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.