Discuss Findings

mean positive-persistence edge shift is -0.002019 +/- 0.000009 and mean antipersistent edge shift is -0.002021 +/- 0.000009, with 95% CIs that overlap almost perfectly; the pm1-gap shifts are only +0.000021 +/- 0.000006 and +0.000020 +/- 0.000006, and support for positive persistence beating antipersistence on edge shift is just 0.14286 +/- 0.00021 across 1845 completed payloads.

Markov sign persistence is not creating a distinctive edge-clustering phase in the Kac ensemble. Both persistent and antipersistent coefficient sequences push the edge-minus-side statistic downward by essentially the same amount, so the effect is a generic departure from IID rather than a persistence-direction asymmetry. The tiny pm1-gap response and weak positive-vs-anti support fraction reinforce that interpretation. Mechanistically the correlations are modifying root geometry, but they are doing so symmetrically enough that the claimed edge-clustering distinction does not survive aggregate analysis.