The Acceleration Scale, Priced: Milgrom's Postulated a₀, the Unspecified μ, and the Flat Curves They Return

Census pricing (row CC-105) of the founding step of Milgrom's 'A Modification of the Newtonian Dynamics as a Possible Alternative to the Hidden Mass Hypothesis,' ApJ 270, 365-370 (1983), against a fixed bench (what is postulated, what is derived, what the postulates return numerically, what they cannot reach). The step is two inputs: a fitted acceleration scale a0 = 1.2e-10 m/s^2 (declared fitted wherever it appears) and an interpolating function mu specified only by its two limits. Verified in the notebook (11 checks, exit 0) from the inputs plus named constants at declared bench masses (instrument inputs, not named galaxies): the deep-limit velocity (GMa0)^(1/4) = 112.34 / 167.99 / 199.78 km/s at 1e10 / 5e10 / 1e11 solar masses, with v^4/(GM) returning a0 identically (the baryonic Tully-Fisher relation as the fitted constant read back at the fourth root); the Newtonian counterfactual beaten by a factor 2.236 at five transition radii. Remainders at full size: at the transition radius (10.779 kpc at 1e11 solar masses) the two standard published mu choices disagree by 28.80 km/s (254.12 simple vs 225.32 standard) -- the transition regime is the unspecified function's freehand; and the fitted constant's scatter is damped by the fourth root (a0 from 1.0 to 1.4e-10 moves the headline velocity only 190.88 to 207.63 km/s). Scout-grade verification disclosed on the manuscript's face (CC-91 form): no verbatim quotation, no page-specific claim. The author is living; the work is priced, the man is not addressed, and no contact was made. EXTENSION. Vacuum catastrophe NOT SOLVED; quantum gravity NOT SOLVED.

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Publication Details

Journal
Zenodo (CERN European Organization for Nuclear Research)
Published
2026-11-04
DOI
https://doi.org/10.5281/zenodo.23937860
Primary Topic
Cosmology and Gravitation Theories
Type
preprint
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preprint

The Acceleration Scale, Priced: Milgrom's Postulated a₀, the Unspecified μ, and the Flat Curves They Return

William Alexander Aldred
Zenodo (CERN European Organization for Nuclear Research)
Cosmology and Gravitation Theories
preprint

The Acceleration Scale, Priced: Milgrom's Postulated a₀, the Unspecified μ, and the Flat Curves They Return

William Alexander Aldred
preprint en

Abstract

Census pricing (row CC-105) of the founding step of Milgrom's 'A Modification of the Newtonian Dynamics as a Possible Alternative to the Hidden Mass Hypothesis,' ApJ 270, 365-370 (1983), against a fixed bench (what is postulated, what is derived, what the postulates return numerically, what they cannot reach). The step is two inputs: a fitted acceleration scale a0 = 1.2e-10 m/s^2 (declared fitted wherever it appears) and an interpolating function mu specified only by its two limits. Verified in the notebook (11 checks, exit 0) from the inputs plus named constants at declared bench masses (instrument inputs, not named galaxies): the deep-limit velocity (GMa0)^(1/4) = 112.34 / 167.99 / 199.78 km/s at 1e10 / 5e10 / 1e11 solar masses, with v^4/(GM) returning a0 identically (the baryonic Tully-Fisher relation as the fitted constant read back at the fourth root); the Newtonian counterfactual beaten by a factor 2.236 at five transition radii. Remainders at full size: at the transition radius (10.779 kpc at 1e11 solar masses) the two standard published mu choices disagree by 28.80 km/s (254.12 simple vs 225.32 standard) -- the transition regime is the unspecified function's freehand; and the fitted constant's scatter is damped by the fourth root (a0 from 1.0 to 1.4e-10 moves the headline velocity only 190.88 to 207.63 km/s). Scout-grade verification disclosed on the manuscript's face (CC-91 form): no verbatim quotation, no page-specific claim. The author is living; the work is priced, the man is not addressed, and no contact was made. EXTENSION. Vacuum catastrophe NOT SOLVED; quantum gravity NOT SOLVED.

Zenodo (CERN European Organization for Nuclear Research)
Cosmology and Gravitation Theories
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