Dualities as Inter-Projection Equivalences of Stable Semantic Structures

Translator This preprint proposes a structural account of mathematical dualities grounded in invariant stabilization and regime-relative projection. Building on a reflexive decoding framework, we treat classical mathematical structures as representational projections of stabilized invariant content rather than as primitive foundations. Dualities are then interpreted as inter-regime correspondences between projections of overlapping invariant strata, with reversibility, asymmetry, and failure determined by invariant overlap, stabilization height compatibility, and projection-induced information loss. The contribution is explanatory rather than constructive: we do not rederive classical duality theorems, but classify well-known dualities (logic–topology, algebra–geometry, computation–logic, probability–geometry) as manifestations of stabilization structure. This perspective normalizes foundational pluralism and clarifies why exact dualities are rare while partial and one-sided correspondences are generic. Related preprints: Invariant Stabilization and Reflexive Reasoning (Zenodo: 10.5281/zenodo.18218117) and Classical Mathematical Structures as Stable Projections of Reflexive Semantics (Zenodo: 10.5281/zenodo.17954563).