• 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.

Seed Notes

• CGI-000001 (v1.0): Seed Note — Coherence-Driven Intelligence (CDI)

  This page describes Seed Note CGI-000001: Coherence-Driven Intelligence (CDI),also referred to descriptively as “Emergent Intelligence” (EI). Update May 2026: The original documents are available now published and listed in the Primary Artifact section below. What this seed note does CGI-000001 fixes naming, claim scope, and provenance pointers for the CDI/EIdemonstration work. It is a seed-level…

• Mathematical Foundations of Coherence Formation and Stability

  CGI-RSR-000010 | We establish a mathematical framework for coherence formation and stability in energy-minimizing phase systems. Introduces the UCCP, SCRC, and CS-SCT.

• A Multi-Phase Extension of Complex Numbers and the Global Coherence Theorem

  CGI-RSR-000009 | This is the foundational document that introduces multi-phase numbers and the Global Coherence Theorem (GCT).

• A First-Order Terminal-Closure Criterion for the Riemann Hypothesis and the Exterior-Rank Source Boundary

  Internal ID: CGI-RSR-000008 | We formulate a strict first-order terminal-closure criterion for the Riemann Hypothesis using a matrix-valued completed explicit formula.

• Universal Kernel Operators and Seed Correspondences in the Direction of the Hodge Conjecture

  Internal ID: CGI-RSR-000007 | We study a natural operator associated with the wedge product on exterior powers and show that its kernel admits a universal representation-theoretic structure.

• Projective Rank-one Closure for Terminal Navier–Stokes Saturation

  Internal ID: CGI-RSR-000006 | We study terminal rank-one saturation mechanisms in a dyadic analysis of the three-dimensional incompressible Navier–Stokes equations. Starting from a high–high OBCI closure module for comparable high-frequency interactions, we analyze the remaining determining-scale paraproduct strain branch using localized output Gram matrices. No terminal nondepleted rank-one output-coherent saturation branch persists under the stated…

• Coherence Geometry Foundations, Part I: Orientation, Closure, and Algebraic Foundations

  CGI-BKS-0001 | Part I of the Coherence Geometry Foundations working reference text. It introduces multi-phase numbers, shared-amplitude phase structure, mathematical closure, projection, coherence relations, coherence matrices, coherence manifolds, projective coherence objects, morphisms, operators, and the canonical convergence and stability results governing coherent systems.

• Coherence Geometry Foundations, Part II: Physical Projections

  CGI-BKS-0002 | Part II of the Coherence Geometry Foundations working reference text. It examines how quantum-like linear dynamics, causal and relativistic structure, residual coherence strain and cosmological background terms, electromagnetic field structure, thermodynamic behavior, and macroscopic transport can be represented as domain-level projections of the shared-amplitude, multi-phase coherence framework.