Centerline Registration and Dimension-Dependent Optimization of Multistripe Torsion Balances for Nonminimal Lorentz Violation

Higher-dimension operators in the gravity sector of the Standard-Model Extension generate anisotropic interactions that grow rapidly at short range. Building on earlier striped-balance studies, we develop a finite-volume response and covariance-based optimization for the $d=6$ and $d=8$ pure-gravity sectors. We compare three, five, and seven stripes at $d=8$ and left, centered, and right pattern registrations in both sectors, using horizontal and vertical stripe axes. Volume integration gives azimuth-dependent transfer matrices, while a Gaussian likelihood accounts for coefficient correlations and the unequal uncertainties of constant and sidereal amplitudes. Three stripes give the strongest aggregate $d=8$ response. Reoptimizing two azimuths for each registration increases the noise-weighted $D$-optimal score by up to $7.3\mathrm{\%}$ at $d=6$ and $35.6\mathrm{\%}$ at $d=8$. The response matrices permit simultaneous fits of all 14 or 22 real coefficient components. The best marginalized $1\sigma$ sensitivities reach ${10}^{-9}{\mathrm{m}}^2$ and ${10}^{-15}{\mathrm{m}}^4$, about two orders of magnitude beyond earlier inverse-square-law limits for the most favorable components. These results identify centerline registration as an additional route to improved short-range tests of Lorentz symmetry.