<p>This paper develops Thinai coherence geometry for finite systems of local observations which are required to lift to a single global interpretation. For a finite case, we define its coherence complex to be the family of all report-index subfamilies whose constraints admit a common lift. This complex converts coherence, defect, and repair into one object: defect circuits are minimal nonfaces, maximal coherent subfamilies are facets, and inclusion-minimal deletion repairs are complements of facets. We prove a Helly bound for tame lift-region geometries and a realization theorem showing that finite Sperner hypergraphs with no singleton edges occur as defect-circuit hypergraphs for Boolean endpoint systems with non-box constraints. Weighted repairs form polyhedral chambers, and matroidal coherence complexes give a greedy repair theory. Temporal coherence is reduced to ordinary coherence over discrete finite-horizon admissible path space. Positive observation channels, pullback consensus, central gates, typed adjudication, and coherence excess are then organized as structural enrichments of the same liftability invariant.</p>