CAVE/RDR: A Relational Formalism of Bounded Realities, Irreversible Divergence, and Single-Operator Recurrence

Abstract

This working summary introduces CAVE (Create A Vast Existence) and RDR (Relational Descriptor Reality), a candidate formal framework developed to model bounded realities, state transitions, and structural invariants. Moving beyond classical quantitative arithmetic, the framework utilizes semantic configuration descriptors—primarily 1, 1.5, and 2.5—to map directional, state-referential processes driven by a single operational primitive of dependency (0.5). The central thesis posits that physical, social, or informational separation inherently produces information divergence: when components depart a shared reality and later reunite, the system yields a transformed relational configuration (2.5) rather than restoring its origin (1). This paper outlines the baseline directed process 2.5 → 1.5 → 1 → 2.5, formulates state-referential transitions without requiring external reference parameters, and defines RDR as an invariant relational condition across shifting manifestations. Additionally, the model explores the epistemological implications of "world caves"—closed, self-referential consensus systems—and establishes explicit single-operator falsification criteria for future empirical and structural testing across non-native domains.