The Modal Triplet Theory Program C: A Typed Dictionary for Geometric, Bundle, and Operator Realizations

Version 2. This paper gives a typed realization dictionary separating internal coordinate geometry, vector and line bundles, vertical operators, and spectral projectors. It proves the joint-projector theorem under strong commutation and the discrete-spectrum theorem under compact resolvent. It records the local decomposition Mat(3,R) = so(3) plus 1+2+3 strain components and distinguishes it from the selected q79 global carrier. It also quarantines the invalid old Iwasawa construction, literal Circle-Lens-Nil products, and automatic worldsheet or duality claims. Scope boundary. Matching ranks do not construct the required connection-, operator-, and Hessian-preserving continuum intertwiner; a selected source law is still needed for physical predictivity.