גאומטריה של אופטימיזציה: צמצום מדויק, סיום קנוני ואישוש מבנה

תקציר מקורי באנגליתarXiv:2609.12991v1 Announce Type: new Abstract: Training data constrains optimizer geometry through the covectors visible to a declared information channel. We study how such partial information determines a full positive cometric relative to a reference and which degrees of freedom remain unidentified. Our central result resolves full-column-rank positive-definite compression under affine-invariant Riemannian geometry. The compression map is a split-Hadamard metric submetry and admits an explicit unique completion that is the affine-invariant nearest full geometry realizing a visible target and yields exact full-to-visible variational reduction. When the channel moves, the completions form a gauge-invariant rank stratification of the positive-definite cone. Its closed-form pullback pair m