A Radial-Response Reduction of the Fine-Structure Constant in HOUQFT: Gauge Universality, Closure Attempts, No-Go Results, and an $E_8$ Octic-Stabilization Program

This preprint is Part I of a two-part HOUQFT framework for the fine-structure constant. It develops a status-sensitive reduction of the Thomson-limit electromagnetic coupling to a locked-vacuum radial source-norm problem. The central question is whether alpha_Th can be obtained from first principles once gauge universality, electroweak source projection, internal-line damping, locked vacuum response, and finite photon transport are all fixed internally by the theory, rather than adjusted to reproduce the observed value. The analysis separates derived identities, conditional closure theorems, diagnostic numerical reconstructions, no-go results, and remaining proof obligations. The electroweak projection fixes the structure of the coupling but not its absolute radial scale. The strict homogeneous locked A4 Einstein-Hilbert sector fixes the gauge-kinetic form but leaves the electroweak source norm unstabilized. Several natural closure attempts, including condensate Hessian, vacuum-cumulant, diagonal electroweak trace, and Hyper-DFT response-functional closures, are shown to reformulate the same missing datum without determining it numerically. The paper then develops a microscopic hidden-radial response framework, an E8 source-space overlap calculation, a quartic/sextic no-go result, and an octic radial-stabilization program. Within this framework, a trace-octic/coarea-normalized benchmark branch is identified. When combined with a finite charged-fermion transport benchmark, this branch places the conditional numerical closure close to the empirical inverse fine-structure constant. This agreement is not presented as a completed first-principles prediction. Instead, it is used to isolate the theoretical conditions required before such a benchmark could be treated as predictive. The remaining first-principles closure conditions are: coarea whitening of the locked E8-to-sector-plane projection, trace-octic selection by the spectral composite-metric action, matching-scale stationarity of the finite radial/transport split, and BRST-complete charged transport including all active charged sectors. These are supplemented by two preconditions: the electroweak source-overlap convention must be derived or replaced by the exact weighted overlap, and the damping/moment ledger must be obtained from the locked HOUQFT vacuum rather than benchmarked. The final status of the work is therefore a rigorous reduction, a set of no-go and obstruction results, and a conditional numerical closure program. It is not yet a completed first-principles derivation of the observed fine-structure constant. Part II, "The Fine-Structure Constant in HOUQFT II: Closure Equations, Operator Audits, and a Conditional Minimal Branch," continues from this endpoint by reformulating the remaining problem as a closure-equation and operator-audit framework.