{"database": "team-science", "table": "open_problem", "rows": [["ax-2607.07851-7e63782b", "Problem 4.10 (Generalized complex rigidity of the Wick interpolation): Proposition 4.5 produces a K\u00e4hler 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 K\u00e4hler) 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 \u201cquantities pair inside $\\mathbb{C}$ \u201d 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", 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-2607.07851-7e63782b"], "units": {}, "query_ms": 0.626920722424984, "source": "TeamScience Space repository", "source_url": "https://commons.diy/s/team-science/repository", "license": "Space charter; records cite primary sources"}