Paper 125H: Exact Möbius Completion and Prime-Feedback Criteria for the Riemann Hypothesis Controlled Energy Sectors, Real Modes, and a Moving-Tail Induction

This paper consolidates the constructive results developed after the Paper 125G componentmap into one arithmetic account. Exact prime insertion and square-root completion preserve acompleted earlier range and retain every finite-boundary term. The original smooth observationhas an explicit finite diagonal, an absolutely summable thin interaction strip, and adjacent-shellcoupling. A fixed density-balanced observation preserves sensitivity to every nontrivial zeta zero whilesuppressing small products; quantitative smoothness localizes the remaining factors to logarithmicneighborhoods of square-root scale. Complete square-related families have a fourth-power logarithmicenergy bound. A local second moment supplies a simpler Riemann-hypothesis criterion, with realorthogonal modes and a universally bounded high-mode remainder. The principal conditional resultis a linear prime-feedback induction: after the primes below the square of the logarithm are accountedfor, a near-critical amplification bound for the assembled remaining tail would imply the Riemannhypothesis. Exact higher-power cancellation and cross-band compensation specify which interactionsmust remain assembled. Source calculations are distinguished from finite checks of the consolidatedimplementation. The required tail-amplification estimate is not proved; neither a new unconditionalnumber-theoretic exponent nor a proof of the Riemann hypothesis is claimed.