Harmonic GUT Benchmark Completion, Quantitative Tests, and Robustness. From Programmatic Claims to Falsifiable Predictions

We close a benchmark-frozen harmonic effective field theory (EFT) program in which gravitational, gauge, and matter phenomena are organized as modal sectors of a single field defined on M 4 × K, with an internal oscillatory coordinate ξ generating a discrete tower. Across the series, Standard-Model-like structures are accommodated through parity/boundary-condition selection rules and a unified mechanism for effective couplings: overlap functionals of internal profiles (“overlap penalty”), yielding hierarchical interaction strengths without sector-dependent ad hoc inputs. In this sense, the harmonic framework can be read as an EFT extension that contains Einstein’s general relativity as its effective gravitational limit, whilegeneralizing it through an internal modal structure that fixes spectra and couplings in a reproducible way. In this final paper we remove residual ambiguity by introducing a master benchmark (HB1) that freezes the internal geometry, parity/BC assignments, deformation-family choices, and normalization/scale conventions uniformly across subsectors. We establish controlled predictivity via explicit tower-truncation remainder bounds, provide an admissibility checklist (no-ghost/no-tachyon in the retained EFT, BC/parity consistency, and gauge protection when claimed), and connect benchmark outputs to testable templates, including a Yukawa-equivalent parametrization of short range gravity corrections and overlap-drivenmatter-sector hierarchies. Every quantitative claim is reported as a benchmark-tied prediction band tagged by (HB1, θ; N max , ? ). This closes the harmonic unification program at the EFT level and defines a minimal falsifiability pack interfacing with current and near term tests.