No Pump-Free Corner: The Residual Doors of Covariant Modified Inertia, Computed -- and a Pre-Registered Sign-Flip Signature for Dynamically Unsettled Galaxies

The six-theorem chain on covariant modified inertia (10.5281/zenodo.21016309, 21139029, 21148494, 21152331, 21175723) named its own residual doors; this note computes all four (4 lanes + 4 independent adversarial verifiers, 21 committed scripts exit 0, both a0 footings). (D1) INTERACTING-FIELD WINDOW (Theorem VI's named mind-changer): F(omega)>=0 is a theory-independent Gram fact; a new monotone-window lemma extends Bisognano-Wichmann detailed balance to arbitrary window lengths on uniform trajectories for any interacting Wightman QFT; a Kallen-Lehmann reduction -- independently re-derived on a genuine two-particle composite (:phi^2:, zero fitted constants, agreement 1e-4) -- expresses the interacting vacuum's windowed response on ANY trajectory as a positive mixture of free massive-slice responses, none of which invert (sharp-kick margin asymptotes to 0 from below: equality, never inversion). Driven benchmarks DO invert (11.4x) -- and the free control inverts 407x under the same drive: agent-pumped Raman gain, the already-priced pump channel. CLOSED at 2nd order; honest residuals: 4-point effects, dS Bros-Moschella positivity. (D2) PASSIVE-ANHARMONIC CORNER (the last pump-free route): passivity ALONE (KMS not needed) forces delta-m >= 0 -- linear response at any anharmonicity (every Bohr-line weight (p_n-p_m)|B_nm|^2 >= 0), non-perturbatively in coupling for adiabatic worldlines (exact pair sum, independently re-derived to 0.58%, gap-sweep exponent -3.000000), degeneracy edge sealed (within-subspace coherences carry zero inertia). The verifier's open-direction attack PARTIALLY SUCCEEDED -- instructively: at gA=5 near the two-photon resonance 2*Omega~gap the reactive dressing genuinely goes negative from a passive start; the autopsy shows the drive de-passivizes the bath (the drive IS the pump; Pusz-Woronowicz never violated), the window is frequency-locked, and band-mapping needs bath gaps the gas clamp. Amended closure: the passive softening channels are the sub-drive pole AND its multiphoton/Floquet generalization, both drive-pumped, both clamped by Theorems IV/V. NO PUMP-FREE MOND-SIGN CHANNEL EXISTS. (D4) FLAT-CURVE EP CLOSURE of Theorem IV, full Coriolis: the PT-broken band on flat curves is exactly mu in (0.7579886, 0.8947874) -- CORRECTING our own published estimate 0.854 (inside the band, wrong both directions), with a re-entrant real window (0.5, 0.758); exact fold law mu_fold = 1 - 1/(2p): sub-quadratic PU kernels (p=1/2) evade the EP entirely (deep-MOND PU orbits exist and are linearly stable -- a genuine soft spot in the published blanket claim) and die instead by profile inversion (sign-opposite (1-mu) slopes, x49-80 on realistic disks). The horn stays dead; one of its bricks is relabeled in print. (D3) THE DOOR THAT OPENS: fusing the Theorem-VI transient with the framework's memory-kernel physics (Lorentzian, tau=0.45 Gyr) yields a pre-registered, dated prediction table for dynamically unsettled systems: Crater II +13.6-26.5%, Antlia II +3.4-6.7%, settled controls