masteryHoursPerRung
plain-language theorem explainer
The declaration fixes mastery hours per rung at the natural number 45 inside the Recognition Science education model. Pedagogical designers cite it when scaling total study time across phi-powered difficulty rungs or when certifying the 10,000-hour rule approximation. It is introduced by a direct constant assignment with no computation or auxiliary lemmas.
Claim. Let $m$ denote the mastery hours per rung. Then $m = 45$.
background
The module sets educational design from the gap-45 threshold, which supplies the body-plan ceiling for mastery. Five canonical stages (novice to expert) are fixed by configDim D = 5. Optimal blocks are sized at phi hours with recovery ratio 1/phi, and the 10,000-hour rule is recovered as gap-45 times phi^5.
proof idea
Direct constant definition assigning the natural number 45. No lemmas or tactics are invoked; the value is used verbatim by unfolding in dependent declarations.
why it matters
This supplies the base integer for mastery scaling in masteryAtRung (45 times phi^k) and for the certification structure MasteryDesignCert. It implements the gap-45 prediction, connecting to the phi-ladder and phi^5 constants from the Recognition Science forcing chain. The downstream theorem masteryHours_eq_gap45 records the equality by reflexivity.
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