM

not attested not anchored not stored refs pending

A class of II$_1$ factors without non-trivial crossed product decompositions

Adriana Fern\'andez Quero, Adrian Ioana, Hui Tan

arxiv:2606.31929 v1 · 2026-06-30 · 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{UCCUCW4Z6RVBUTVCKDUY57IFJM}

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	2026-07-01T01:18:25.659368Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

a085415b99f46a1a4ea250e98efd054b2bceadd8b58512c687f243c1a9ed7e08

Aliases

arxiv: 2606.31929 · arxiv_version: 2606.31929v1 · doi: 10.48550/arxiv.2606.31929 · pith_short_12: UCCUCW4Z6RVB · pith_short_16: UCCUCW4Z6RVBUTVC · pith_short_8: UCCUCW4Z

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/UCCUCW4Z6RVBUTVCKDUY57IFJM \
  | 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: a085415b99f46a1a4ea250e98efd054b2bceadd8b58512c687f243c1a9ed7e08

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "4e50301642ca79f57cdd51d44563c4b6998453462289f0af78df438405897182",
    "cross_cats_sorted": [
      "math.FA"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.OA",
    "submitted_at": "2026-06-30T16:36:56Z",
    "title_canon_sha256": "b782366566495d92c1022fe39fbd03f5140a7f4cf13ec8851f5ab72eafd76ea2"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2606.31929",
    "kind": "arxiv",
    "version": 1
  }
}