M28c The ISHE Triad at R=3.5: The Strong/Gravity Bridge and the Yang-Mills Habitat

M28c constructs the ISHE Triad at R = 3. 5, the half‑rank bridge between the rank‑3 Triad and the rank‑4 Triad. It completes the Triad architecture by introducing the unique operational layer that connects ln and slog worlds. The ISHE Triad mediates between R = 3: Cpow, Apow, aᵇ R = 4: Ctet, TMultB, HCt by assigning to each pair a half‑rank operation. Its structure is governed by a mixed logarithmic coordinate: L (x) = sqrt (ln (x) * slogB (x) ), combining SC (ln) and TC (slog) tamers into a single invariant scale. The ISHE dynamics introduces a conserved quantity K₃. 5 = const and a corresponding half-rank Hermit condition, interpolating between the SC and TC non-classical quadratics. Conceptually, M28c establishes that the Manifold contains three fundamental half-rank “Hyperzeug levels”: R = 1. 5 (between addition and multiplication) R = 2. 5 (between multiplication and Rank 3 Triad) R = 3. 5 (between Rank 3 Triad and Rank 4 Triad) which together connect all integer ranks into one coherent operational structure. The core insight is that R = 3. 5 is not transitional but structural: it is the bridge layer where laws morph, and where SC and TC geometries meet in a single algebra. M28c thus defines the interface of the two Triads, completing the ladder: SC (ln) TC (slog) and prepares the framework for the physical interpretation developed in the later M28d & Appendix papers.