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תקציר מקורי באנגליתarXiv:2610.01738v1 Announce Type: cross Abstract: Asynchronous online learning offers temporal flexibility at a structural cost: learning communities tend to fragment rather than cohere. $\beta_0$, the number of disconnected behavioral clusters from Zigzag Persistent Homology, serves as a cohort-level indicator of this structure. Two questions remained unverified at scale: (1) does apparent $\beta_0$ convergence reflect genuine behavioral alignment or learner dropout? and (2) do assessment deadlines produce reproducible fragmentation-convergence cycles? We address both across all 22 OULAD courses (N > 22,000; 857 week-pairs). Changes in $\beta_0$ strongly co-vary with active learner changes (pooled r = 0.387; median per-course r_delta = 0.459, 20/22 courses), identifying $\beta_0$ as a par