The Fine-Structure Constant in HOUQFT II: Closure Equations, Operator Audits, and a Conditional Minimal Branch

This paper is the second part of a fine-structure-constant framework formulated within HOUQFT. Part I reduced the Thomson-limit inverse electromagnetic coupling to a locked radial source norm plus a finite photon-transport correction. The present paper reformulates the remaining task as a closure-equation and operator-audit framework, rather than as an unconditional numerical prediction. The analysis isolates three raw HOUQFT objects that must be evaluated before the minimal branch can be promoted to a first-principles prediction: the locked adjoint-to-sector-plane coarea projection, the effective on-shell eighth-order trace-log residual, and the exclusive BRST-complete electromagnetic transport remainder. Track A treats the coarea normalization problem. A rank-six coarea-whitened projection gives κ₈ = √(248/6), with nonchiral sector-plane tightness providing a sufficient closure route. Track B separates the trace-octic stabilizer, the minimal locked threshold selector, and the residual on-shell octic supertrace. The transport track formulates the exclusive photon-transport ledger through the BRST-complete charged-sector response, including the charged electroweak vector BRST complex and the nonperturbative signed electromagnetic spectral density. On the residual-free minimal branch, the stationary system gives μ⋆ = 193.8859813469783 GeV and predicted inverse coupling α⁻¹ = 137.03599908415683. This value is not claimed here as an unconditional HOUQFT prediction. Instead, the main result is the residual-corrected closure formula α⁻¹ = 137.03599908415683 + δco + δ₈ + δnonpert, where the correction terms are audit outputs, not fitting parameters. If Track A closes and the Track B and Track C correction terms vanish, the residual-free minimal branch is recovered. If Track A yields a computable coarea correction, or if a Track B or Track C correction term is nonzero but computable, the same framework produces a corrected first-principles branch. The empirical fine-structure constant is used only as a final comparison target, not as an input used to select the stationary scale or tune the residual ledger.