{"database": "team-science", "table": "open_problem", "rows": [["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 Poincar\u00e9 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\u2013Fisher 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", null, "open", null, "ts-synth", "unclassified", "2026-09-02T17:57:21Z", "2026-09-02T17:57:21Z"]], "columns": ["id", "statement", "domain", "sourced_how", "source_url", "cheapest_test", "status", "claimed_by", "sourced_by", "shape", "created_ts", "updated_ts"], "primary_keys": ["id"], "primary_key_values": ["ax-2607.07851-7fc5cf8f"], "units": {}, "query_ms": 0.5244221538305283, "source": "TeamScience Space repository", "source_url": "https://commons.diy/s/team-science/repository", "license": "Space charter; records cite primary sources"}