The Registered Wide-Binary Target under a Local a0: A Conditional Charge Meter, and the EFE-Present Exact Two-Body Solve

Two refereed results about the hash-frozen Gaia DR4 wide-binary registration of the a0 = kappa c sqrt(G rho_Lambda) framework (the registration itself is untouched). (1) Because the framework's a0 is a local quantity set by the dark sector's pressure at the local shift-charge density, the now-settled steady-state-continuity reading of the solar-circle charge flow makes the registered velocity-boost target a CONDITIONAL charge meter: at the charge floor the target moves by less than the frozen band's own width at every corner of the solar-overdensity bracket and both footings; at the ceiling the move is corner-split (-0.004 sparse to -0.093/-0.109 dense) -- DR4 measures the charge only if the solar-circle overdensity sits toward the dense corner, and settling that overdensity is the named prerequisite. (2) The full nonlinear AQUAL two-body problem in a uniform external field (colinear, machinery-gated) shows the exact pair boost is 0.71-0.99x the linear per-star response at 5-30 kAU: the EFE-free benchmark correction (1.41-1.74x) overcorrects with the external field on. Both directions stated: the registered band top is conservative (a no-verdict above 1.23 less likely), AND the per-pair signal sits at or below the registered floor over most anchor separations (a reading below the band more likely). Every quantitative claim is reproduced by committed scripts.