The Asymptotic-Safety Third Corner in MTT: A Conditional Diagnostic Between Coherent Geometry and the String Branch

Modal Triplet Theory currently approaches ultraviolet gravity through two partly developed routes: selected q79 heterotic geometry and projection-filtered four-dimensional constructions. Functional renormalization group asymptotic safety can serve as a third diagnostic corner, but it is not yet equivalent to either route. This paper gives a theorem-light map of the three descriptions. The q79 branch has exact finite algebraic data and a partial heterotic worldsheet contract; the physical visible-hidden bundle, continuum HYM operator, and infrared conformal field theory remain open. The FRG corner has conditional endpoint, conjugacy, truncation-error, and unstable-subspace theorems, but no selected MTT-to-coupling chart. Agreement of fixed points or critical exponents can therefore be used only after overlap domains, maps, conventions, and defects are supplied. The useful claim is a conditional triple diagnostic: independent encodings may test one selected upper construction. The paper does not claim equivalence of ultraviolet completions.