11-Residual Freedom After Structural Closure of Vacuum Residues

Recent work has established a structural closure for admissible vacuum residue extraction schemes, showing that finite, invariant, and reproducible residues necessarily arise from a twosector organization of conjugated asymptotic contributions. This result fixes the structural form of admissible constructions while remaining neutral with respect to physical interpretation.In the present work, we analyze the consequences of this closure and identify the residual freedom that remains once all structural constraints are satisfied. We distinguish sharply between features that are fixed by necessity—such as the two-sector structure, asymptotic correlation, and invariance—and those that remain legitimate physical choices, including the magnitude and interpretation of the residue, its coupling to gravity, symmetry assumptions, and the choice of realization.We also identify classes of constructions that are no longer admissible after closure, including monosector reductions, ad hoc tuning, prescription dependence, and attempts to absorb global vacuum contributions into local dynamics. These exclusions follow directly from the requirements of reproducibility and invariance.Finally, we situate the standard cosmological model within this framework as an example of a structurally admissible but under-determined construction. While compatible with the structural constraints, ΛCDM does not derive the value of the cosmological constant from an intrinsic mechanism, leaving its origin external to the model.Taken together, these results clarify the boundary between structural necessity and physical choice. The organization of vacuum contributions is now constrained; what remains is the task of identifying which physical realizations nature has selected.