What question did this study set out to answer?

This note aims to explore mechanisms that allow delta-m<0 in galactic bands with non-stationary responses.

July 5, 2026Open Access

Scale Yes, Shape Yes, Sign No: A Sixth Theorem Closing the Finite-Time/Non-Stationary Corner of Covariant Modified Inertia

CZCarl P. ZimmermanAd-Tech (United States)

Key Points

This note aims to explore mechanisms that allow delta-m<0 in galactic bands with non-stationary responses.
Theorem validation across three mechanisms, considering transient and linear coupling responses.
Analysis of structured baths and their prolonged effects on occupancy and power.
Reconstruction of finite-time broadening through windowed dS-Unruh responses.
Free fields exhibit state-blind responses verified across multiple states, failing parametric engineering.
Transient gain shows significant occupancy deficits and enormous regeneration factors in deep-MOND.
Wightman positivity confirms that effective scale remains floored, indicating constraints on sign outcomes.

Abstract

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 with F (-w) -F (w) = (w/2pi) Intchi² (re-derived adversarially from the Hadamard coincidence structure; tested on acceleration bursts, top-hat windows, parametric pumps; max pₑ/pg=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 = cHLambda/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, aT = 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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