A Note on Phase Relations in Finite Oscillatory Systems: A Primitive Framework for Coupling, Cancellation, and Coherence

This publication presents a conservative mathematical framework for describing phase relations within finite oscillatory systems. The work develops a terminology for cancellation, reinforcement, coherence, coupling, boundary selection, and energy accounting using finite sums, elementary inequalities, graph relations, and classical mathematical methods. The publication does not propose a device, engineering implementation, energy source, or experimental apparatus. It is intended as a conceptual mathematical note establishing definitions, classifications, and analytical vocabulary for future mathematical, numerical, or experimental investigation. The work remains within conventional conservation principles and explicitly separates source terms, coupling mechanisms, boundary effects, and observable outputs.