M20d Operational Logic Engineering: I: Non-Derivative Operational Circuits & II: Cryptographic Implementations & III: The RH Hunt - Computational Tools

This monograph develops applied directions of Operational Logic Engineering, focusing on how algebraic and logical structures emerging from the operational framework give rise to new classes of computational objects and problem formulations. The emphasis is not on deployment or optimisation, but on identifying structural hardness sources, novel computational regimes, and experimentally testable reformulations of classical problems. The first part investigates non‑derivative operational circuits, examining how logic systems beyond the Boolean and polynomial domain can be realised abstractly through operational semirings. Tropical, fuzzy, phase‑based, and non‑commutative logical structures are analysed as computational primitives, yielding a unifying design language for circuits whose behaviour is governed by rank, algebraic symmetry, and non‑associativity rather than by linear composition. The second part introduces a family of cryptographic problem formulations derived from intrinsic algebraic properties such as cloning, rank ambiguity, and operational non‑invertibility. No claims of security, efficiency, or readiness for use are made. Instead, the work isolates candidate hardness assumptions and formal problem classes, positioning them as objects of future cryptanalytic and complexity‑theoretic study rather than as cryptographic schemes. The third part develops computational tools motivated by the operational reformulation of analytic number‑theoretic questions. These tools are presented as experimental instruments designed to probe structural conjectures through computation, without asserting resolution of any classical open problem. The emphasis is on translating abstract operational identities into falsifiable numerical experiments. Throughout, the monograph maintains a strict separation between theoretical formulation, computational experimentation, and practical deployment. It is intended as a source of new questions, frameworks, and testbeds, not as a catalogue of finished technologies. All constructions are presented at the level of mathematical structure and problem definition, leaving implementation, optimisation, and security analysis explicitly open.