Pith Number

pith:PFI67XSA

pith:2024:PFI67XSAOQ3LQ3ORUT7Y3UVERI

not attested not anchored not stored refs pending

On the boundedness and Schatten class property of noncommutative martingale paraproducts and operator-valued commutators

Hao Zhang, Zhenguo Wei

arxiv:2407.14988 v3 · 2024-07-20 · math.FA

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\usepackage{pith}
\pithnumber{PFI67XSAOQ3LQ3ORUT7Y3UVERI}

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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

Schatten properties of commutators on metric spaces

Receipt and verification

First computed	2026-07-05T09:37:09.237507Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

7951efde407436b86dd1a4ff8dd2a48a2f50a65069b6b3391b44a71f8ba43156

Aliases

arxiv: 2407.14988 · arxiv_version: 2407.14988v3 · doi: 10.48550/arxiv.2407.14988 · pith_short_12: PFI67XSAOQ3L · pith_short_16: PFI67XSAOQ3LQ3OR · pith_short_8: PFI67XSA

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/PFI67XSAOQ3LQ3ORUT7Y3UVERI \
  | 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: 7951efde407436b86dd1a4ff8dd2a48a2f50a65069b6b3391b44a71f8ba43156

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "47973f63dc66dbdb6b0177220f914c42172cc26a6b9dd31d33debcd25c89a16e",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.FA",
    "submitted_at": "2024-07-20T21:44:50Z",
    "title_canon_sha256": "acc9007d572def0a98d2259a11894fa4c44f69fdf23159fc740a1f9dd1268cfd"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2407.14988",
    "kind": "arxiv",
    "version": 3
  }
}