Resonance Selection in Black Hole High-Frequency QPOs

High-frequency quasi-periodic oscillations (HFQPOs) in black hole X-ray binaries are commonly interpreted in terms of low-order resonance models, most notably the 3:2 frequency ratio.However, several well-known sources exhibit persistent departures from this canonical value, including the ∼69 Hz and ∼41 Hz oscillations observed in GRS 1915+105. In this work, we examine whether such anomalous ratios may reflect a broader resonance-selection hierarchy operating in weakly dissipative, near-marginally stable accretion flows. Motivated by Floquet theory and trace-map structures associated with period-doubling Hamiltonian systems, we explore the conditional relevance of Lichtenberg (Jacobsthal-type) ratios as secondary resonances. Using only simultaneous observational epochs, we show that the GRS 1915+105 frequency pairs are inconsistent with a 3:2 interpretation and are instead consistent with a ratio near 5:3 within observational uncertainties. We emphasize that this framework does not propose a new excitation mechanism, nor a universal ratio sequence, but rather a source-dependent resonance-filtering process. The hypothesis makes testable predictions regarding when such ratios should, and should not, be observed.