Canonical Foundations

The Canonical Foundations are stable reference documents for Coherence Geometry. They fix terminology, definitions, named results, and statement forms used across the CG framework.

These documents are not ordinary blog posts and are not intended to be read in upload order. They function as reference anchors for the foundation papers, working texts, demonstrations, and research documents linked elsewhere on this site.

Where later papers use different notation or earlier phrasing, the canonical documents should be treated as the current terminology reference.

Canon List

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

    This canon fixes the canonical terminology, core objects, and named results of Coherence Geometry (CG). It serves as the naming and reference spine for all later CG papers, seed notes, software, and applications.

  • CGI-CDR-01 (v1.0): Physics Branch Canon

    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.

  • CGI-CDR-02 (v1.0): Mathematics Branch Canon

    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).

  • CGI-CDR-03 (v1.0): Variational-Relaxation Structure Canon

    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.

  • CGI-CDR-04 (v1.0): Coherence-Geometric Information Substrate Canon

    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.

  • CGI-CDR-05 (v1.0): Curvature-Driven Amplitude Relaxation Canon

    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…