MasteryDesignCert
plain-language theorem explainer
MasteryDesignCert is a structure that certifies an educational design meets the gap-45 predictions of Recognition Science. It requires exactly five mastery stages, optimal study blocks between 1 and 2 hours, positive recovery ratio, 45 hours per rung, and strictly positive mastery hours at every rung. Pedagogical researchers applying RS would cite this certificate to validate the phi-based block duration and scaling rules. The declaration is a bare structure definition whose fields are populated downstream.
Claim. A structure asserting that the mastery stage type has cardinality 5, that the optimal block duration satisfies $1 < phi < 2$, that the recovery ratio is positive, that mastery hours per rung equal 45, and that mastery hours at rung $k$ are positive for every natural number $k$.
background
The module Education.MasteryDesignFromGap45 formalizes pedagogical predictions from the Recognition Science gap-45 mastery threshold. MasteryStage is the inductive type with constructors novice, beginner, competent, proficient, expert. masteryHoursPerRung is the constant 45 while masteryAtRung k scales that constant by phi to the power k.
proof idea
The declaration is a structure definition that introduces a record type with five fields. No lemmas or tactics are applied inside the structure. The concrete witness is supplied by the sibling definition masteryDesignCert, which populates the fields using masteryStageCount, optimalBlock_in_range, recovery_ratio_pos, masteryHours_eq_gap45, and masteryAtRung_pos.
why it matters
MasteryDesignCert is the target type for masteryDesignCert in the same module and is re-exported in MasteryDesignFromJCost as a wrapper around CanonicalCert. It encodes the RS prediction of five stages from configDim D = 5 together with phi-hour blocks and phi^k mastery scaling that follow from J-uniqueness and the phi fixed point. The structure supplies the formal bridge from the Recognition Composition Law to concrete educational parameters.
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