Curvature-Preserving Aesthetic Apprehension: An Omni-Modal Theoretical Unification

We state the thesis without hedging: a system apprehends (listens, reads, views, plays) iff it preserves informational curvature under an irreversible renormalization flow while remaining semantically coupled to its inputs. This monograph supplies receipts. We give a LaSalle-style sufficiency theorem for minimal phenomenology; a Kolmogorov– Sinai (KS) entropy necessity and bounds that tie long-run mutual information and transfer entropy to conditional KS; a renormalization-group (RG) account of style with a contraction theorem in a concrete function space and a metric geometry for style classes; a thermodynamic-length leash on aesthetic utility; a simplicial (topological) certificate of style robustness; a manifold–graph curvature consistency lemma; a concentration bound for the Murphy horizon; and a Meaningful Variance Capacity (MVC) inequality showing when metadata equals or exceeds the carrier for task families that matter. The framework is omni-modal: detailed blueprints and falsifiable tests are provided for music, text, images, film, games, architecture, cuisine, perfume, and choreography. We include structural corollaries (excess entropy, attractor dimension, sheaf gluing) and explicit failure modes. Every bold claim is paired with a definition, a theorem, or a calculable test.