Coherent Structural Universe and Defect-Conservation Ontology: A Logical Encirclement of Geometric Legitimacy and Higher-Power Inheritance

Relation to Previous Work This manuscript is intended as a structural-ontology supplement and conceptual backbone to the earlier work entitled:“Dimensional Reduction Mapping of Fermat’s Hyper-Equations: A Complete Discrete Isolation Proof Based on the Logical Over-Premise Negation Theorem”.Whereas the previous paper focused primarily on formal discrete-isolation logic, dimensional reduction behavior, and logical over-premise negation mechanisms, the present manuscript develops the deeper ontological and structural foundation underlying those conclusions. In particular, this supplementary framework introduces: the rigid cube realization of cubic powers,the Defect-Conservation Principle,the closed discrete structural system model,and the inheritance behavior of higher-dimensional power structures. Together, these concepts provide the philosophical and structural continuity supporting the earlier dimensional-reduction framework. This paper therefore should not be interpreted as an unrelated standalone proposal, but rather as the ontological extension and conceptual reinforcement of the previously established discrete-isolation architecture.The purpose of this supplementary manuscript is to clarify the internal structural logic that motivated the original dimensional-reduction mapping framework, especially regarding why higher-order Fermat-type equations may exhibit persistent non-closure behavior under rigid discrete geometric realization. Statement of ScopeThis document does not claim to provide a universally accepted formal proof of Fermat’s Last Theorem in the modern institutional sense of arithmetic algebraic geometry. Instead, it establishes a narrower but logically stronger claim: within the Coherent Structural Universe defined below, the ontology-driven “defect conservation framework” cannot presently be internally contradicted through ordinary mathematical refutation. Any attempt to dismiss this framework purely by denying the cuberepresentation must face a profound hurdle regarding historical geometric legitimacy. Research Note (June 2026) This publication represents the second public stage of the Fermat Exploration Project. The ideas discussed here originated from an earlier publication and were later critically reassessed in a subsequent paper. Related publications: • Dimensional Reduction Mapping of Fermat's Hyper-Equations:A Complete Discrete Isolation Proof Based on the Logical Over-Premise Negation Theoremhttps://doi.org/10.5281/zenodo.20580690 • The Search for Mirabilem:How an Independent Learner Explored Fermat's Last Theorem with AIhttps://doi.org/10.5281/zenodo.20840419 Readers interested in the complete context of this exploration are encouraged to consult all related publications together.