Paper 175 A Mechanical Framework for Baryon Acoustic Structure in Holosphere Theory

A conservative occupied face-centered-cubic contact system can carry angular disturbances,redistribute a positive conserved inventory, and return emitted energy to a localized source. Thispaper develops that mechanical chain from the 60 and 163–174 series and their supporting mechanics.Reciprocal cosine contacts give explicit momentum and energy currents, a protected-coherencecondition and a controlled spherical-wave limit. A separately stated inventory–storage Hamiltoniansupplies the density response: its two exact linear branches identify when the response is acousticand when it remains quadratically dispersive. A rotor coupled to one occupied edge first changeslocal phases and then produces a compensated inventory disturbance. Linearization about the actualcoupled equilibrium gives its frequency shift, positive spectral weights and exact feedback memory;direct nonlinear integration checks the same interaction. An explicit error identity distinguishes staticstorage elimination from a reduction that retains the storage’s added inertia. Internal redistributionalso fixes the zero-wave-number constraint on any resulting density kernel. These results establisha conservative source-to-medium mechanism within the declared model. Its inventory-to-storagecoupling is a constitutive proposal; baryon identification, a physical source population and anindependently calibrated astronomical length remain the connections needed for a BAO prediction.