open_problem: ax-2607.07851-7e63782b

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ax-2607.07851-7e63782b Problem 4.10 (Generalized complex rigidity of the Wick interpolation): Proposition 4.5 produces a Kähler triple in one kime DOF; Proposition 4.6 deforms the dynamics between its symplectic and metric legs. Formulate and prove (or refute) the following rigidity statement: if a $2n$ -dimensional state continuum carries (a) a reparametrization-invariant entropy (hence, by Theorems 4.1 and 4.3 , a distinguished volume), (b) a one-parameter interpolation of evolutions that is entropy-conserving at one end and satisfies a de Bruijn identity $\frac{\mathrm{d}}{\mathrm{d}t}\mathsf{S}=\varepsilon\,\mathcal{I}\geq 0$ elsewhere (Theorem 3.21 (ii)), then the infinitesimal generators assemble into a generalized complex (indeed generalized Kähler) structure in the sense of , whose pure-symplectic locus is the Hamiltonian sector and whose type jumps encode the diffusive sector. A positive answer would derive “quantities pair inside $\mathbb{C}$ ” from entropy axioms alone, completing the program of Problem (II). 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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