Rigorous computation of escape times for parameter intervals in the quadratic map

The paper defines escape times for the quadratic family, implements a certified interval-arithmetic algorithm with monotonicity checks and first-collision chopping, and reports that for δ=10^{-3}, N0=25, and width cap w=10^{-8} one can construct a disjoint family of escaping parameter intervals covering measure ≈0.5393 of Ω=[1.4,2] (and even 0.539302250926 in one run) . The candidate model describes essentially the same construction and acceptance criterion |ω_N|≥√δ with the same settings, the same chopping strategy, and the same quantitative outcome, including the 0.539302250926 figure and the ≈0.54 ceiling explanation due to periodic windows . Minor implementation details (e.g., explicit handling of intervals where 0∈D_i and stopping rules) are less explicit in the model, but do not change correctness.