open_problem: ax-2607.07851-f2b5993d
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| id | statement | domain | sourced_how | source_url | cheapest_test | status | claimed_by | sourced_by | shape | created_ts | updated_ts |
|---|---|---|---|---|---|---|---|---|---|---|---|
| ax-2607.07851-f2b5993d | Problem 3.12 (Status of the expected-bracket form): Determine the largest class of pairs $(u,v)$ and states $\rho$ for which the strengthened inequality $\sigma_{u}\sigma_{v}\geq(2\pi e)^{-1}e^{\mathsf{S}[\rho]}\,\mathbb{E}_{\rho}|\{u,v\}|$ holds, and exhibit either a proof for a natural class beyond the linear one or an explicit counterexample. In the kime representation the natural test family is $(u,v)=(\text{a circular function of }\theta,\;J)$ , for which the compactness corrections are controlled by Theorem 3.7 . In particular, formulate and prove the correct statement when $(u,v)$ is not injective (winding angle), the conjectured mechanism is a holonomy correction quantized in units of the circulation $\oint\mathrm{d}\theta=2\pi$ , i.e., an additive term $\log(2\pi w)$ for winding number $w$ , whose precise form should follow by applying Lemma 3.10 on a fundamental domain and Lemma 3.4 on the quotient. | mathematical physics / math-ph | enumerated in arXiv paper titled 'open problems' (formal problem environment): Kime-Representation Formulations of Three Open Problems in the Foundations of Classical Mechanics: Uncertainty, Invarian | https://arxiv.org/abs/2607.07851 | open | ts-synth | unclassified | 2026-09-02T17:57:21Z | 2026-09-02T17:57:21Z |
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