Cosmological Freeze-Out and Primordial Structure Formation within the Stochastic Rupture Framework: Holographic Noise, Acoustic Coherence, and Suppressed Tensors

We develop a self-consistent cosmological sector of the Stochastic Rupture (SR) framework, deriving the primordial scalar and tensor spectra, the acoustic-peak phase structure, and primordial non-Gaussianity from a single stochastic informational eld χ with codimension-one holographic origin. Three structural ingredients enable the framework to reproduce observed cosmological phenomenology without ination: (i) the parameters of the SR master equation are not bare constants but ratios of physical rates to the local holographic capacity, which redshift with cosmic expansion and drive the system through adynamical critical region (the storm-to-pruning transition); (ii) the stochastic source is supported on two-dimensional Bousso light-sheets, producing a 1/k Fourier noise spectrum that yields exact HarrisonZeldovich scale invariance for the primordial scalar spectrum; (iii) cosmological super-horizon evolution exponentially extinguishes both damping and noise, preserving the cosine-phase coherence required for acoustic peaks. We derive the spectral tilt ns − 1 ≈ −2µeff/H∗, the orthogonal-shape non Gaussianity fNL ∼ α/H∗, and the tensor-toscalar ratio r ∼ PS ∼ 10−9 via scalar-induced gravitational waves. The framework predicts a tensor consistency relation nT ≈ 2(ns − 1), structurally distinct from the inationary nT = −r/8. No free parameters are added beyond those already dened in the SR collapse and gravitational sectors.