A Positive-Subordination Bound on the Cross-Sector Force Kernel in Brane-Localized Two-Sector Gravity

Abstract

This preprint establishes a positive-subordination lower bound on the normalized cross-sector tensor-force kernel in a class of brane-localized two-sector gravitational models with one compact internal dimension. Under the stated regularity, positivity, and static linear-response assumptions, the complete Kaluza–Klein tower obeys QF(r)≥−1/3. The proof combines Sturm–Liouville completeness, heat-kernel positivity, and a positive subordination representation of the Yukawa force multiplier. The same −1/3 floor appears in the four-dimensional Hassan–Rosen companion benchmark, but by a different mechanism: two-state orthogonality in four dimensions versus spectral completeness in five. This is a structural correspondence only; no dimensional reduction, embedding, or identification m1=mFP is assumed. The accompanying reproducibility archive contains the canonical numerical validation, adversarial spectral-isolation searches, independent transfer audits, reference data, environment information, and release-integrity checks. The spectral-isolation statement remains conjectural; the numerical campaigns provide supporting evidence rather than a proof. Reproducibility archive SHA-256: 6B7020DF04D596EF88BB87CA9C4F060BF3AD2CF2031D1F2BF8F8E0C585B07A62