Cosmological Structure Without Inflation: The Perturbation Spectrum from Pre-Geometric Construction

This paper demonstrates that all four problems the inflationary paradigm was introduced to solve are addressed by the pre-geometric seed proposed in 'The Last Evaporation: Planck Remnants as Cosmological Seeds in Empty Spacetime' (Weller, 2026). The primordial perturbation spectrum (the decisive test for any alternative to inflation) is produced by the correlation structure of tetrahedral edge-sharing during the construction of geometry from the seed. The per-edge failure probability is determined by an information-theoretic principle: each edge is a binary degree of freedom carrying ln 2 nats of information, and the saddle-point action S₀ = 2π² is the only available scale, giving p = ln 2/ (2π²) with no free parameters. The spectral tilt nₛ = 1 − ln 2/ (2π²) = 0. 96489 matches observation at 0. 004σ. The tilt is constant across CMB scales: the adjacency structure of iterated Pachner moves produces a bulk spectrum that is exactly Harrison–Zel'dovich at leading order, and the logarithmic running of S₀ through an operator trace identity gives nₛ − 1 = −p₀ at all scales, with predicted running αₛ ≈ +p₀² ≈ +0. 0012 (Planck: −0. 0045 ± 0. 0067). The EPRL vertex amplitude |Aᵥ| ≈ 0. 035, computed independently in the spin foam program, agrees with this value -- a prediction of the framework, not an input. Phase coherence (the adiabatic initial condition that produces the observed acoustic peaks) is derived from the regularity of ζ at the origin, without requiring inflationary horizon exit. The tensor-to-scalar ratio vanishes at leading order from the Td symmetry of the regular tetrahedron, providing a dynamical mechanism for Penrose's Weyl curvature hypothesis; the first correction gives r = 4 (1+3p) /135 (1−p) = 0. 034, at the current BICEP/Keck bound r < 0. 036 and immediately testable. Non-Gaussianity is derived from the per-block third cumulant of the binary defect distribution: fNL is positive, equilateral-type (fNLˡocal = 0 at leading order, since different Pachner generations are statistically independent), and falls as ℓ⁻³, giving fNL ~ 7. 5 at the quadrupole but ~10⁻⁴ at Planck scales -- consistent with all current bounds. The generation-to-harmonic mapping ng = (3 · 4ᵍ) ^1/3 connects the discrete Pachner generations to the continuum S³ harmonic decomposition, placing the quadrupole at generation 1, where the action cost ΔS = (3/4) S₀ suppresses large-scale defects by e^−3π²/2 ≈ 4 × 10⁻⁷. The perturbation amplitude is exp (−2π²) to leading order from the saddle-point action. Flatness, homogeneity, and the absence of magnetic monopoles are default properties of the initial state. See also: https: //doi. org/10. 5281/zenodo. 20559451 https: //doi. org/10. 5281/zenodo. 20559917