The Sixfold Earth - Gravitational Privacy in Multi-Sector Compactifications - No-Go Theorems, Simplex Bounds, Screening and Passive-Response Obstructions, and Six-Dimensional Flux Realizations.

This work develops theoretical constraints on gravitational privacy in connected multi-sector compactifications. It establishes zero-mode and rank obstructions, connected-component and multigravity nullity results, simplex and minimax finite-distance bounds, screening and environmental-response constraints, positive spectral-measure restrictions, and passive finite-frequency resource bounds.The study also presents an explicit six-dimensional flux-balanced six-center control geometry and analyzes its symmetry-breaking Eg_g threshold, including independently reproducible static and positive kinetic-sector checks.The accompanying archive contains the final manuscript, rendered PDF, numerical validation code, machine-readable results, fixed inputs, regenerated figures, manuscript media, provenance records, and reproducibility documentation. The release includes a documented 828,000-check passive-response validation suite with zero theorem failures.The work is theoretical.