A Non-Markovian Interacting-Dark-Sector Closure with a Memory-Excess Expansion-Growth Observable

This version replaces the previous v36.5 draft with a cleaner and more technically disciplined preprint formulation of the same core model. The main change is that the strong ontological language of “future latency” has been removed from the central argument. The manuscript is now presented as a phenomenological non-Markovian interacting-dark-sector closure with a memory variable (m(x)), a strict Markovian regression channel, and a reproducible expansion-growth memory diagnostic. The central observable has also been corrected. The raw expansion-growth hysteresis area is no longer treated as a null test, because two distinct proxy histories can leave a finite Markovian baseline even when (\Delta \to 0). The paper now defines the baseline-subtracted memory-excess statistic [S_{\rm mem}=\int |R_\Delta(h)-R_0(h)|,dh,] which isolates the genuinely non-Markovian contribution. The corrected diagnostic satisfies [S_{\rm mem}=c_1\Delta+O(\Delta^2)] in the small-memory regime and provides a quantitative kill-test for implementations. This version adds: a small-(\Delta) gradient expansion of the one-pole memory kernel; the Markovian mimicry result ( \hat p_{\rm eff}=\hat p-\Delta \hat p' ); a corrected distinction between raw hysteresis area and memory-excess area; an explicit observational window (1 \le H/H_0 \le 3); a phase-lag diagnostic as a second memory estimator; a reproducible benchmark with printed proxy and toy-growth parameters; an updated kill-test table; explicit discussion of proxy normalization, gauge status of (\delta \hat p=0), and limitations of the toy benchmark. The revised manuscript is therefore intended as a cleaner preprint-level version of the v36.x non-Markovian dark-sector line: less ontological, more falsifiable, and more suitable for external review or future CLASS/CAMB implementation.