What question did this study set out to answer?

Formulate an observer-centered mathematical construction for the empirical galactic radial acceleration relation (RAR) and evaluate its predicted universal acceleration scale.

August 14, 2026Open Access

An observer-centered conditional construction for the galactic radial acceleration relation

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YYi

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Implication

Theoretical analysis derives the empirical radial acceleration relation across galaxies, suggesting a direct mathematical link to cosmological scales.

Key Points

Formulate an observer-centered mathematical construction for the empirical galactic radial acceleration relation (RAR) and evaluate its predicted universal acceleration scale.
Derived the feedback resolvent profile using operator algebra, observation channel partitioning, and dual Schur complements.
Tested the fixed analytical scale a* = 1.20055 × 10⁻¹⁰ m s⁻² against 2060 radial points across 93 galaxies from the SPARC database across different mass-to-light ratios.
Constructed the exact empirical RAR profile g_obs/g_bar = 1/(1 − exp[−√(g_bar/a*)]) yielding the deep limit v_f⁴ = G M_b a*.
Observed that the fixed scale differed from the freely fitted value (1.21804 × 10⁻¹⁰ m s⁻²) by Δ(−2 ln L) = 0.647 on the 93-galaxy SPARC sample at a frozen disk mass-to-light ratio of 0.5, with gaps exceeding 100 at ratios of 0.4 or 0.6.

Cite This Study

Yi (2026) studied this question.

synapsesocial.com/papers/6a7ec775b70b84ec8b913dc4 https://doi.org/10.5281/zenodo.21897318

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Implication

Theoretical analysis derives the empirical radial acceleration relation across galaxies, suggesting a direct mathematical link to cosmological scales.

An observer-centered conditional construction for the galactic radial acceleration relation

Discussion

Member takes

Implication

Key Points

Cite This Study

An observer-centered conditional construction for the galactic radial acceleration relation

Discussion

Member takes

Implication

Key Points

Cite This Study

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