Version 4 is a fundamental reformulation of the Hernandez Hypothesis. Versions 1–3 implemented the framework as an exponential suppression ofquantum-vacuum recombination by local matter density, with galacticdynamics supplied by an ultralight scalar field (a fuzzy-dark-mattervariant). Version 4 replaces that mathematics entirely with a singlealgebraic modified-gravity law, gₒbs = gbar + C · f (gbar/gcrit), f (x) = √x / (1 + √x), with C = 6. 5×10⁻¹¹ m/s² and gcrit = 5. 0×10⁻¹¹ m/s². The physicalmotivation — that vacuum behavior depends on the local gravitationalenvironment — is retained; the mathematical implementation, thedark-matter mechanism, and the dark-energy conclusion are new. The framework is AQUAL-class (its character function is algebraically aFermi-Dirac distribution) and its deep-regime limit reduces to MOND withimplicit scale a₀ = C²/gcrit = 8. 45×10⁻¹¹ m/s². It is tested acrossseveral domains against public data, with successes and failures reportedsymmetrically: • Outperforms MOND-simple on low-density gas-dominated dwarfs (Sample B; 17/19 galaxies at matched parameter freedom) and on six ultra-diffuse galaxies (6/6 head-to-head). • Predicts the Baryonic Tully-Fisher scatter (0. 067 dex) and slope (3. 89) consistent with observation, plus a novel residual-correlation signature. • Satisfies LIGO/Virgo constraints structurally (~20 orders of magnitude). • Implicit a₀ matches the cosmological de Sitter acceleration c²√ (Λ/3) / (2π) within ~2–3%. • Underperforms MOND on Milky Way classical dwarf spheroidals (7/8) and at cluster cores; the cosmological sector predicts the wrong sign for the dark-energy equation of state (a candidate manifold-tension fix is offered but requires fitted parameters) ; solar-system consistency requires a screening parameter that is not derivable from the framework. This version also corrects two specific v3 claims: the dark-energy sector’sphantom prediction (w −1, opposite to the v3 prediction. Both are documented in Appendix A, “Changes from Version 3. ” The deposit includes the full paper, the analysis code, the curated galaxysamples, and a methods-and-assumptions ledger, so that every numericalclaim can be reproduced against the public SPARC database. The work ispresented as a documented phenomenological exploration — an idea articulatedin reproducible, falsifiable form — not as a validated theory.
Frank Hernandez (Wed,) studied this question.