open_problem: ax-2607.07851-8ad272ac

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id statement domain sourced_how source_url cheapest_test status claimed_by sourced_by shape created_ts updated_ts
ax-2607.07851-8ad272ac Conjecture 3.22 (Equipartition duality): Fix $n\geq 2$ , an entropy value $s$ , and an action marginal $\rho_{\bm{J}}$ on $(0,\infty)^{n}$ . Among all states on $\mathbb{T}^{n}\times(0,\infty)^{n}$ with entropy $\geq s$ and action marginal $\rho_{\bm{J}}$ , the phase-equipartitioned product state (unique when it exists) simultaneously (i) maximizes the entropy, (ii) minimizes every within-DOF uncertainty $u_{j}$ , and (iii) is the unique state at which the per-DOF conjectured bound of Problem 3.17 (b) is saturated for all $j$ ; moreover it is the unique fixed point, with the given marginal, of the multi-DOF kime-deformed semigroup $\partial_{t}\tilde{\rho}=\sum_{j}(-\omega_{j}\partial_{\theta_{j}}+\varepsilon\,\partial^{2}_{\theta_{j}})\tilde{\rho}$ . 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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