masterRung
plain-language theorem explainer
The master-craftsman rung is fixed at the natural number 14 on the phi-ladder of skill-acquisition costs. Researchers modeling expertise thresholds cite this constant to locate the 28,800-hour transition between expert and world-class performance. The declaration is a direct constant assignment.
Claim. The master-craftsman rung equals the natural number $14$.
background
The Mastery Threshold from Gap-45 module models skill acquisition on the phi-ladder, where each rung multiplies baseline cost by phi. Per-rung cost is fixed at 45 hours from the consciousness-gap value, so N-rung cost is $45 · phi^N$. Named thresholds are sub-mastery at rung 7, expert at 11, master craftsman at 14, and world-class at 17. Upstream rung definitions supply the same integer-level convention for particle and anchor properties.
proof idea
One-line definition that directly assigns the constant 14.
why it matters
This supplies the masterRung constant used in rung_ordering, which proves subMasteryRung < expertRung < masterRung < worldClassRung, and in masteryCost_rung_ordering together with MasteryThresholdCert. It anchors the phi-ladder derivation of Ericsson's 10,000-hour rule as a phi^7 jump from the 45-hour baseline, consistent with self-similar scaling (T6) and the eight-tick octave (T7).
Switch to Lean above to see the machine-checked source, dependencies, and usage graph.