module module moderate

`IndisputableMonolith.Education.PedagogyOptimalRateFromGap45`

This module defines the optimal pedagogical rate from the gap-45 hours per rung in Recognition Science. Education theorists applying RS to learning design would cite it for session planning and spacing. The module consists of chained definitions for perRungHours, sessionCount, perSessionHours, optimalSpacingRatio and a terminal certificate, all resting on the base time quantum imported from Constants.

claimThe gap-45 supplies perRungHours = 45 \tau_0 with \tau_0 the RS time quantum; sessionCount and perSessionHours obey total_eq_session_times_count and per_session_in_band, yielding optimalSpacingRatio \in (1,2) and the certificate PedagogyOptimalCert.

background

The module sits in the Education domain and imports only IndisputableMonolith.Constants. Its upstream doc-comment states: 'The fundamental RS time quantum (RS-native). τ₀ = 1 tick.'

Sibling definitions include perRungHours, sessionCount, perSessionHours, per_session_eq, per_session_value, total_eq_session_times_count, per_session_in_band, optimalSpacingRatio, spacing_ratio_pos, spacing_above_one, spacing_below_two and PedagogyOptimalCert. These encode the gap-45 hours per rung as the base unit for optimal spacing.

proof idea

This is a definition module, no proofs.

why it matters in Recognition Science

The module supplies the gap-45 hours per rung that anchors pedagogical rate calculations inside Recognition Science. It directly produces PedagogyOptimalCert and the supporting spacing lemmas; no external parent theorems are recorded yet.

scope and limits

Does not derive the numerical value 45 from the forcing chain or RCL.
Does not address learner-specific adjustments or subject content.
Does not link the rate to the eight-tick octave or D=3.
Does not claim empirical validation outside the RS-native units.

depends on (1)

Lean names referenced from this declaration's body.

IndisputableMonolith.Constants module_import

declarations in this module (13)

def perRungHours L53
def sessionCount L56
def perSessionHours L59
theorem per_session_eq L61
theorem per_session_value L65
theorem total_eq_session_times_count L69
theorem per_session_in_band L75
def optimalSpacingRatio L80
theorem spacing_ratio_pos L82
theorem spacing_above_one L85
theorem spacing_below_two L88
structure PedagogyOptimalCert L91
def cert L99