Constructive Inference Theory on Frozen Organizational Geometry: From Admissible Observation to Genealogy-Preserving Reconstruction

This paper develops Constructive Inference Theory as the inverse continuation of the observation architecture established in Paper VIII of the Organizational Field Theory research program. The inherited configuration manifold, metric, connection, curvature, field equations, admissible solution classes, numerical realization, observation operator, measurement map, comparison functional, and validation rules are treated as frozen and versioned components of the forward theory. Within this constraint, the inverse layer may select, reconstruct, or rank only states already admitted by the constructive architecture; it may neither redesign that architecture nor infer a new ontology directly from data. The framework introduces exact and tolerance observational fibres, quotient-resolved reconstruction operators, structural identifiability, stability, recoverability, admissible regularization, observational degeneracy, fibre geometry, and constructive experimental design. Exact uniqueness is claimed only when the relevant observational fibre reduces to a single declared equivalence class, while noisy observations are addressed through tolerance fibres accompanied by explicit discrepancy, uncertainty, and stability records. The resulting formulation clearly separates agreement with data, inferential selection, and constructive admissibility, establishing valid inference as the disciplined and auditable reconstruction of latent organization already encoded in a frozen forward map.