The Oort Cloud as an External-Field-Effect Instrument: a Conditional Joint Signature with Gaia DR4

Of everything a star owns, only its comet cloud extends into the regime where the acceleration scale a0 = kappa c sqrt(G rho_Lambda) = 9.36e-11 m/s^2 becomes dynamically relevant (r_M ~ 8,000 AU for the Sun). Three results, priced in both directions. (1) At solar-neighbourhood external fields the external-field effect removes almost the entire deep-MOND zone: an Oort cloud is Newtonian inside ~r_M and anisotropic quasi-Newtonian beyond, governed by the same committed response tensor (1.4732 parallel / 1.2598 perpendicular) as the hash-frozen Gaia DR4 wide-binary registration. A uniform gravity boost nearly self-cancels in comet-injection physics (the energy spike shifts only as G_eff^(1/7)); the surviving signal is directional: ~7% modulation of the spike position and ~17% of the injection rate with aphelion direction. (2) The exo-Oort version of this test -- KIC 8462852 (Tabby's Star) read through its dips -- is dead by 6.7 orders of magnitude: the dip-to-gravity inference chain leaks ~9e5x of model slack against a ~0.17 signal, priced arrow by arrow. (3) In the full relativistic completion the extra structure is silent at cloud scales (mass-term oscillation radius >= 23 kpc at the pinned Q0 band; a0-bump >= 280 kpc; a0(z) flat to 5e-7), but the pressure promotion makes a0 local, so the comet anisotropy becomes charge-dependent (16.7% at the nu0 floor, 12.1% at the ceiling) and CO-VARIES with the DR4 wide-binary gamma: one dimensionless charge moves both observables together. Constant-a0 MOND predicts a fixed 17% with no partner observable; the correlated pair is the framework-specific signature. This note prices a door; it claims no detection and freezes nothing. Every number is reproduced by a committed script.