Regime Theory: Grassmannian Vacuum Selection and a Regime-Dependent Effective Coupling

We propose that several long-standing tensions across quantum theory, gravitation, and high-energy unification may reflect the use of effective descriptions outside their domains of validity, rather than an inconsistency of fundamental laws. Within Grassmannian Convergence Theory (GCT), a vacuum selector κ labels a small set of preferred Grassmannian manifolds Gr(k, n) that organize local effective descriptions. We focus on one concrete and testable implication: an environment-dependent effective gravitational coupling, Geff(ρ) = Glab F(κ(ρ)), with F(κlab) = 1, where ρ is a coarse-grained energy density and F is a smooth regime-response function. We define ρ operationally as ρ ≡ ⟨T00⟩V, with V a fixed astrophysical coarse-graining volume, and state consistency requirements under which Solar System tests, lunar laser ranging bounds on Ġ/G, binary pulsars, and early-universe constraints remain effectively unmodified. Using an explicit worked example (an exponential disk), we show that a continuous, non-monotone response profile F can reproduce an approximately flat rotation-curve band over a decade in radius while remaining compatible with suppressed coupling in sufficiently underdense environments. The framework yields observational targets for forthcoming surveys: void weak-lensing amplitudes and their dependence on void depth and definition provide a direct probe of F in the low-density regime. We discuss how present void-lensing measurements that report a modest under-lensing relative to ΛCDM expectations are consistent with an intermediate suppression in Geff/Glab, and we outline a hierarchy in which deeper void interiors could exhibit stronger departures. Throughout, we distinguish geometric identities from phenomenological interpolants intended to be constrained by data.