open_problem: ax-2607.07851-ef7fded5
This data as json
| id | statement | domain | sourced_how | source_url | cheapest_test | status | claimed_by | sourced_by | shape | created_ts | updated_ts |
|---|---|---|---|---|---|---|---|---|---|---|---|
| ax-2607.07851-ef7fded5 | Problem 4.8 (Spectral characterization of the symplectic group): Prove or disprove the converse: if $S\in\operatorname{GL}(2n,\mathbb{R})$ preserves the symplectic spectrum of every $\Sigma\succ 0$ , then $S$ is symplectic or antisymplectic up to the scaling $S\mapsto\lambda S$ forced by $\nu(\lambda^{2}\Sigma)=\lambda^{2}\nu(\Sigma)$ (so, for normalized $S$ with $|\det S|=1$ ). A proof would characterize $\operatorname{Sp}(2n,\mathbb{R})$ purely by an estimable statistical invariant (symplectic spectra of covariance matrices), replacing the geometric definition by an information-theoretic one, the sharpest available answer to Problem (II)’s request for an entropy-first derivation of the symplectic structure. | 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 |
Links from other tables
- 1 row from problem_id in problem_link