Gravitational Manipulation Theory v1.6: Geometry-Resolved Slab Screening and Symmetron Reconciliation of the Eöt–Wash–HUST Overlap

Gravitational Manipulation Theory (GMT) v1.6 is a focused companion to GMT v1.4 that evaluates two modeling choices underlying the previously reported Eöt–Wash–HUST independent-overlap result: the reduction of HUST's thin extended plates to an effective sphere and the potential dependence of the two-body mutual-screening response. The v1.6 analysis reconciles the geometry machinery with the Z₂ symmetron potential used by the v1.4 solver and computes the slab-versus-sphere geometry correction as the dimensionless within-geometry mutual-screening ratio R_{\rm mutual}^{\rm slab}/R_{\rm mutual}^{\rm sphere}.] At the frozen v1.4 apparatus geometry, the corrected geometry factor is modest and non-monotonic, reaching approximately 1.9 inside the Eöt–Wash–HUST overlap window. The v1.4 single-body screening ratio is also faithfully reproduced to better than 0.2% using the frozen penetrable bare reference. The principal result is that the independently covered Eöt–Wash–HUST overlap survives the geometry-resolved, potential-consistent refinement under both counting rules considered. Under the v1.4 coverage (band-membership) definition, the overlap remains structurally invariant at the validated v1.4 reference value of 319 cells (ΔN = 0). Under a constraint-active exclusion criterion, which does respond to the geometry correction, the reconstructed overlap changes only from 33 to 34 cells (ΔN = +1). Separately, the corrected geometry factor strengthens the inferred HUST constraint by up to approximately 27% (approximately 0.14 dex) inside the overlap. The release includes the compiled manuscript, complete LaTeX source, all seven figures, README, citation metadata, and license information. Results are conditional on the minimal double-well environmental-potential class and do not constitute a claim of experimentally demonstrated gravitational manipulation or engineering controllability. Companion: GMT v1.4, DOI: 10.5281/zenodo.21927558Version: 1.6License: CC BY 4.0