The Theory of Relational Evaluation in Compounding Systems (RECS): The Boundary-Value Paradox

Abstract

This paper presents the formal mathematical and structural framework for the Theory of Relational Evaluation in Compounding Systems (RECS), introducing the Boundary-Value Paradox. Conventional analytics evaluate compounding growth sequences through absolute value metrics over time. This framework proves that the objective valuation and human perception of "explosive growth" are non-intrinsic attributes generated retroactively by a finite systemic boundary ($B$). We formalize three core systemic laws—Compression, Horizon Shift, and Terminal Enforcement—governing value extraction within exponential frameworks, providing a unified model applicable to macroeconomic theory, technology scaling, and systems biology. Version 1.1 includes revised terminology, improved mathematical notation, an updated conceptual figure, enhanced document formatting, and other editorial refinements while preserving the core theoretical framework.