KFX: Finite Adjudication-Based Formal Systems

KFX is a collection of finite, explicit, and adjudication-defined formal systems investigating how structured order, long-range correlation, and constant-like statistical behaviour can emerge from constraints alone. All systems in this collection share the same foundational stance: all primitives are finite and explicitly defined; no assumptions of continuity, infinity, probability, or causal dynamics are introduced; world histories are not generated by dynamical laws, but recognised through legality, constraints, and adjudication; all claims are verifiable via finite enumeration or exact checking. The collection includes several complementary formal world kernels: kfx–Rabbit Hole (v4) A discrete world-level formal system defined by local freedom, sliding-window constraints, incommensurate subcycle closures, and a final adjudication layer.It demonstrates that non-trivial ratios, apparent randomness, and irrational growth rates can arise purely from legality and constraint, without probabilistic or continuous assumptions. kfx–Plato Cave An adjudication-defined reformulation of Plato’s Cave.Truth, error, liberation, and conflict are defined structurally via visibility domains, projection, accessibility, and information constraints, rather than epistemology, psychology, or metaphor. KFX–Laozi A finite phase-segmented formal system with global settlement conditions and exhaustive enumerability, serving as a minimal example of how sparse and structured outcomes can be induced purely by global constraints. Scope and Non-Claims These systems are not physical theories, not models of empirical reality, and not attempts to derive or explain physical constants or prime numbers.Their purpose is formal: to provide clean, falsifiable examples showing how order, disorder, and constant-like structures can arise in purely discrete, adjudicated systems. Language Note The Chinese and English documents in this record are not translations of each other. They are independent formal expositions written in different languages.Formal meaning in this framework is carried primarily by definitions, constraints, and structural relations, not by natural-language phrasing.Given the availability of modern translation tools, strict linguistic equivalence is neither required nor intended, and enforcing it would inevitably discard structural information. Readers should therefore treat different language versions as complementary views, not interchangeable copies.