What question did this study set out to answer?

This research aims to resolve gravitational singularities and derive galactic rotation curves using a new effective field theory on M3.

April 25, 2026Open Access

Covariant q-Deformed Topological Field Theory on M3: Emergent Temporality, Singularity Resolution, and Galactic Scale Validation

Key Points

This research aims to resolve gravitational singularities and derive galactic rotation curves using a new effective field theory on M3.
Developed a covariant q-deformed effective field theory on a ternary manifold (M3).
Conducted numerical fitting with the SPARC dataset to analyze galactic rotation curves.
Evaluated the theory's singularity resolution and predicted lensing deviations.
The theory successfully replaces classical gravitational singularities with a non-projective ∅-state.
Fitting to the SPARC dataset shows galactic rotation curves match observations without requiring dark matter.
Predicted second-order lensing deviation is measurable with future high-precision observations.

Abstract

We present a covariant q-deformed effective field theory (EFT) on a ternary topologi-cal manifold (M3), demonstrating that spacetime dynamics and temporality are emergentmanifestations of constrained information flux. We provide two major theoretical advance-ments: (1) a formal resolution of gravitational singularities via capacity saturation, wherethe classical singularity is replaced by a non-projective ∅-state, and (2) a derivation of flatgalactic rotation curves from conserved topological vacuum flux. Numerical fitting to theSPARC (Statistically Pure Samples of Rotational Curves) dataset indicates that the frame-work accounts for galactic dynamics without dark matter. The theory remains ghost-freeand admits a consistent Newtonian limit, while predicting a second-order lensing deviationmeasurable by future high-precision observations.

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