Quasi-Periodic Oscillations and Particle Dynamics around Regular Scale-Dependent Black Holes

Regular scale–dependent gravity (SDG) eliminates the Schwarzschild singularity by introducing a dimensionless running parameter [Formula: see text] that modifies strong-field geodesics. We derive analytic Keplerian and epicyclic frequencies in the exact SDG metric, trace the shift of the innermost stable circular orbit (ISCO) with [Formula: see text], and embed these results in the relativistic-precession model of twin peak high-frequency quasiperiodic oscillations (HF-QPOs). Using Markov chain Monte Carlo fits to the 3:2 HF-QPO pairs observed in five microquasars—GRO J1655–40, XTE J1550–564, GRS 1915+105 and H1743–322—we constrain the running parameter to [Formula: see text] at the level [Formula: see text], with a mild preference for negative values (derunning). This bound tightens contemporary iron-line spectral limits by a factor of two and demonstrates that current X-ray timing already probes quantum-inspired deformations of black-hole spacetimes, paving the way for joint tests combining QPOs, spectral lines, and forthcoming shadow-diameter measurements.