• 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…

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.