A Universal Gravitational Formula Unifying Dark Matter Phenomena and High-PrecisionTests

Abstract Core Content• Proposes a universal formula for gravitational acceleration that explains observationalphenomena across scales from laboratory experiments to cosmological distances.• Introduces a characteristic acceleration scale a0≈1.0×10−10 m/s2.• Reproduces predictions of Newtonian mechanics and General Relativity in strong-fieldregimes; naturally accounts for "dark matter" and "dark energy" effects in weak-field andlarge-scale contexts.• Validated against 15 independent observational and experimental datasets; quantitativeagreement demonstrated in detail using the Hubble Tension as a representative case.• No additional hypotheses such as dark matter or dark energy are required.