V₀ Disappearance Theory: Master Theory Record v1.7 — NP-v0.2 Control-Bridge Integration

Abstract This technical research record consolidates the V₀ Disappearance Theory through the DT0–DT5R, KMA0–KMA5, RSP0–RSP15, GBO0–GBO10, CS0–CS15, REALIZATION, SPECIFICITY, REOPEN, and subsequent ordinary/BSM competitor-analysis stages. The inherited Master v1.6b establishes bounded results concerning structured hidden-sector competitors, whole-body transfer constructions, gravitational-link closure, bridge-phase conversion, and switchable bimetric models. It also provides self-contained mathematical proofs for two structured whole-body transfer models and preserves explicit limitations on their physical interpretation. New in version 1.7 — Section 20: NP-v0.2 Control-Bridge Integration Version 1.7 adds a mathematical control-interface analysis based on the separately published NP-v0.2 preprint. The new section establishes three bounded mathematical results: In a commuting single-generator sector-transfer model, exact cancellation of the integrated control eliminates the net sector transfer rather than generating a residual cubic transition. An analogous cancellation applies to the corresponding commuting many-body sector-mixing model. Noncommuting time-dependent controls can produce a nonzero cubic transition after cancellation of the first-order contribution in an explicit two-sector model. These results clarify which operator-control structures can support nontrivial higher-order transitions and which cannot. They do not establish the physical origin of the required controls, intact-body all-link disappearance, or a V₀-specific transition mechanism. Scientific status The central scientific verdict remains unchanged. A physical disappearance law, independently established V₀-specific positive property, cross-sector physical law, and discriminating ordinary observable have not been obtained. The V₀ disappearance hypothesis remains open and physically unestablished. Sections 1–19 preserve the inherited Master v1.6b content. Section 20 is the new contribution of this edition. Publication status: Technical research record, version 1.7. Not peer reviewed. Related mathematical preprint: DOI 10.5281/zenodo.23239014. Version 1.7 DOI: 10.5281/zenodo.23241351.