bibkey: kimura2025normalweightedbw authors: Gen Kimura; Aina Mayumi; Hiromichi Ohno; Jaeha Lee; Dariusz Chruściński year: 2025 title: “Beyond Robertson–Schrödinger: A General Uncertainty Relation Unveiling Hidden Noncommutative Trade-offs” doi: null url: https://arxiv.org/abs/2504.20404 claim: “Supplementary Theorem 1 proves the doubly weighted commutator inequality, case (i), when one factor is normal.” strata_touched:

• D5/S3/Quantum/Matrix/WeightedBotcherWenzel license: citation-only triage: anchor

Beyond Robertson–Schrödinger: A General Uncertainty Relation Unveiling Hidden Noncommutative Trade-offs

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Source: https://arxiv.org/abs/2504.20404

The supplementary normal-factor result concerns the doubly weighted case (i). It does not settle case (ii) for arbitrary factors.