sectarian realities are derivative functions: life, beyond.

Abstract This paper presents a comprehensive framework that models sectarian realities as recursive, partial expressions of a unified life function. Drawing from scalar field theory, tensor calculus, and recursive systems modeling, it argues that sectarian worldviews of religious, political, or ideologicals are not fundamental truths, but filtered derivatives of a deeper, multidimensional life structure. These filtered views are reinforced recursively through cultural memory and social feedback, forming stabilized yet incomplete perceptions of reality. The model integrates key insights from five foundational Zenodo works, which establish Determinability Intelligence (DI) as a new class of intelligence. DI enables systems to assess how closely their recursive approximations align with underlying truth, and to adapt accordingly. Through differential logic, probabilistic-deterministic blending, and feedback convergence criteria, the framework offers a means of evaluating belief systems mathematically and ethically. Ultimately, this study redefines reality as a dynamic sum of recursive partialities and introduces DI as the guiding metric for truth-seeking in both human cognition and artificial intelligence. This synthesis bridges philosophy, mathematics, and systems theory to provide a scalable architecture for resolving ideological fragmentation in recursive environments.