Restart Consistency and Computable Reversal Lag Bounds for Caputo Operators

A numerical restart of a Caputo operator must preserve its inherited history, whereas a reset deletes that history. We study the resulting sign-change locations under prescribed loading reversals. For a monotone prehistory with loading rate bounded between two positive constants, followed by a constant reverse rate, we prove uniqueness of the first reversal lag and sharp comparison bounds, whose endpoints are attained by constant-rate histories for each admissible rate-bound pair. For equal-spacing triangular loading, we prove that odd lags decrease and even lags increase toward a common limit, with an explicit separation bound. A positive exponential quadrature gives a computable uniform response-error budget that includes frequency truncation, rate approximation and restart-state errors. A residual estimate converts this budget into lag enclosures. Numerical checks include 72 nonlinear-prehistory cases and 40 lag enclosures verified with ball arithmetic. At fractional order 0.60, 768 states on the band [10-10,1010 ] give a uniform response bound below 4.705×10-4 over 0≤s≤9 and lag radii below 0.001044 for the first eight reversals. These enclosures separate continuous memory from a fixed window and reset for the stated protocol. The results concern scalar operators; material strain and dissipation require a separate constitutive embedding.