IndisputableMonolith.Education.PedagogyOptimalRateFromGap45
The module defines optimal pedagogical session structures from a 45-hour gap per rung on the phi-ladder. Education researchers grounding learning rates in Recognition Science would cite it for quantitative spacing prescriptions. It chains definitions of per-rung hours, session counts, and spacing ratios with positivity and bound lemmas to reach a certification of optimality.
claimLet $τ_0$ be the RS time quantum. Define per-rung hours as $45 τ_0$, session count and per-session hours to satisfy the optimal spacing ratio $r$ with $1 < r < 2$, and certify pedagogical optimality under the gap-45 constraint.
background
The module imports the fundamental RS time quantum $τ_0 = 1$ tick from Constants. It introduces the gap-45 hours per rung as the base unit for educational pacing on the phi-ladder. Sibling definitions establish perRungHours, sessionCount, perSessionHours, the spacing ratio with positivity and upper-bound lemmas, and the final PedagogyOptimalCert.
proof idea
This is a definition module, no proofs.
why it matters in Recognition Science
The module supplies the gap-45 hours per rung foundation that feeds the PedagogyOptimalCert and connects core RS constants to educational applications. It fills the practical translation step from the phi-ladder structure to learning-rate prescriptions.
scope and limits
- Does not derive the numerical value 45 from the forcing chain.
- Does not address curricula spanning multiple rungs.
- Does not include empirical student data or validation.
- Does not generalize to non-phi spacing models.
depends on (1)
declarations in this module (13)
-
def
perRungHours -
def
sessionCount -
def
perSessionHours -
theorem
per_session_eq -
theorem
per_session_value -
theorem
total_eq_session_times_count -
theorem
per_session_in_band -
def
optimalSpacingRatio -
theorem
spacing_ratio_pos -
theorem
spacing_above_one -
theorem
spacing_below_two -
structure
PedagogyOptimalCert -
def
cert