Flux-fixed cosmological curvature and local support in fixed-sector GCV black holes: No constant-mode hair, source-resolved Misner-Sharp mass, and regular-core obstruction

Core GCV baseline claim:The core GCV priority claim is a source-assignment criterion for exact spacetime-constant vacuum shifts: under explicit no-leak conditions, the exact zero mode renormalizes the global flux/topological sector rather than an independently running local cosmological-constant coupling. Local matter, radiation, fields, curvature-dependent terms, shells, semiclassical stress, perturbations, and other local excitations remain in the local stress tensor and gravitate normally. The source-assignment claim concerns only the exact spacetime-constant vacuum zero mode. Black-hole core claim:This standalone black-hole baseline record applies the fixed-sector GCV source-assignment rule to black-hole spacetimes. It imports the earlier fixed-sector exterior no-hair theorem, where the governed constant mode cannot become smooth radial exterior hair in a connected membrane-free fixed flux sector, and extends the analysis to static spherical interiors. Main result:For static spherical geometries, the paper separates the geometric Misner-Sharp mass into a locally supported part and a fixed cosmological-curvature part. The fixed curvature contribution is not counted as local black-hole substance. The paper also reconstructs the full local support tensor: local density, radial pressure, and tangential pressure. This gives a diagnostic for any proposed static spherical black-hole interior once Lambda_eff is treated as fixed cosmological curvature rather than local black-hole stress. Regular-core obstruction:A de Sitter-like core whose curvature differs from the fixed flux-sector value Lambda_eff requires explicit local support, a shell, a membrane or flux-sector transition, boundary or corner structure, or a source-assignment-compatible strong-field mechanism. The exact spacetime-constant vacuum mode alone cannot be the local material support of a black-hole core. Consistency checks:The record includes standard spherical consistency checks: Schwarzschild, Kottler/Schwarzschild-de Sitter, pure de Sitter/anti-de Sitter, and a generic de Sitter-like regular core. These checks show that the fixed Lambda_eff term contributes cosmological curvature but not local black-hole substance. Scope and non-claims:This is not a new black-hole metric proposal, not a singularity-resolution theorem, not an evaporation or information-loss analysis, not a rotating Kerr-interior calculation, and not an observational black-hole measurement. It is a fixed-sector GCV support theorem and no-leak baseline for black-hole interiors. Its role is to state what the exact constant vacuum mode cannot become inside a lawful fixed sector, and to define what any GCV-compatible regular-core or strong-field continuation must supply instead. homepage: johansson.digital