open_problem: ax-2607.07851-7fc5cf8f

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id statement domain sourced_how source_url cheapest_test status claimed_by sourced_by shape created_ts updated_ts
ax-2607.07851-7fc5cf8f Problem 5.10 (Sharp uncertainty relation on $\mathcal{O}_{m,s}$ ): Prove the relativistic extension of Theorem 5.3 : an entropic inequality on $\mathcal{O}_{m,s}$ , invariant under the PoincarĂ© group and under all Hamiltonian flows, that reduces to ( 13 ) on the little-group fiber in the rest frame and to ( 4 ) on the translational factor in the nonrelativistic limit. Identify the extremal family (conjecturally: relativistic Gaussian in $(x,p)$ $\otimes$ von Mises–Fisher in the direction, coupled only through the Tulczyjew constraint) and the role of the two Casimirs as the invariant scales, with $W\cdot W=-m^{2}c^{2}s^{2}$ playing the part of $\prod_{j}\nu_{j}$ in Theorem 3.16 . 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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