The Echo of Standing Waves
kibrom kidane · · DOI 10.5281/zenodo.20144382
Abstract
The conformal embedding E8(1) ⊃G2(1) ×F4(1) determines which interference patterns close into standing waves with definite mass and which standing waves imprint the common mode attractively. This paper develops the gravity branch: the same protected residue that fixes lepton masses (PvP = 0, Pv2P = 1 2 P) and quark masses (via the F4 bridge) also fixes the induced Newton constant through the mixed (7,26) sector. The bridge has dimension Nbridge = 7 · 26 = 182, conformal weight hbridge = 2 5 + 3 5 = 1, and non-minimal coupling ξbridge = αG2/2 = 1/(48π). The Lagrangian algebra condensation (D2local = 1) and vanishing coset charge (ccoset = 0) identify the 182 bridge modes as scalar-like coherence channels; they give Gind/GN = 0.994 (UV) or 1.007 (broken phase). The induced Einstein-Hilbert term then gives the nonlinear infrared Einstein equation, and the same result follows from the Jacobson-Clausius horizon derivation using the acoustic horizon temperature and area entropy of the closed branch. Seven competing branches are tested; only protected G2 forgetting applied exactly once closes all three layers (lepton, quark, gravity)
Keywords
induced gravity, Sakharov mechanism, conformal embedding, E8, heat kernel, Newton constant, analogue gravity, cosmological constant