module module moderate

`IndisputableMonolith.Education.MasteryThresholdFromGap45`

This module sets the per-rung baseline mastery cost at 45 hours tied to consciousness gap 3 inside the Recognition Science education model. It supplies the supporting constants and ordering lemmas for masteryCost, rung levels, and monotonicity. Education researchers tracking skill thresholds reference these values when calibrating learning models. The module contains only definitions and basic lemmas with no proofs.

claimThe per-rung baseline cost equals $45\,\tau_0$ hours where $\tau_0$ is the RS time quantum and the consciousness gap equals 3. The mastery cost function is strictly increasing with rung level and satisfies the listed rung orderings.

background

Constants supplies the RS time quantum $\tau_0=1$ tick. Cost supplies the underlying cost structures used throughout Recognition Science. This module specializes those structures to education by fixing the per-rung baseline at 45 hours for consciousness gap 3 and introducing the auxiliary rung predicates subMasteryRung, expertRung, masterRung, and worldClassRung together with their ordering.

proof idea

this is a definition module, no proofs

why it matters in Recognition Science

The module supplies the numerical thresholds that anchor the Education domain inside Recognition Science. It directly implements the consciousness-gap parameter for rung advancement and supports any later theorems that quantify learning progressions or mastery levels, even though the current dependency graph lists no immediate users.

scope and limits

Does not derive the 45-hour figure from core J-cost or phi-ladder axioms.
Does not model individual variation in time to mastery.
Does not incorporate spatial dimensions or the eight-tick octave.
Does not address gaps other than the baseline value of 3.

depends on (2)

Lean names referenced from this declaration's body.

IndisputableMonolith.Constants module_import
IndisputableMonolith.Cost module_import

declarations in this module (15)

def perRungCost L45
theorem perRungCost_eq L47
def masteryCost L52
theorem masteryCost_pos L55
theorem masteryCost_strict_mono L60
theorem masteryCost_succ L68
def subMasteryRung L77
def expertRung L80
def masterRung L83
def worldClassRung L87
theorem rung_ordering L91
theorem masteryCost_rung_ordering L101
structure MasteryThresholdCert L110
def masteryThresholdCert L119
theorem mastery_one_statement L128