total_eq_session_times_count
plain-language theorem explainer
The equality shows that the 45-hour total per mastery rung equals eight sessions each of 5.625 hours. Education researchers calibrating distributed-practice schedules against the gap-45 threshold would cite this identity to confirm arithmetic closure of the session structure. The proof is a direct substitution of the per-session equality followed by unfolding and numerical normalization.
Claim. Let $T$ be the total hours per rung, $n$ the number of sessions per rung, and $t$ the hours per session. Then $T = n t$, where $T = 45$, $n = 8$, and $t = 45/8$.
background
The module derives optimal pedagogy rates from the 45-hour mastery threshold per rung given by the upstream MasteryThresholdFromGap45 result. Definitions fix per-rung hours at 45, session count at 8 by the eight-tick octave, and per-session hours as their rational quotient. The upstream per_session_eq theorem states that this quotient equals 45/8 exactly.
proof idea
The proof is a one-line wrapper. It rewrites using the per_session_eq theorem, unfolds the definitions of sessionCount and perRungHours, then normalizes the arithmetic.
why it matters
This identity supplies the total-equality field required by the PedagogyOptimalCert definition, which certifies the full parameter set for the optimal rate. It completes the accounting step that realizes the 8-session structure from the gap-45 threshold. In the Recognition framework it instantiates the eight-tick octave (T7) at the level of educational time allocation, linking rung mastery times directly to the phi-ladder constants.
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