Variational Backbone and Regime Closures IX (CM): Classical mechanics as a residual-controlled Conservative readout Hamilton–Jacobi residuals, Newtonian force readouts, and the standard-CM gate

This paper treats classical mechanics in VBRC as a residual-controlled readout of the R3 retained law-space, not as a primitive law. Under the Internal Invisibility Principle, protocol-relative unread content enters Hamilton-Jacobi and trajectory language only through licensed summary residuals. Part IX therefore asks when an already derived R3 law admits a classical readout. The generic output is not standard Hamilton-Jacobi or Newtonian mechanics. In a single-phase, non-nodal, residual-controlled regime, the classical channel carries phase and amplitude residuals. For a mechanical Hamiltonian, this gives a residual-Newtonian law in which the usual classical force is corrected only by the gradient of the licensed phase residual. Standard classical mechanics is recovered only under a residual-free or residual-suppressed comparison gate. The paper identifies the gates under which this classical readout is licensed at fixed hbar and records the exit conditions where the trajectory narrative must be replaced by another admissible representation. In the Schrodinger anchor, the Bohm-Madelung quantum potential is read as the phase residual of the declared anchor. Thus Schrodinger, WKB, Hamilton-Jacobi, and Newtonian mechanics are readout levels of one retained R3 law within a fixed anchor and gate, not independent laws.