per_session_value
plain-language theorem explainer
The theorem asserts that the optimal per-session duration equals exactly 5.625 hours in the gap-45 pedagogy model. Education researchers calibrating mastery acquisition against the Recognition Science eight-tick structure would cite this equality when fixing session lengths at 45/8 hours. The proof is a one-line wrapper that rewrites the prior fractional equality and normalizes the arithmetic to the decimal form.
Claim. The per-session duration equals 5.625 hours, or equivalently satisfies the equality 45/8 = 5625/1000.
background
The module deepens the per-rung mastery threshold of 45 hours by distributing those hours across an 8-session structure. Per-rung hours is the fixed 45-hour mastery threshold per rung; session count is the octave-derived value 8; per-session length is their ratio in rationals. The upstream equality per_session_eq states that this ratio equals 45/8 directly from unfolding the definitions of per-rung hours and session count.
proof idea
The proof is a one-line wrapper that rewrites using the equality per_session_eq and applies norm_num to obtain the decimal representation 5625/1000.
why it matters
This equality supplies the concrete session length required by the 8-tick + gap-45 argument for optimal pedagogy. It feeds the PedagogyOptimalCert by confirming that 45 hours divided by 8 sessions yields the 5.625-hour duration that aligns with empirical spacing data around φ. The result instantiates the T7 eight-tick octave inside the education domain and closes the arithmetic step that links the mastery threshold to distributed-practice recommendations.
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