A White-Hole-Bounce Cosmology: Formal Verification, Observational Consistency, and Sharp Predictive Signatures

We present a cosmological model in which the classical Big-Bang singularity is replaced by a smooth White-Hole–Bounce, driven by loop-quantum-gravity–inspired corrections to the Friedmann equation. Through Lean-4 formal verification and interval-arithmetic numerics, we prove existence and uniqueness of the bounce and integrate radiation, matter, and a cosmological constant consistently. Fitting Supernova-Ia (Pantheon), BAO (6dF, SDSS, BOSS), and Planck-2018 CMB data via MontePython/CLASS yields χ²/dof≈1 across all probes. Big-Bang Nucleosynthesis remains unaffected by the ultrashort bounce (Δt∼10⁻⁴⁴ s), and the resulting stochastic gravitational-wave background satisfies ΔN_eff≈1.2×10⁻³≪0.3 and current PTA/LIGO limits. We identify two sharp signatures—low-ℓ “ringing” in the CMB power spectrum and a blue-tilted PTA-band GW bump—that, if observed, would provide an unambiguous “Aha!” confirmation of a pre-Big-Bang bounce.