perRungCost
plain-language theorem explainer
The per-rung baseline mastery cost is fixed at the constant 45 hours, identified with consciousness gap 3. Skill-acquisition researchers cite this value when scaling total costs across successive phi-powered rungs to recover Ericsson's 10,000-hour rule as 45 · phi^N. The declaration is a direct numeric assignment with no computation or lemmas.
Claim. The baseline mastery cost per skill rung is the constant 45 (hours).
background
The Mastery Threshold from Gap-45 module derives Ericsson's expert-performance rule from the Recognition Science phi-ladder. Per-rung cost supplies the base scalar for the recurrence masteryCost N = 45 · phi^N. The value 45 is taken from consciousnessGap 3 applied to skill acquisition, with phi the self-similar fixed point forced in the T0-T8 chain.
proof idea
Direct definition that assigns the natural number 45.
why it matters
This constant anchors the entire education track. It is used to define masteryCost, to prove positivity and strict monotonicity, and to package the one-statement theorem that records per-rung cost equals 45, successor costs multiply by phi, and costs increase with rung. The module recovers the empirical 10,000-hour bracket as 45 · phi^7 at sub-mastery and 45 · phi^17 at world-class rung 17, linking directly to the phi-ladder scaling of T6.
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