IndisputableMonolith.Education.MasteryDesignFromGap45
This module defines educational structures for mastery learning drawn from Recognition Science constants. Optimal study blocks are fixed at φ hours with related quantities like mastery hours per rung tied to gap-45 on the phi-ladder. Education researchers modeling efficient learning schedules from RS-native units would cite these definitions. The module consists of type definitions, positivity lemmas, and direct equalities with no complex derivations.
claimLet $φ$ denote the golden ratio. Define MasteryStage as a finite progression with masteryStageCount stages. Set optimalBlockHours $= φ$ (in RS-native hours) and masteryHoursPerRung $= φ^{rung-8+gap(45)}$ satisfying masteryHours_eq_gap45. Recovery ratio and masteryAtRung functions are positive on the ladder.
background
The module imports the RS time quantum τ₀ = 1 tick from Constants and works in RS-native units where c = 1. It introduces MasteryStage as an inductive type for learning progression and defines functions such as optimalBlockHours, recoveryRatio, and masteryAtRung that map rung indices to hours via the phi-ladder. Gap-45 appears as a fixed parameter adjusting the exponent in the mass-style formula adapted here to study time.
proof idea
This is a definition module, no proofs.
why it matters in Recognition Science
The module applies the phi-ladder and gap parameters from the Recognition framework to education design, supplying concrete quantities for mastery scheduling. It sits downstream of Constants and supports domain-specific extensions in the education slug. No used-by edges are recorded, leaving open how these definitions integrate into larger learning theorems.
scope and limits
- Does not derive φ from the T5-T8 forcing chain.
- Does not include empirical data or validation against real learners.
- Does not model individual differences or decay rates beyond the recovery ratio.
- Does not connect to specific subjects or curricula.
- Does not prove global optimality of the φ block length.