The standard structures of classical mechanics — Newton I/II/III, conservation laws, the Lagrangian and Hamiltonian formalisms, and Newtonian gravitation — are conditionally reconstructed within a budget-constrained (I²+R²+C²=1) cubic-lattice substrate, given the microscopic update taken from companion work in preparation and explicit semiclassical, symmetry-lifting, soliton-sector, and weak-field assumptions, without introducing the Newtonian axioms as independent postulates. The derivation yields the classical Lagrangian L=T-V through the chain dissonance functional Hamiltonian unitary update low-energy Schrödinger band dynamics collective-coordinate and Hamilton--Jacobi limits; Links 1 and 2 are substrate-level inputs taken from companion work in preparation, and the present paper develops the resulting mechanical consequences. Newton's three laws then follow from the Euler--Lagrange equation — Newton III in the instantaneous conservative two-body limit — while momentum and energy conservation arise in the long-wavelength autonomous effective theory, and angular-momentum conservation arises at leading isotropic order under conditional Haar averaging over the polycrystalline grain ensemble, with residual anisotropy not derived here. Newtonian gravitation is conditionally recovered from an assumed local, linear, isotropic, gapless scalar response with trace-source coupling, whose static Green function yields the 1/r potential; G c³ a²/ then follows as a Buckingham- closure when the substrate length is identified with the Planck length. The scalar gravitational potential is assigned to the A₁₆ sector of the substrate dissonance and sourced through a working trace-coupling ansatz to the stress-energy tensor, not a microphysical derivation. Buckingham's -theorem precludes a numerical prediction of G from dimensional analysis alone, but a microdynamical derivation of the coupling prefactor plus one independent dimensional anchor would close the framework numerically. Classical mechanics thus appears as the macroscopic-soliton semiclassical limit of the lattice dynamics.
Oliver Marc Wittwer (Wed,) studied this question.