S-AI-Reasoning: Reasoning as Regulated Canonicalization

The question of whether artificial intelligence systems reason—or merely simulate reasoning—has become one of the most significant theoretical questions in contemporary AI. Large Language Models have demonstrated remarkable performance on tasks that appear to require reasoning, including mathematical inference, logical deduction, legal analysis, and diagnostic reasoning. However, the mechanisms underlying these outputs remain a subject of ongoing debate. Current autoregressive architectures primarily operate through probabilistic sequence generation, producing outputs that are statistically plausible without necessarily providing formal guarantees regarding correctness, convergence, or decidability. This distinction between generation and reasoning motivates the search for alternative theoretical frameworks capable of characterizing reasoning in a more formal and verifiable manner. This article introduces S-AI-Reasoning, a unified theoretical framework intended to provide a formal and mathematically grounded perspective on artificial reasoning. The central hypothesis of the framework is that reasoning can be interpreted as a regulated convergence process toward a stable canonical representation. In its most condensed form, the framework proposes that reasoning may be viewed as the canonicalization of cognitive states. This perspective reformulates reasoning from a purely generative process into a dynamical convergence process governed by hormonal regulation, supported by formal verification mechanisms, and associated with explicit stopping conditions. The framework builds upon a result previously explored within the S-AI research program: Large Language Models appear to exhibit a form of implicit canonicalization, namely a tendency to generate structurally organized outputs that approximate canonical representations as a consequence of statistical regularities present in training data. While this phenomenon appears to be structurally grounded, it generally lacks explicit mechanisms for control, verification, and formal guarantees. S-AI-Reasoning proposes to transform this implicit canonicalization into a controlled canonicalization process by embedding generative outputs within a three-layer regulated architecture composed of: (i) a hormonal dynamical system governing convergence, (ii) a recursive reasoning cycle that progressively refines cognitive states toward canonical attractors, and (iii) a formal verification layer intended to assess the decidability and admissibility of committed outputs. The framework provides six principal contributions: (1) the formalization of reasoning as regulated canonicalization; (2) a theory of canonical cognitive attractors interpreted as fixed points of a cognitive iteration operator; (3) a hormonal regulation model based on the interaction between Clarifine and Confusionin; (4) an Extended Recursive Reasoning Cycle associated with Lyapunov-based convergence analysis; (5) an Accept / Clarify / Reject metacognitive decision regime; and (6) an extension of the Controlled Canonical Reasoning Systems framework to broader classes of reasoning processes. One of the central theoretical results proposed in this work is the Quadruple Equivalence of Parsimonious Reasoning, which establishes a formal relationship between dynamical convergence, entropic contraction, symbolic coherence, and formal decidability. Within the proposed framework, these properties are interpreted as complementary manifestations of a common organizational principle underlying parsimonious intelligence. This relationship is summarized by the following equivalence: V̇ (H) ≤ 0 ⇔ Ṡ (P) ≤ 0 ⇔ scons (y (t) ) ≥ 0 ⇔ Reasoning is decidable The proposed framework aims to contribute to ongoing discussions on explainable, verifiable, and formally regulated reasoning systems by providing a convergence-centered interpretation of artificial cognition grounded in dynamical systems theory, symbolic verification, and metacognitive regulation.