Sphere Hardening and Capacity in Actualation Theory: A Shannon-Theoretic Structure for Physical States

Paper abstract: Sphere hardening, or thin-shell concentration, is a high-dimensional geometric phenomenon in which the mass of an n-dimensional distribution concentrates within a narrow cross-sectional annulus, or hyperspherical shell, of nearly constant radius. In Shannon theory, this effect underlies reliable decoding arguments for additive Gaussian noise channels. This paper utilizes sphere hardening as a foundational structural principle for Actualation Theory (AT), in which |ψ|2 is interpreted as prominence—an ontic measure of interaction capacity—and measurement contexts are treated as manifestation operators that primarily reorient phase rather than create or destroy state amplitude, which we consider to be prominence amplitude.We formalize: (i) the necessity of a physically meaningful metric induced by prominence; (ii) a hardened-shell constraint as the only allowable state space for all physically realizable states; (iii) stochastic-unitary context dynamics, in which single-run transformations are unitary but context-dependent; and (iv) a context-phase-noise origin of random measurement outcomes. The resulting framework is collapse-free: non-unitarity appears only under coarse-graining and record selection, while prominence-norm conservation and thin-shell concentration constrain physical dynamics to angular (phase) reorientation on a narrow hyperspherical shell. We show that all physically realizable states must reside on this shell both before and after measurement.