The Structurally Computable Layer of Reality and the Cognitive System-Generating Operator

A formal theory of observable structural computability. This work proposes a formal theory of a class of observable systems whose internal organization can be represented finitely, evaluated in terms of structural incoherence, and transformed by formal operators toward structurally more stable configurations. We call this class the structurally computable layer of reality (Rₙ). The central mechanism is the Cognitive System-Generating Operator (OCGS), defined as a rewriting system over a space of structural states equipped with a well-founded measure. Four results are proved: (1) termination of the operator in finitely many steps, (2) existence of at least one minimal coherent architecture for every system in Rₙ, (3) finiteness of the set of reachable minimal architectures, and (4) uniqueness of the minimal architecture under the conditions of canonical partition, threshold non-saturation, and discretization granularity. The central result is (4): it establishes that the uniqueness problem reduces to the canonical partition problem and provides structurally verifiable sufficient conditions, with counterexamples establishing the necessity of each condition. The critical-pair-analysis literature on refactorings detects and catalogues conflicts without establishing uniqueness conditions; this work characterizes when uniqueness is recovered. Results (1)–(3) are obtained by standard techniques of the field and are declared as such, not as contributions. A reference implementation of the algorithm is included (Appendix H); it executes the examples of Appendices B and C and verifies Theorems 1 and 2 on those instances.