expertRung
plain-language theorem explainer
expertRung fixes the expert-mastery threshold at rung 11 on the phi-ladder, producing a cumulative practice cost of roughly 6800 hours that sits near Ericsson's 10,000-hour empirical benchmark. Cognitive scientists and education researchers modeling skill acquisition via Recognition Science constants would cite this named rung when calibrating mastery transitions. The declaration is a direct numerical assignment with no proof obligations.
Claim. The expert-mastery rung on the Recognition Science phi-ladder is defined as $11$.
background
The Mastery Threshold from Gap-45 module derives Ericsson's 10,000-hour rule from a 45-hour per-rung baseline obtained by applying consciousnessGap 3 to skill acquisition. Mastery cost for crossing N rungs is then given by 45 · φ^N, with named thresholds marking sub-mastery at rung 7, expert mastery at rung 11, master craftsman at rung 14, and world-class performance at rung 17. Upstream rung definitions in particle-mass and asteroid contexts supply the general notion of an integer index, which is here specialized to cognitive-progress steps on the phi-ladder.
proof idea
The declaration is a direct constant assignment expertRung := 11. No lemmas or tactics are invoked; the value serves as a fixed anchor for the downstream rung_ordering theorem and MasteryThresholdCert structure.
why it matters
expertRung supplies the expert threshold inside the rung_ordering theorem and the MasteryThresholdCert structure, which together certify strict monotonic growth of masteryCost across subMasteryRung < expertRung < masterRung < worldClassRung. It instantiates the phi-ladder scaling (T6) for human cognitive milestones and closes one concrete step in the Gap-45 derivation of the Ericsson rule. The module falsifier remains a longitudinal study showing per-skill costs outside the band 45 · φ^k · [0.5, 2].
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