R-layer Mode Theory XXII: Information Flow and Emergent Dynamics — Unified Dynamical Structure Across Scales

Volume XXII establishes the dynamical foundations of the R-layer Mode Theory (RLMT) by showing that motion, force, time, energy, entropy, and gravitational curvature arise from the flow of information within the tension-field. Building on the structural unification developed in Volume XXI, this volume demonstrates that quantum evolution, classical motion, and gravitational dynamics are not separate physical regimes but different projections of a single informational continuum.

The central results include:

• Information flow as the origin of dynamics: Motion is interpreted as the evolution of informational modes across hierarchical layers, rather than the displacement of objects in an external spacetime background.

• Emergent temporal structure: Time is defined as the rate of informational change, and the arrow of time arises from the asymmetry between accessible and dispersed information.

• Energy and entropy from information density: Energy corresponds to gradients in information density, while entropy measures informational accessibility across layers.

• Hierarchical dynamics: Microscopic fluctuations propagate upward to generate classical behavior, while global informational gradients propagate downward to shape local evolution.

• Emergence of classical motion: Classical trajectories minimize informational dispersion across layers, providing an informational interpretation of the principle of least action.

• Gravitational dynamics as global information flow: Curvature and gravitational attraction arise from global informational gradients within the tension-field.

Volume XXII completes the dynamical foundation of RLMT and prepares the ground for Volume XXIII, where the informational continuum is extended to cosmology and large-scale structure.