Published January 29, 2026 | Version v2
Preprint Open

Cosmic Crystallization: How Icosahedral Geometry Wrote the CMB

  • 1. ROR icon University of Southampton

Description

We show that cosmic recombination parameters emerge from icosahedral geometry with remarkable precision. The binding threshold 53 = E + F + D gives recombination temperature T_rec = 2979 K (99.3% match). The face-vertex difference F − V = 8 gives redshift z_rec = 8/α = 1098 (99.4% match). The face fraction (F−1)/F = 19/20 gives cosmic age t₀ = 13.75 Gyr (99.8% match). All three parameters derive from icosahedral constants V = 12, E = 30, F = 20, D = 3. The dimensional constant D = 3 plays dual roles: mod 3 locks IN color confinement at recombination, while mod 5 locks OUT further particle creation. The gap 55 − 53 = 2 = χ (Euler characteristic) is derived from the icosahedron's triangular face structure. Prime products confirm the boundaries with factor 3 at e^142 and factor 15 at e^184. Version 2.0 adds the dual modular lock framework, references to the Digit Gaps and Icosahedral Digital Boundary papers, timeline of crystallization, and prime product evidence.

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