Admissibility-Time Bounds from Fixed-Point Damping Exact Exit Times, Certified Proper-Time Filters, and the MTT Source Boundary

This paper separates the exact admissibility exit time of a damped incoherent sector from the earliest time certified by an exponential semigroup bound. It proves the certified threshold formula and obtains the exact formula when a nonnegative self-adjoint generator is reduced by the incoherent projector. Declared operator, projector, spectral-window, tolerance, and time data then determine a unique functional-calculus filter with a controlled error decomposition and an explicit circle benchmark. The result is conditional rather than a first-principles scale prediction: MTT geometry must still select those source data and their physical intertwiner before the filter can replace a regulator or modify a propagator.