Reactive Series and the Geometric Reinterpretation of φ: A Hierarchical Expansion via (i/ω)ⁿ

This paper presents a novel interpretation of wave propagation and reactive dynamics based on a converging series expansion of action and reaction terms. The scalar field φ is redefined as a geometric sum of the form: where each term represents a phase-shifted and attenuated response to an initial action A. This formulation implies that physical reactions are not instantaneous, but emerge as layered echoes through closed surfaces. The paper further shows that wave propagation itself is governed by this reactive hierarchy: energy is preserved when no resonance occurs, but is absorbed through geometric coupling with external structures when resonance conditions are met. High-frequency components (larger ν) are more likely to excite smaller bodies and thus decay rapidly, making them less observable at long distances. This framework offers a geometric basis for interpreting dissipation, resonance, and energy transfer beyond conventional point- Tetsuo Konno(今野哲夫)https://orcid.org/0009-0002-1842-7865