Conservative Orbital Resonance Networks as Local Environmental Diagnostics for Extreme Mass Ratio Inspirals
LLow order orbital resonances provide localized probes of the conservative geometry sampled by extreme mass ratio inspirals. We study fixed eccentricity and inclination slices of the ordered $3{:}2$, $5{:}3$, and $2{:}1$ polar to radial resonance surfaces in source consistent anisotropic black hole environments, treating rotation strictly to first order. A horizon regularized Dehnen sequence produces unequal resonance displacements, reaching $-7.17\%$, $-5.45\%$, and $-3.94\%$ in a fixed global benchmark. After matching both the total environmental mass and the enclosed mass at $10M_\bullet$, we compare Dehnen and Einasto inspired families. Two dimensionless network spacing ratios are organized primarily by the local logarithmic enclosed mass slope: for the common $β=2$ regularization their maximum cross family departure from a shared linear relation is $4.1\times10^{-4}$, while varying the horizon taper through $β=2$--$4$ increases the departure to at most $2.1\times10^{-3}$. The unequal ordering of the three resonance displacements holds at every point of a directly evaluated finite eccentricity and inclination grid. A six observable conservative response analysis is numerically full rank but strongly ill conditioned and nearly aligned with orbital nuisance directions. The result therefore establishes local conservative profile sensitivity, not unique tomography or a detector level parameter recovery forecast.