EMI v2 — Energia Multidimensionale Inclusiva / Emergent Minimal Invariants: An Axiomatic Framework for the Emergence of Geometric Representational Regimes

EMI — Energia Multidimensionale Inclusiva — is grounded in the hypothesis that observable physical structure emerges from a single form of energy constrained in its representability across dimensional regimes. The geometric constraints derived here are not external descriptions of that energy but the structural conditions it must satisfy to appear as stable observable configurations.From three axioms — a pre-geometric origin regime (A1), an asymmetric binary TIC/TME dynamics (A2), and a minimal stabilization principle (A3) — the framework derives a sequence of representational regimes D0→D1→D2→D3 without assuming any metric or topological primitive.EMI does not introduce new geometric objects: it derives why the simplest ones must appear. The minimal relational closures that emerge are the simplices of combinatorial topology: triangle (∂∆2, the boundary cycle of a triangle) and tetrahedron (∂∆3, the closed surface of a tetrahedron).Dimensional regimes emerge as the minimal extensions required to resolve representational conflicts generated by saturation of the previous regime. Each transition is the unique minimal configuration restoring representability after saturation of the previous regime. Two additional principles — Global Transverse Access (A4) and Minimal Trace (A5) — describe how higher regimes leave structural traces within lower ones. The mathematical tools employed are standard combinatorial topology; the contribution of EMI lies in the axiomatic mechanism forcing their emergence, not in the structures themselves.One problem remains explicitly open: the connection between geometric constraints and an absolute energy scale. EMI's relations are dimensionless and scale-invariant; without an energetic anchor the framework identifies structural conditions for representable configurations but not the physical scale at which they are realized. This is the primary open problem for subsequent development, together with the derivation of regime D4. EMI v1 (Zenodo, December 2025) explored geometric constraint compatibility with observed physical scales using a provisional energy framework derived from the total energy balance of the proton, in an attempt to express observable physical scales through geometric ratios. The energy values used in v1 should be understood as a first-order approximation of that approach, not as established physical derivations. It should be read as an early reconnaissance conducted before the axiomatic structure was consolidated. Its epistemological framing is superseded by the present version.