CGI-CDR-00 (v1.0): Canonical Definitions and Results

This canon fixes canonical terminology, primary objects, and top-level variational statements for the mathematics branch of Coherence Geometry (CG). It defines the coherence field, the Unified Coherence Functional (UCF), and the canonical projection naming scope across mathematical domains (algebraic, geometric, analytic, topological, probabilistic, and logical/computational).

This canon fixes canonical terminology, primary objects, and claim scope for the physics branch of Coherence Geometry (CG). It records the Unified Coherence Action (UCA) framing and a registry-style naming index for physics-domain projections, while keeping derivations and extended artifacts externally referenced.

This canon fixes the variational and relaxational formulation underlying Coherence Geometry, including canonical definitions of the coherence structure functional, coherence basins, and the variational–relaxation principle governing coherence-driven structure formation. It clarifies the distinction between intrinsic variational structure and the dissipative dynamics by which stable coherent configurations are reached.

This canon records the canonical coherence-geometric interpretation of information as a pre-symbolic, basin-structured phenomenon arising from constrained amplitude–phase configurations. This canon specializes the variational–relaxation framework established in CGI-CDR-03 to informational stability, noise, decoding, and inference, fixing terminology, scope, and conceptual boundaries without introducing new dynamics or implementations.

This canon records the coherence–geometric interpretation of curvature-driven amplitude relaxation (CDAR) as a physical organizing mechanism underlying diffusion–reaction–like pattern formation and spatial structure. It fixes scope, terminology, canonical claims, and representative field equations, positioning classical diffusion, reaction, and band-selection behavior as projected or limiting descriptions of a more structured coherence–geometric relaxation substrate. This document is a provenance and scope record and intentionally omits full derivations and implementations; referenced technical artifacts are tracked via SHA-256 hash commitments included in the release package.