Relativity and Cosmology |
Authors: Jason Merwin
We report the first computation of a discrete analog of the CMB angular powerspectrum Ck derived entirely from a causal integer graph grown by pure fission rules,with zero free parameters. Starting from a complete graph K5 as the seed, a 1000-nodegraph is grown via an additive-plus-half-split fission engine constrained by a 137-elementregistry capacity. When the ratio of maximum hub degree to total node count transits ascale-invariant resonance window md/N ∈ [0.015, 0.021], the graph Laplacian eigenvalueratio λ3/λ2 locks near the S1/2 prediction of 1.102. The locked graph exhibits positivespatial curvature, volumetric dimension dvol = 3.49 ± 0.05, and a well-defined lastscattering surface (LSS) at BFS radius r = 4 containing 452 nodes. Propagatinga primordial perturbation via the wave equation Green’s function cos (√λk t) at thephysically motivated time t∗ = π/√λ1 and projecting the field on the LSS onto abinned eigenmode basis recovers two robust acoustic peaks at ℓeff = 1.121 and 1.811,giving ℓ2/ℓ1 = 1.615. The Planck 2018 value is ℓ2/ℓ1 = 1.94. The 16.7% deviation isquantitatively consistent with lattice dispersion at N = 1000: discrete graphs suppresshigh-frequency modes, compressing harmonic ratios below the continuum limit. Wepredict that the ratio converges monotonically to the Planck value as N increasestoward the physical scale (md = 137, N ≈ 9000), providing a falsifiable test of theframework.
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