We present a fully deterministic and closed-form framework for computing the Hubble constant using two independent cosmological probes: CMB acoustic geometry and low-redshift luminosity distances (Pantheon+SH0ES). All formulas are analytic and expressed in exact algebraic form. The resulting inverse problems satisfy existence, uniqueness, dimensional consistency, and Hadamard stability. No regression, sampling, Monte-Carlo, or iterative optimization procedures are used. Both pipelines yield consistent numerical estimates of the Hubble constant while remaining fully reproducible from finite sums and explicit integrals. The repository includes LaTeX derivations, deterministic Python evaluation, and optional Lean formal verification.
Quoc Truong Nguyen (Sat,) studied this question.