What does this research mean for the field?

A monotone interpolation function family in the AQUAL framework successfully satisfies solar-system constraints without altering the fundamental acceleration constant a0, albeit with a slightly reduced fit quality for galaxy rotation curves. Novelty: ClaimNovelty.NOVEL_FINDING. Consensus alignment: ConsensusAlignment.NEUTRAL.

What question did this study set out to answer?

To determine whether adopting a monotone interpolation function in AQUAL gravity can eliminate Solar System constraint conflicts while preserving the standard acceleration constant a0.

August 23, 2026Open Access

The Amplitude Law: the obstruction is the interpolation function, not the carrier -- and a monotone kernel escapes it with a0 untouched

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To determine whether adopting a monotone interpolation function in AQUAL gravity can eliminate Solar System constraint conflicts while preserving the standard acceleration constant a0.
Tested the monotone interpolation family μn(x) = x/(1+xn)^(1/n) across 175 SPARC galaxy rotation curves with refitted stellar mass-to-light ratios.
Calculated Solar System boundary metrics using the AQUAL quadrupole against Cassini data and evaluated the 1-AU monopole against Mars ephemeris bounds.
At n = 10, the Cassini quadrupole drops to 0.08–0.21× the empirical ceiling across ±2σ of the measured external field, and the 1-AU monopole measures 4×10^-28 of the Mars budget.
The kernel preserves the deep-MOND acceleration constant a0 within 5×10^-7 but yields a poorer fit to galaxy rotation curves (scatter of 0.127 vs 0.108 dex; χ²/dof of 49.1 vs 21.1).

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Implication

Gravitational modeling demonstrates that a monotone interpolation kernel satisfies Solar System constraints in AQUAL gravity, indicating transition functions resolve local observational limits.

Cite This Study

Carl Zimmerman (2026) studied this question.

synapsesocial.com/papers/6a8aade47677a341144465ac https://doi.org/10.5281/zenodo.22044021

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Implication

Gravitational modeling demonstrates that a monotone interpolation kernel satisfies Solar System constraints in AQUAL gravity, indicating transition functions resolve local observational limits.

The Amplitude Law: the obstruction is the interpolation function, not the carrier -- and a monotone kernel escapes it with a0 untouched

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Discussion

Implication

Cite This Study

The Amplitude Law: the obstruction is the interpolation function, not the carrier -- and a monotone kernel escapes it with a0 untouched

Key Points

Discussion

Implication

Cite This Study

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