masteryDesignCert
The masteryDesignCert definition supplies a MasteryDesignCert instance whose base field holds a CanonicalCert drawn from the J-band. Curriculum designers optimizing practice-to-mastery time ratios cite this when mapping observed r values to recognition cost. It is realized as a direct structure constructor that populates the base field from the imported canonical certificate.
claimLet MasteryDesignCert be the structure whose single field is base : CanonicalCert. Then masteryDesignCert is the instance with base set to the canonical certificate cert.
background
The module develops educational design principles by applying the J-cost functional to the ratio r of observed practice time to mastery time per rung. It compounds with the companion MasteryThresholdFromGap45 module that fixes 45 hours per rung. Recognition cost is zero only at exact calibration; both over- and under-practice incur positive cost, with the canonical band marking the boundary between effective and ineffective curricula.
proof idea
The definition is a one-line wrapper that constructs the MasteryDesignCert structure by assigning its base field directly to the canonical certificate cert.
why it matters in Recognition Science
This supplies the J-cost variant of the mastery design certificate that the Gap45 implementation of masteryDesignCert builds upon. It realizes the E5 step by grounding curriculum calibration in the J-cost zero point at perfect practice-to-mastery ratio, closing the interface to the five-stage model without new axioms.
scope and limits
- Does not derive the explicit J-cost formula for arbitrary r ratios.
- Does not establish numerical bounds on the canonical band.
- Does not connect to the eight-tick octave or spatial dimension results.
- Does not provide falsifiable predictions for student performance metrics.
formal statement (Lean)
25def masteryDesignCert : MasteryDesignCert where
26 base := cert
proof body
Definition body.
27
28end MasteryDesignFromJCost
29end Education
30end IndisputableMonolith