Rederivation of the Acceleration Map by a Real-Center Reading in a Closed Two-Body AB Phase System

Abstract

A derivation-replacement paper for the published inverse-square acceleration paper of the Wave Information Readout series. The virtual rotation center at the future phase position is removed: the only centers are the real ones — the parent-closure center O and the partner B on the same circle. The reading closes with three circles (parent radius R, B's intrinsic radius R' = (m/M)R derived from the resolution axiom, and the relational distance R'' = 2R sin(theta/2)). Elementary geometry gives the differential component g = omega^2 R''/2 of the centripetal identity, which is kinematically identical to a bound two-body orbit about the common barycenter (equal-response case) — gravity-type motion is not a new force but the local two-body differential representation of the common constrained motion on the parent closure. The equivalence principle is derived, within the adopted readout class, as a corollary of the conserved-readout classification theorem (phase blindness): a kinematic, pre-geometric prototype whose scope is stated explicitly. The published inverse-square law alpha_n = R Omega^2 / Delta-theta_n^2 is rederived as exactly the same formula. The scale variable of the square-type gravitational grammar is identified with the resolution ratio m/M. The Kepler-type closure condition omega^2 R''^3 = const. is stated as the central open problem for the sequel. Derivation only — no new numerical experiments; all numerical facts rely on the published reproduction packages. Japanese and English versions included.