Structured Vacuum Field Theory: Can the Vacuum Fix Its Own Couplings?

This paper tests whether Structured Vacuum Field Theory (SVFT) can derive the dimensionless coefficient of the dark-energy density from its own structure, rather than taking it as an input. The test is one structurally honest route: a ratio of the gravitating response to the coherence norm, in which the kernel normalization and the λ₀ = 1 convention might cancel to leave a scheme-invariant function of the spectral gap. The ratio is computed. It does not force the coefficient — the decisive, convention-independent reason is that the quantity it depends on, the modal occupation of the spatial coherence field, is itself unforced. The dark-energy coefficient is therefore a constitutive input, the same position conventional physics occupies; this is a clean negative result, reported as such. Pursuing the companion parameter yields the paper's constructive results: the gravitational coupling efficiency α_grav = 1 is derived rather than assumed, from the kernel's infrared normalization; the kernel's Hilbert stress tensor is computed in its exact pieces; and the construction is anchored in the infinite-derivative (nonlocal) gravity literature. The coherence-to-curvature identification on which the gravitational results rest is identified as SVFT's foundational, falsifiable posit, not a theorem. The work builds on the published SVFT reconciliation (Why the Vacuum Does Not Gravitate), which fixed the relations among the theory's constants and the scale of the dark-energy density but not its dimensionless value — the open question this paper takes up. Scope is bounded to this one route. Paper I of the SVFT Open-Issues Program