Pith Number

pith:LT4GNKHH

pith:2026:LT4GNKHHAY2ITR7VEGTYDF6N6W

not attested not anchored not stored refs pending

Kaplansky's second test problem in operator algebras

Chunlan Jiang, Minghui Ma, Rui Shi, Yuanhang Zhang

arxiv:2607.20593 v1 · 2026-07-22 · math.FA · 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{LT4GNKHHAY2ITR7VEGTYDF6N6W}

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	2026-07-24T00:23:24.399753Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

5cf866a8e7063489c7f521a78197cdf5b82fdc4d3fe88bfbea36585a8ed3100f

Aliases

arxiv: 2607.20593 · arxiv_version: 2607.20593v1 · doi: 10.48550/arxiv.2607.20593 · pith_short_12: LT4GNKHHAY2I · pith_short_16: LT4GNKHHAY2ITR7V · pith_short_8: LT4GNKHH

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/LT4GNKHHAY2ITR7VEGTYDF6N6W \
  | 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: 5cf866a8e7063489c7f521a78197cdf5b82fdc4d3fe88bfbea36585a8ed3100f

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "4c9a9fb0e6c54277c2ecf11b521e805452a0599cb2320548d1ec1006e468e624",
    "cross_cats_sorted": [
      "math.OA"
    ],
    "license": "http://creativecommons.org/licenses/by-nc-nd/4.0/",
    "primary_cat": "math.FA",
    "submitted_at": "2026-07-22T15:49:53Z",
    "title_canon_sha256": "f85c21e9ed9bae576ccd10d5f15fe19a186eba9520ea845be3654f51bad69e76"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2607.20593",
    "kind": "arxiv",
    "version": 1
  }
}