Positive Evidence and Calibrated Mediation in Relational Spatial Reconstruction

We study how positive effect information and executable transformations can determine the same operational geometry without supplied physical locations or a primitive clock. For an arbitrary response-mode set, a calculus of finite positive evidence generates all covers of the normalized response space. A direct separation proof establishes completeness of its infinitary rules and identifies its nucleus with the faithful quotient used by transfer programs. This construction is distinguished from both metric identification and implementation under unknown calibration. On an arbitrary-mode weighted instruction family, a target distance is identifiable from linear resource comparisons exactly when its coefficient belongs to the norm-closed span of the comparison probes, provided the compatible calibrations contain a uniformly interior point. A finite certificate combines unresolved positive evidence, calibration approximation and bounded readout error in one explicit inequality. For finite instruction systems, calibration-independent divisible programs have a minimax cost equal to the largest calibrated endpoint cost over the convex hull of the allowed calibrations. A two-instruction example has an exactly identified endpoint metric but a strictly larger cost for every universally chosen program. We also retain compact, geodesic, infinite-dimensional response classes and characterize full profile realization by reflection of positive covers. The contribution is a source-explicit reconstruction and certification framework connecting these questions, not a new general duality or minimax theorem. Complete proofs, exact finite witnesses, numerical solver checks and an unchanged cumulative technical record accompany the article.