Bounce Regularisation of Singularities and Parameter Free Cosmology in Discrete Geometric Physics

The bounce mechanism is introduced as a natural regularisation of singularities in discrete geometry. When the deformation determinant falls below the threshold J<0.01J<0.01 and the local energy exceeds ηcritEcritηcritEcrit, a velocity inversion occurs in the Velocity‑Verlet scheme. It is proved that the energy remains bounded: E(t)≤E0exp⁡(−γt)E(t)≤E0exp(−γt) with γ=1/56γ=1/56, preventing collapse in the Einstein equations and replacing the Big Bang singularity with a Big Bounce. Cosmological parameters are derived from the kinetics of soliton coagulation described by the Smoluchowski equation with kernel K(y,z)∝∣y−z∣αK(y,z)∝∣y−z∣α and α≈1.5α≈1.5. The numerical solution gives the spectral index ns=0.9647±0.002ns=0.9647±0.002, the dark energy equation of state parameter wDE=−1.03wDE=−1.03, and the BAO peak rBAO=100.2rBAO=100.2 Mpc. These values agree with Planck 2018 and DESI 2024 data to within observational uncertainties. The theory is free from singularities and free parameters; all observable quantities follow from the geometry of the Oh lattice. References to Volume 1, Chapter 2 (bounce mechanism) and to the work "Dark Components as Informational Fields" are provided.