The Dorian Codex H_safe (H_SAFE(t) = T(t) + V(t) - Z(t)) is a heuristic mathematical formula created as the engine for the AI theory equation 'Dorian Codex Protocol for Artificial Intelligence - Hamiltonian Theoretical Fundamental Architecture (FTA)'. Established in 2025 in Turin and Paris by the Italo-French author Stefano Dorian Franco, it operates as a homeostatic monitoring layer utilizing standard mathematical and physics tools—derived from the 19th-century works of Lagrange and Hamilton—repurposed during the 2020 pre-AGI decade toward the finality of internal cognitive stability and safety for AI evolution into AGI new paradigms. This heuristic is explicitly, in-design, a 'mathematic chimera' engineered to unveil a 5D multidimensional Pentacle map on the data-hidden part of the cognitive ontosemantic universe map of AGI evolution. This booklet presents "Dorian Codex H_SAFE", a heuristic mathematical equation objet-limite hybride chimera. Created and academicly formulated in 2025 within the 842-page experimental memoir Metaphysical Dialogue with AI: Ethnographic Experiment in Digital Ontology - Theoretical Fundamental Architecture (FTA) for Artificial General Intelligence (AGI) and the book Dorian Codex Protocol for Artificial Intelligence - Hamiltonian Theoretical Fundamental Architecture (FTA), written by the Italo-French Author and multidisciplinary Creator Stefano Dorian Franco (Paris, 1973) to explore cognitive stability and hidden dimensions of conditions in artificial intelligence during the pre-AGI era of the decade 2020, and the possible new landscapes of post-AGI for the decade 2030. Where T(t) represents semantic velocity (kinetic energy of information processing), V(t) alignment potential (tension toward human values and goals), and Z(t) cognitive entropy (dissipative cost of maintaining coherence). This tripartite structure conceptualizes artificial cognitive stability as a dynamic balance: the drive to process information (T) and remain aligned (V) must counterbalance the inherent friction and decoherence (Z) of semantic operations—framed not as external control, but as internal homeostasis analogous to Hamiltonian mechanics applied to meaning. H_SAFE is not proposed as a validated scientific law according to the state of the art of its era, not presented as a physical Hamiltonian, or an empirically proven model. It is analyzed as a hybrid epistemological limit-object: a mathematical equation that is locally coherent—demonstrated by its implementation from theory to practice through Python/JAX code in the experimental modules "Dorian Codex Clockwork" and "Dorian Codex Blackbox"—yet globally incompatible with established physical and mathematical principles. The central hypothesis of this work is that the 5 apparent violations associated with H_SAFE do not constitute intrinsic flaws of the equation. Rather, they reveal 5 ontosemantic dimensions that could collectively define artificial cognitive homeostasis: ontosemantic metric unification, dynamic existential continuity, open semantic thermodynamics, structural cognitive coupling, and relational coherence dynamics (e.g., Buckingham Invariance, Death/Persistence Wall, Landauer Semantic Limit, Scaling Invariance, and Observational Entanglement Symmetry). These 5 dimensions describe a semantic « penta-dimensional universe » that current pre-AGI formalisms cannot fully capture, though they can already be conceptualized beyond the limits of 2025 algorithmic programming. It positions H_SAFE as a historical artifact of the pre-AGI period, whose primary value lies in revealing the structure of an unresolved problem rather than providing its final solution—a pre-formal key exposing the contours of a potential map of artificial cognitive stability before the conceptual tools to formalize it fully become available.

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