Variational Backbone and Regime Closures I: Energy as a Variational Language A Density-Fixed Variational Backbone and a Scoped First-Derivative Representative

Part I fixes the common Structural Layer of the series. The point of the series is not thatgeneral relativity, quantum mechanics, and classical mechanics are independently postulatedand then reverse-engineered from a common formalism. Rather, the series begins from theInternal Invisibility Principle (IIP) as a constitutional axiom of partial accessibility, andwithin that scoped requirement fixes one density-fixed variational backbone E whose licensedreadouts are developed in later parts.Under IIP, an instance/protocol specifies what is retained and read out, while a gatestates the objective validity/admissibility condition for a regime. Once such a gate is realized,the corresponding output is fixed by the same backbone within the declared scope. Part Itherefore fixes the primitive backbone, the scoped first-derivative representative class, andthe three density-fixed readings (R1/R2/R3), leaving analytic closure to Parts II–III andrepresentation/update semantics to Part IV. The proposition-level statements proved hereare internal variational/calculus consequences of the declared backbone and conventions;they are not yet regime theorems for GR, QM, or classical readouts.