The Emergence of Inertia and Energy:A Reconstruction of Classical Dynamics within the ZTD Discrete Spacetime Framework

Classical mechanics regards inertia and energy as fundamental concepts, typically taking Newton’s second law or the principle of least action as its logical starting point, without inquiring into their ontological roots. Within the ZTD (Marker Ontology) discrete spacetime theoretical framework, this paper provides a conditional reconstruction attempt of the foundations of classical mechanics. The framework starts from the ontological tension between "holistic invariance" (the statistical stability of isolated systems) and "local variation" (the finitude axiom prohibiting absolute rest). This paper first argues that this tension leads to second-order dynamics: the solutions of first-order discrete diffusion equations monotonically approach a deadlock (irreversible) and lack inertia, whereas the physical assumption that "the natural form of continuous change is reversible oscillation" prevents the system from coming to rest. Second, through rigorous Taylor expansion and symmetry classification, the tension is mathematized into a three-term cost function; under the assumption of the stationary-value mapping of the cost functional, the sign structure satisfying ground-state stability is uniquely locked as the cost-difference functional 𝐿=𝑇−𝑉, and the discrete oscillator equation is derived via variation. On the discrete graph, this paper rigorously proves that the total cost function 𝑆 is the conserved quantity of the system, and based on Noether’s theorem, proves that it is the Noether charge corresponding to global time-translation invariance. This indicates that energy is not an a priori entity, but the conserved measure of the system maintaining its intrinsic tension. To move towards a falsifiable physical theory, this paper proposes the "Partially Synchronous Constrained Refresh Model (PSCRM)", rigorously derives the 𝑝 scaling law of macroscopic inheritance error, and perfectly reproduces this prediction through two-dimensional Monte Carlo numerical simulation (fitted slope 0.5042, goodness of fit 𝑅2=1.0000). In Appendix E, we generalize this microscopic statistical mechanism to macroscopic cosmology and propose the "phase separation" conjecture: vacuum (asynchronous cancellation) and matter (directional accumulation) originate from the same primitive network with constant density. This model not only naturally yields the characteristic scale of the electroweak interaction (10−19 m) and the statistical integration domain of dark energy (approximately 400 km) at the pure geometric level, but also resolves the singularity at the center of black holes. Based on this, the paper provides clear experimental targets for the next-generation long-baseline interferometers (long-baseline phase ambiguity) and ultra-high-energy cosmic ray observations (1018–1019 GeV UV cutoff dispersion). Keywords: Local variation; Holistic invariance; Second-order dynamics; Inertia; Cost function; Noether charge; PSCRM model; Monte Carlo verification; ZTD framework