the phase map contains 14.18243 +/- 0.05769 winning points and 6.61794 +/- 0.01205 boundary crossings on average, with 95% CI [6.59433, 6.64155] for the crossing count; across completed payloads the boundary count stays almost entirely in the 6-7 range, so the drift-sign boundary is geometrically sharp rather than diffuse.
The history-dependent Parrondo boundary is a stable codimension-one object in parameter space, not a noisy mosaic. The small variability in crossing count means the alternating-game winning region has a reproducible topology even when the precise drift values fluctuate. That matters because it supports a genuine boundary interpretation: sign changes in mean drift occur along a narrow structured curve rather than being scattered by sampling noise. The implication is that history dependence creates a robust winning wedge that can be tracked and potentially optimized by boundary-following methods.
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