This series presents, in a unified manner from principle to execution, how a system changes and how it reaches its next state. Traditionally, change has been understood as a continuous and gradual process. However, this theory shows that when certain conditions are met, there exists a mechanism by which a system can switch states directly, without passing through intermediate stages.
This sequence is described through four phases: what occurs (Principle), the space in which it occurs (Structure), which path is selected (Selection), and how it actually occurs (Execution).
Part I — The Executable Spacetime Principle
The Executable Spacetime Principle: Phase-Jump Transitions in Gauge-Constrained Dynamical Systems — Boundary-Layer Dynamics, Structural Superposition, and Residual Intelligence This part shows that change arises not as a breakdown or discontinuity, but as a reconfiguration of constraint structures, and it introduces the fundamental transition concept known as the Phase-Jump.
Part II — Logical Distance Compression and Residual-Guided Phase Selection in Executable Systems
Logical Distance Compression and Residual-Guided Phase Selection in Executable Systems This part defines the ease of reaching a state as logical distance and provides the geometry by which this distance is deformed through causal structure.
Part III — Causality as Irreducible Concentration — Selection Mechanism in Executable Systems
Causality as Irreducible Concentration — Selection Mechanism in Executable Systems This part interprets causality not as correlation but as concentration, and it presents the principle that determines which transition is actually selected.
Part IV — Logical Distance Warping and Executable Transition Dynamics — Observational Correspondence in DART Orbital Residuals and Structural Reconfiguration of FAQ Fields in Ken‑OS
Logical Distance Warping and Executable Transition Dynamics — Observational Correspondence in DART Orbital Residuals and Structural Reconfiguration of FAQ Fields in Ken‑OS This part establishes the execution mechanism (Warp) in which logical distance effectively collapses, allowing a state to switch instantaneously. It also shows how this mechanism corresponds to both observational data and social systems.
What this tetralogy demonstrates is a view in which change does not proceed gradually over time, but instead occurs when the difficulty of reaching the next state disappears. A system does not move step by step; it transitions to its next state at the moment the necessary conditions are satisfied. In this sense, change is not a continuous process but a phenomenon that is realized as execution.
