Modal Triplet Theory: From MTT to General Relativity

We derive classical General Relativity (GR) from Modal Triplet Theory (MTT) by coherent-sector projection and internal pushforward. Starting from the ten-dimensional product geometry M10 = Y4 × B1 × B2 × B3, we restrict the 10D MTT action to the harmonic sector and integrate out internal factors. We prove: (i) a variational reduction theorem showing that the effective 4D action is of Einstein–Hilbert type with Newton and cosmological constants determined by internal spectral data; (ii) that the reduced Euler–Lagrange equations are exactly the Einstein equations with covariantly conserved stress–energy; (iii) a geodesic-limit theorem establishing the equivalence principle for projected test bodies; and (iv) recovery of the Newtonian and post-Newtonian limits with explicit parameter dictionaries. Controlled corrections, such as quadratic curvature and scalar–tensor terms, appear only when stability or finite-gap assumptions are relaxed, and are quantitatively bounded. The result places GR as the unique, stable, low-frequency, large-scale sector of MTT.