What question did this study set out to answer?

February 16, 2026Open Access

Relational Constraint Foundations (RCF)

Key Points

Establish a minimal axiomatic framework for structural entropy and persistent observability.
Develop axioms for relational possibility spaces with constraints
Derive a canonical definability algebra and graded definability hierarchy
Investigate the relationship between definability entropy growth and capacity growth.
Introduced a framework governing structural observability
Proved necessary and sufficient inequalities for entropy growth and capacity
Showed growth of intrinsic structural entropy based on definability.

Abstract

Relational Constraint Foundations (RCF) establishes a minimal axiomatic framework for structural entropy and persistent observability based on relational possibility spaces equipped with proper constraints. From these primitives, a canonical definability algebra and graded definability hierarchy are derived, inducing intrinsic structural entropy growth. The framework proves that persistent cumulative structural observability is governed by a necessary and sufficient inequality between structural definability entropy growth and extraction definability capacity growth. RCF provides a constraint-first foundation for structure, entropy, and observability without assuming metric, probabilistic, or physical structure. Related resourcesAdditional preprints, theoretical frameworks, and ongoing work by the author are available at:https://murad-ahmadov.github.io/

Relational Constraint Foundations (RCF)

Key Points

Abstract

Cite This Study