Logical Closure of the Cosmological Constant Problem in Flux-Fixed GR (GCV): A modular proof spine and falsifier map for the GR-exact branch

Version note (v1. 2. 0) This version reframes the record as a compact logical map of the Gauged Constant Vacuum-Mode (GCV) cosmology programme after completion of the core CCP modules. The paper explains how the structural GR-exact branch, the semi-explicit UV existence benchmark, magnitude localisation, and positive-Λ realisation combine to support the programme-level cosmological constant problem (CCP) closure claim. No new numerical results are introduced; the note summarises the logical structure and falsifier map of the completed module stack. This record provides a concise, journal-neutral logical overview of the GCV framework on its GR-exact branch and the module structure supporting the CCP closure claim. Core claim. GCV realises a GR-exact structural branch in which the strictly spacetime-constant vacuum mode is gauge/flux-controlled and does not appear as a local gravitational source (not a parameter redefinition). Local dynamics remain GR-exact with a flux-fixed integration constant Λₑff in the Einstein equations, while the local stress-energy tensor contains only local excitations, excluding strictly constant vacuum contributions. Once Λₑff is inferred from late-time geometry, the background expansion on this branch is indistinguishable from flat ΛCDM (wDE = −1). Role of this record. The present note provides a compact logical map explaining why the CCP closure claim follows from the completed programme modules. The canonical synthesis statement of the CCP closure claim is provided in the flagship paper; the present note explains the logical structure connecting the module records listed below. Scope. This note: summarises the structural GR-exact backbone and the radiative-stability statement for the strictly constant vacuum mode, describes the semi-explicit UV existence benchmark establishing consistency of the mechanism within a controlled compactification scenario, explains magnitude localisation of Λ via operational conditioning and close-out selection modules, summarises the late-time viability argument leading to positive-Λ realisation, and lists the minimal falsifiers associated with each pillar. The note does not introduce new numerical results, survey analyses, or code. Detailed calculations, data products, and robustness checks are provided in the cited module records. Project homepage: https: //johansson. digital Project overview hub: https: //github. com/gcv-framework/gcv-vacuum-energy