Fixed Points II: Projected Fixed Points and Equilibria in a 10D Modal Model

We apply the canonical Fixed Points I machinery to a ten-dimensional control setting written as a four-dimensional base times a compact six-dimensional internal space. The compact six-manifold carries three compatible vertical structures represented by strongly commuting nonnegative self-adjoint operators. Overlap is allowed; nesting requires supplied inclusion maps and is not inferred from the rank flag of one, two, and three. In the q79 realization this flag acts on a separate lane tensor factor, not inside an irreducible HYM gauge bundle, while the shared circle is a separate flat line factor and is not counted as a seventh internal product dimension. We prove existence of projected fixed points for a declared time step by applying the Fixed Points I Schauder and Darbo gates, and prove coherent uniqueness under base coercivity or strong monotonicity. A projected fixed point is promoted to a full equilibrium only under a strict Lyapunov identity. Fiber gaps control only the noncoherent sector and are never used as coherent damping.