The Dialog of Energies on a Discrete Lattice: A Computational Model of Mass, Propagation and Gravitation from M’TAM Axioms

A companion paper, The Mechanics of Becoming, states the M'TAM notion of the dialog of energies as a set of axioms: Zouhetu exist and events happen; each event is the reception of Yennu, an adjustment of internal state to keep harmony, and the transmission of Bayuali; and one change of state is one unit of action. This paper gives those axioms a computational form and tests whether the resulting model reproduces established features of physics. Zouhetu occupy a body-centered cubic lattice. Each event is a hop to one of eight neighbors followed by an internal adjustment, and a Zouhet's state carries amplitude and phase. Rest mass enters only as a density of internal becoming, theta. Positional Bayuali are broadcast on the same lattice. Positional Yennu slows all of a Zouhet's becoming, internal becoming by (1 + Phi) and change of position by (1 + 2Phi), and each Zouhet sends positional Bayuali exactly as strongly as it receives positional Yennu. The model reproduces the following. A Zouhet's rest frequency equals theta exactly, its inertia equals that frequency in every direction, and the lattice deviations vanish as theta^2. Positional messages travel at a single speed c and fall off as the inverse square of distance. Once the lattice's own inertia correction is allowed for, different masses fall alike to within about 0.1%, and at the rate the model predicts to within 0.15%. Light is deflected as the model predicts (mean ratio 1.0004), and the coupling of positional change doubles the deflection (2.04 +/- 0.02). Two Zouhetu attract through their own messages with Newton's strength to within 0.8%, a force law of d^(-1.993 +/- 0.002), and initial forces equal and opposite to within 0.4%; over a run, matter and fields together conserve momentum to within 0.3% of the momentum transferred. Flavor oscillation arises as a beat between two densities of becoming and converges to the relativistic value. The source rule, taken from the framework, makes each Zouhet send positional Bayuali exactly as strongly as it receives positional Yennu; with the coupling selected by light bending, it reproduces T^00 + T^i_i, the source of the Newtonian potential in linearized general relativity. Every event rule is unitary, so the free dynamics conserve sum |psi|^2 exactly; in a field the step is computed by a truncated series, which conserves it to within 3 x 10^-5 over a run. The Born rule is consistent with the model, as in quantum mechanics, where it is a postulate. The results hold in the weak-field regime; the lattice, three dimensions and theta are assumed, as in physics. No verified equation is altered. The model is offered as a correspondence and not as new physics, and it makes no claim about whether existence is discrete or continuous.