perSessionHours
plain-language theorem explainer
The definition computes per-session hours as the rational quotient of the 45-hour rung total by the 8-session count. Pedagogy modelers working from the gap-45 threshold cite it when converting the mastery yardstick into session lengths. The construction is a direct division on rationals with no auxiliary lemmas.
Claim. Let $h$ be the gap-45 hours per rung and $n$ the 8-tick session count per rung. The per-session length is the rational $h/n$.
background
The module deepens the gap-45 mastery threshold by distributing its 45 hours across an 8-tick octave. Upstream, perRungHours is the constant 45 and sessionCount is the constant 8, both taken from the eight-tick forcing chain. This yields the concrete session length 45/8 hours that the surrounding theorems then verify lies in the 5-6 hour band and satisfies the total-equals-product identity.
proof idea
The definition is a one-line wrapper that casts perRungHours to rationals and divides by sessionCount. No tactics or lemmas beyond built-in rational arithmetic are required.
why it matters
It supplies the numerical session duration that populates the PedagogyOptimalCert structure and the theorems per_session_eq, per_session_in_band, per_session_value and total_eq_session_times_count. The step closes the gap-45 to optimal-rate derivation inside the E5 deepening, anchoring the eight-tick octave (T7) to empirical session lengths of 5-8 per skill. It touches the open falsifier that any trial with at least 1000 learners must keep the spacing ratio inside the phi band.
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