Chronosphere: Geometric Origin of Masses and Cosmological Parameters

This work presents a rigorous mathematical foundation for the Chronosphere theory, according to which all physical scales arise from the incommensurability between the discrete structure of spacetime and its emerging boundary. The theory is based on the fundamental number β = (π-3) / (4π) ≈ 0. 011267585362. . . , which arises from discretizing a sphere with a regular icosahedron. The paper develops a discrete model ℋN = Γ₀䃕 × 0, …, N, where Γ₀䃕 is the Cayley graph of the icosahedral symmetry group A₅. Using representation theory, the spectrum of the angular Laplacian Δ₀䃕 is computed exactly: Spec (Δ₀䃕) = 0, 12, 15, 20 with multiplicities 1, 25, 16, 18. For the full Laplacian on ℋN, the eigenvalue asymptotics are derived: λₙ (μ) = μ + (πn/N) ² + β·ln n / N² + o (ln n/N²) Numerical verification for N=10000 after subtracting the exact quadratic part yields βₙum = 0. 01126759 ± 0. 00000001, coinciding with the theoretical value within 0. 31σ. It is shown that without subtracting the quadratic part, the apparent coefficient βₐpp ∼ 1/N. From the holographic principle, a universal formula for hadron masses is obtained: mₙ² = Λ² (n + δ + β ln n) Analysis of 14 meson trajectories (62 states) confirms the formula with χ²/dof = 1. 12. The model without the logarithmic correction is rejected at >3σ significance. New resonances are predicted, including Υ (6S) with mass 11027 ± 5 MeV (testable at Belle II). Cosmological consequences include mass evolution with redshift: m (z) = m₀ (1+z) ^α. From DESI DR2, CMB, and H₀ data, αβ = 0. 0117 ± 0. 0011 is obtained, giving α = 1. 04 ± 0. 09 — linear mass evolution explaining the Hubble tension. Analysis of three BH-NS merger events from GWTC-3 with a modified waveform yields β = 0. 0115 ± 0. 0078, consistent with the theory. Three crucial experiments with clear falsification criteria are formulated: the mass of Υ (6S) at Belle II, the phase correction in LIGO O5, and the evolution of H₀ (z) in LSST. This repository contains the complete LaTeX source of the paper and all numerical codes used for verification.