Modal Triplet Theory and the Hull–Strominger System: A Conditional Fixed-Point Correspondence and the q=79 Completion Boundary

The Hull–Strominger system couples a conformally balanced Hermitian metric, holomorphic gauge bundles, Hermitian–Yang–Mills connections, torsion, and the differential Green–Schwarz identity on one compact complex threefold. This paper asks a precise question: when does a fixed point of a Modal Triplet Theory evolution determine a solution of that system? We define a typed bridge from an upstairs MTT configuration space to Hull–Strominger data and prove exact and residual fixed-point descent theorems. Exact descent requires the bridge to intertwine the selected MTT flow with a lower geometric flow, such as the Anomaly flow together with the required bundle evolutions. Approximate intertwining yields only a quantified equation residual. These results establish a conditional correspondence, not compactification selection. The former selection-potential, global-convexity, and automatic Fu–Yau claims are withdrawn. Established Fu–Yau and Anomaly-flow results provide a mathematically appropriate lower target, while the selected q=79 program still lacks one common rank-three visible–hidden Hull–Strominger tuple and a connection-preserving intertwiner from the MTT carrier.