TMD: Triadic Dynamics of Reality, Part 3.: Emergent Lorentz Symmetry from: a Discrete Triadic Network

This work presents the third part of the TMD (Triadic Dynamics of Reality) series. It demonstrates that a discrete triadic network with local orientational interactions gives rise, in the continuum limit, to an isotropic wave equation whose symmetry group is the Lorentz group with an emergent invariant speed . Triads are treated as elementary orientational units interacting through a weighted discrete operator defined on their local geometry. As the network becomes sufficiently fine and statistically isotropic, this operator converges to the Laplacian , yielding the effective wave equation Time dilation, length contraction, and Lorentz transformations thus arise as purely mechanical consequences of triadic dynamics, without postulating relativity. This part completes the foundational triad of the TMD framework: triads → triadic wave → emergent relativity.