The RTLI Coherence Action: A Geometric Field Theory Unifying Gravity and Quantum Matter

This work develops the information-geometric foundations of the RTLI coherence corridor, demonstrating that the universal coherence parameter \lambda—observed across quantum systems, Standard Model couplings, cosmology, and galactic dynamics—arises from a precise Fisher-metric structure in information space.

We show that the coherence interval [ \sqrt{e},\, 7/4 ] forms a geodesic of length \pi, implying an underlying S^{1} topology. Introducing an angular coordinate \theta(\lambda), we demonstrate that the empirically observed value \lambda \approx 1.70 corresponds to the geometric equator of this information circle. This explains the recurrence of the same coherence parameter across energy scales separated by more than 60 orders of magnitude.

Using this geometric foundation, we derive an RG flow with two stable fixed points and a long-lived central saddle, providing a natural mechanism for the universality of \lambda. From this structure, we construct a universal coupling law

g^{-1} = (\Delta C)^{\lambda} e^{-f(\lambda)},

which reproduces QED, QCD, electroweak, Higgs, and CKM hierarchies without introducing new free parameters.

Finally, we outline a predictive framework for Beyond-Standard-Model physics—including SUSY scales, neutrino mass ordering, dark matter candidates, and proton lifetime enhancement—all emerging from the same information-geometric structure. This establishes RTLI as a unified, testable cross-scale framework grounded in geometry.