This note closes the gap in covariant modified inertia impacting sign determination with transient responses.
The five-theorem chain on covariant modified inertia (10.5281/zenodo.21016309, 21139029, 21148494, 21152331) closes the local, field-mediated, and stationary-environment routes to the MOND sign -- under one standing assumption: STATIONARITY. This note closes the remaining corner, which is also the mechanism class of a concurrent proposal (M.J. Luo, arXiv:2602.14515): can a non-stationary bath state or a finite-time/transient response hold delta-m<0 in the galactic band without unexplained power? Three legs, each adversarially verified, all 13 scripts committed (exit 0), both a0 footings carried. (i) FREE FIELDS ARE STATE-BLIND AT ALL TIMES: for linear coupling the response kernel is the field commutator, a c-number at every finite time, for every state (verified exactly in non-Gaussian Fock and cat states) and every non-stationary linear dynamics (time-dependent couplings, parametric/FRW frequency drive); the in-band parametric kernel-engineering escape fails by x30-36. A coupling quench mimics mu<1 hugely (mu(0+)=-62.5) but dies in ~1 drive period with an anti-MOND asymptote. (ii) STRUCTURED BATHS: transient gain is REAL (exhibited two independent ways; Theorem IV is genuinely stationary-only) but persists min(T1, 1/Gamma_2, 1/detuning); in deep-MOND the one-shot preparation is ~3e11 short in occupancy, regeneration ~10 orders in power (coherence discount over inversion is exactly <=x2; the redshift-drift dephasing floor ~15 H0 makes coherence ~5x WORSE), and resonant band coverage needs a ~405-channel comb whose phase-random component over-heats disks x342-788. (iii) FINITE-TIME BROADENING (Luo's effect) is real and reconstructed: windowed dS-Unruh response obeys a_eff^2 = a^2 + H-floor + kappa^2 c^2/T^2 (kappa=1.746), and its Delta-T-mapping shape is EXACTLY this framework's nu(y)=sqrt(1+1/y) (sympy identity, a0=2a_Lambda) -- convergent support for the SHAPE. But Wightman positivity locks the sign for every window and every trajectory: F(w)>=0 with F(-w)-F(w)=(w/2pi)Int[chi^2] (re-derived adversarially from the Hadamard coincidence structure; tested on acceleration bursts, top-hat windows, parametric pumps; max p_e/p_g=0.54), the dynamical dressing stays delta-m>=0 (vacuum passivity), and every window's effective scale is FLOORED at cH = Z*a0: the framework's a0 = cH_Lambda/Z sits a factor Z=5.79 BELOW the floor, unreachable from the transient side (sharpening the kappa-closure, 10.5281/zenodo.20965016). The genuinely non-stationary window scale is velocity-dependent, a_T = kappa*c*v/R (2-5 orders above a0 in disks), yielding a mechanism-level discriminator: a window-generated interpolation scale would migrate the RAR transition with c/v across populations -- SPARC shows it does not. CONCLUSION: finite-time de Sitter-Unruh physics supplies the scale window and the exact interpolation shape, and cannot supply the sign. The pentad is a hexad. Quantified residual door: one-shot transients ~1.6% per 10 orbits in dynamically UNSETTLED systems -- nothing for the RAR, but landing on the framework's live non-adiabatic sigma-spread front; named mind-changers: an interacting-field windowed calculation exhibiting inversion without violating Pusz-Woronowicz, or a dynamical lock of the window to ~10/H. The author retracted all earlier theory-of-everything claims (2026-06-23); this note claims a closure and two locks, not a completion.
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Carl P. Zimmerman (2026) studied this question.
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