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ZENODO
Preprint . 2026
License: CC BY
Data sources: ZENODO
ZENODO
Preprint . 2026
License: CC BY
Data sources: Datacite
ZENODO
Preprint . 2026
License: CC BY
Data sources: Datacite
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The MOND Acceleration Scale as a de Sitter Curvature Scale: Gauged SO(4,1) Gravity Reduces a0 = c^2 sqrt(Lambda/32pi) to a Single Free Number

Authors: Zimmerman, Carl P.;

The MOND Acceleration Scale as a de Sitter Curvature Scale: Gauged SO(4,1) Gravity Reduces a0 = c^2 sqrt(Lambda/32pi) to a Single Free Number

Abstract

Galaxy dynamics organize around an acceleration scale a0 ~ 1e-10 m/s^2 that numerically coincides with c*sqrt(Lambda) and cH0. This paper develops the hypothesis that the coincidence is structural -- that a0 is a de Sitter curvature scale, a0 = c^2*sqrt(Lambda/32pi) = (c/2)*sqrt(G*rho_DE) = c*H_Lambda/Z, Z = sqrt(32pi/3) = 5.789, evaluated on the dark-energy density alone, giving a0 = 9.36e-11 m/s^2 -- and separates, with machine verification, what the proposal DERIVES from what it POSITS. (i) Gauging the de Sitter group SO(4,1) (MacDowell-Mansouri) gives Einstein-Hilbert + Lambda; an exhaustive symbolic enumeration certifies this is the unique two-derivative parity-even invariant in its class (exactly two quadratic-in-curvature SO(4,1) four-forms exist; exactly one is two-derivative). (ii) The deep-MOND form a0 ~ c^2*sqrt(Lambda) is over-determined: a false-discovery-controlled audit certifies FOUR structurally independent mechanisms force it (correcting an earlier inflated count of seven), with the de Sitter-Unruh modified-inertia interpolation reproducing flat rotation curves and v^4 = G*M*a0. (iii) The gravitational route fixes the kernel sqrt(8pi/3) including the half-integer power of pi that no curvature-free thermal route produces, leaving the entire residual unforced content as ONE O(1) number, kappa = 1/2: a0 is exactly half the gravitational free-fall acceleration at the dark-energy density. The limits are stated plainly: the value of Lambda is an input; the inertia mechanism's covariant completion is unbuilt and exists only as a sibling effective field theory degenerate with AeST on the static locus but not joined to it; and the Standard Model is not produced -- the generation number N = 3 is shown to be a topological parity obstruction for the natural index over the de Sitter nucleation saddle, so it stays fitted (the universal status of the flavor puzzle, not a special failure). The proposal is therefore an effective theory at a frontier with a certified gravity spine and a fitted Standard Model -- NOT a theory of everything yet, as frustrating as it may be. Two tests decide its distinctive content: Cassini (in hand) discriminates modified inertia, which it passes by a factor ~30, from an ungated modified-gravity completion, which it fails; and the declining prediction a0(z=3) = 0.74*a0(0), cleanly separable (~6x) from both LCDM and a rival rising branch, is falsifiable with ELT-class spectroscopy this decade, hostage to whether DESI confirms evolving dark energy. Earlier claims that a discrete-holography (DSSYK) kernel forces the galaxy-scale sign and that the coefficient is fixed by a unique entropy calculation are withdrawn.

New, distinct work from the earlier records (DOI 10.5281/zenodo.19244651 and successors); publish as a NEW record, not a new version. All quantitative claims are reproducible from https://github.com/carlzimmerman/zimmerman-formula (opus_48_extended_research/). The three certification scripts and the graded derivation chain are archived there.

Keywords

modified inertia, cosmological constant, MacDowell-Mansouri, gauge gravity, DESI, acceleration scale a0, radial acceleration relation, external field effect, MOND, de Sitter horizon, Cassini, emergent gravity, dark energy, modified gravity

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selected citations
These citations are derived from selected sources.
This is an alternative to the "Influence" indicator, which also reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Citations provided by BIP!
popularity
This indicator reflects the "current" impact/attention (the "hype") of an article in the research community at large, based on the underlying citation network.
BIP!Popularity provided by BIP!
influence
This indicator reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Influence provided by BIP!
impulse
This indicator reflects the initial momentum of an article directly after its publication, based on the underlying citation network.
BIP!Impulse provided by BIP!
0
Average
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