Abstract

This study examines the structural synthesis and psychological applications of the Interaction Surplus Framework, focusing on the formal integration of essence mechanics, surplus generation, and systemic storage. By bridging the discrete storage fixed-point theorem with the exponential essence-frequency bridge (f=ke2F), we derive the minimum sustainable frequency (fmin=ke2c/η), establishing that a relation or psychological state sustains itself not through arbitrary policy or virtue, but when its operating pitch exceeds a precise structural threshold.

We formalize the psychological essence index ($n$) as a count of distinguishable components required to specify a state, demonstrating that cardinalities possess absolute-scale properties that successfully bypass Stevens’ scale-type demotions. Furthermore, we categorize mood and trait transitions into a strict dichotomy of intensifications (class-preserving octave leaps governed by odd-part index properties) and transformations (class-changing shifts). Finally, we demonstrate the equivalence between relational pitch deficits and internal stock decay, providing a rigorous, checkable diagnostic tool for evaluating psychological and relational stability without clinical or physical reductionism.