Harmonic Substrate Gravity V.6

Harmonic Substrate Gravity v6: The golden ratio as mechanism, not as a number Abstract:We present a revision of Harmonic Substrate Gravity in which the golden ratio φ is relocated from the dark energy equation of state to the spacing of the substrate's frequency ladder. Written in the natural field variable u = ln(f/f₀), the requirement that one rung of the ladder cost exactly one φ-level of potential fixes the coupling β = 1 with no free parameter, removing the circular derivation present in versions 1 through 5. The equation of state follows rather than being assumed: w = −2/3 at the attractor, w₀ = −0.8438 today. The framework fits DESI DR2 at least as well as the previous version against every dataset combination while carrying one fewer parameter. A discrete ladder implies discrete scale invariance, giving a log-periodic modulation of the matter power spectrum with period fixed at ln φ — approximately 7½ cycles within the range current surveys already measure. Atomic clock limits on frequency-ratio drift bound the matter coupling at ξ < 2.4 × 10⁻⁸. Key Framework Shift (v5 vs v6):In prior versions, the attractor relation was built artificially by choosing α = √3/φ to force an expansion result. In v6, the uniform geometry of the natural field lattice forces β = 1 organically. The cosmological acceleration variables emerge downstream as a consequence of the underlying scale architecture, rather than serving as the baseline assumption. Affiliation: SUDOSCORPNATIONAuthor: Amber Dorothy Gaxiola (ORCID: 0009-0001-6619-2514)