MasteryStage
MasteryStage enumerates the five discrete expertise levels in the Recognition Science education model tied to the gap-45 threshold. Curriculum designers cite it when mapping study blocks to progression on the phi-ladder. The declaration is a direct inductive enumeration that derives decidable equality and finite type structure automatically.
claimThe set of mastery stages is the five-element collection $S = $ {novice, beginner, competent, proficient, expert}, equipped with decidable equality and Fintype structure.
background
Recognition Science derives educational design from the gap-45 body-plan ceiling: each rung on the phi-ladder requires 45 hours for mastery, optimal study blocks equal φ hours (≈97.6 min), and the recovery ratio is 1/φ. The 10,000-hour rule is recovered as gap-45 × φ⁵ ≈ 495 deep hours. Five canonical stages are introduced to realize configDim D = 5 in the framework.
proof idea
Direct inductive definition with deriving clauses for DecidableEq, Repr, BEq, and Fintype; no proof body or tactics required.
why it matters in Recognition Science
MasteryStage supplies the discrete stages required by the downstream MasteryDesignCert structure, which asserts Fintype.card MasteryStage = 5 together with the block-range and mastery-hours constraints. It realizes the configDim D = 5 prediction from the RS education model and closes the link between pedagogical design and the phi-ladder plus eight-tick octave.
scope and limits
- Does not assign numerical thresholds for advancing between stages.
- Does not model individual differences in learning rates.
- Does not map stages onto specific rung indices on the phi-ladder.
formal statement (Lean)
30inductive MasteryStage where
31 | novice | beginner | competent | proficient | expert
32 deriving DecidableEq, Repr, BEq, Fintype
33