per_session_in_band
plain-language theorem explainer
Per-session length derived from the 45-hour mastery threshold divided by 8 sessions satisfies the bounds 5 to 6 hours. Education researchers applying the gap-45 model would cite this to align session durations with distributed practice findings. The proof rewrites the definition to 45/8 and checks the inequalities by numerical normalization.
Claim. $5 ≤ 45/8 ≤ 6$, where the per-session length equals total rung hours divided by session count.
background
This module deepens the mastery threshold result by deriving optimal time distribution within each 45-hour rung. The eight-tick structure fixes the session count at 8, yielding per-session length of 45/8 hours. Upstream per_session_eq establishes the equality perSessionHours = 45/8 by unfolding the definitions of perRungHours and sessionCount.
proof idea
The proof first rewrites using the equality from per_session_eq. It then applies refine to split the conjunction into two goals and uses norm_num to confirm both 5 ≤ 45/8 and 45/8 ≤ 6 hold.
why it matters
This theorem confirms the per-session duration matches the empirical range of 5-6 hours, supporting the optimal pedagogy rate in the Recognition Science framework. It builds on the eight-tick octave from T7 and contributes to the overall PedagogyOptimalCert. The result ties the gap-45 threshold to practical session lengths without introducing new hypotheses.
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