Cosmic Crystallization: How Icosahedral Geometry Wrote the CMB
Abstract
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.
Fields of Study & Subjects
Galaxies: Formation
Evolution
Phenomena
Cosmology and Gravitation Theories
Advanced Mathematical Theories and Applications
Publication details
- Journal / source
- Zenodo (CERN European Organization for Nuclear Research)
- Publication date
- 29 January 2026
- Document type
- Preprint