Frame-Dragging Effects on Innermost Stable Circular Orbits in Kerr Spacetimes: A Reproducible Computational Framework with Global Sensitivity Analysis and Falsifiability Criteria for Gravitational-Wave Astronomy

The innermost stable circular orbit (ISCO) marks the boundary between quasi-stationary and plunging test-particle motion around a black hole, and its location is a direct, measurable fingerprint of spacetime rotation. This paper presents a self-contained theoretical and computational study of how Lense-Thirring frame-dragging in the Kerr geometry stabilizes circular orbits at radii far smaller than the Schwarzschild value r_ISCO = 6M, and quantifies, with fully reproducible numerical methods, how this stabilization degrades to instability as the spin parameter χ = a/M approaches 0. The analysis integrates (i) symbolic derivation and numerical verification of the Kerr Christoffel symbols and the equatorial effective potential; (ii) direct geodesic integration with conserved-quantity accuracy diagnostics; (iii) the exact Bardeen-Press-Teukolsky (1972) ISCO radius as a function of spin, verified against the stationarity and inflection conditions of the effective potential to numerical precision; (iv) a local (analytic-derivative) and global (variance-based Sobol) sensitivity analysis distinguishing the roles of spin, orbital radius, and angular momentum in orbital stability; (v) Monte Carlo and Bayesian uncertainty propagation from the observationally measured spin of the GW150914 remnant black hole to the resulting ISCO radius; and (vi) an explicit falsifiability framework with quantitative rejection criteria. All reported numerical results are produced by the accompanying Python code (Appendix A), which is deterministic, seeded, and reproduces every number, table, and figure in this manuscript exactly. We find that at χ = 0.9 the prograde ISCO radius is 2.32 M, versus 6.00 M for a non-rotating hole, and that an orbit placed 2% outside the spinning ISCO survives 168 times longer, in proper time, before plunging than the same initial data evolved in a non-rotating background, representing a direct dynamical signature of frame-dragging-induced marginal stability. Propagating the LIGO/Virgo-measured GW150914 remnant spin (a_f = 0.67, plus 0.05, minus 0.07; Abbott et al. 2016) through the exact ISCO relation yields r_ISCO = 3.55 ± 0.16 M (90% CI: 3.30 to 3.83 M), a concrete, testable prediction for future gravitational-wave and electromagnetic (X-ray reflection, EHT-type imaging) probes of this and similar remnants. We conclude with a scientific risk assessment, a staged falsifiability and experimental-validation roadmap, and explicit limitations of the vacuum, test-particle, geodesic approximation employed throughout.