subMasteryRung
plain-language theorem explainer
The sub-mastery rung is fixed at the natural number 7 in the Recognition Science education model. Researchers modeling skill-acquisition timelines against Ericsson's 10,000-hour benchmark would cite this constant when scaling cumulative costs on the phi-ladder. The definition is a direct constant assignment requiring no computation or lemmas.
Claim. The sub-mastery floor is the natural number $7$.
background
The Mastery Threshold from Gap-45 module models skill acquisition costs with a per-rung baseline of 45 hours taken from consciousnessGap 3. Costs then scale as $45 · φ^N$ for crossing N rungs on the phi-ladder. Upstream rung definitions in particle-mass and spectroscopy modules supply the integer positions that this education track re-uses for human performance thresholds.
proof idea
Direct definition that assigns the constant 7.
why it matters
This constant supplies the lower bound in rung_ordering and is embedded in the MasteryThresholdCert structure that certifies monotonic cost growth from sub-mastery (7) through expert (11), master (14) and world-class (17) rungs. It anchors the module's derivation of Ericsson-style timelines inside the Recognition Science phi-ladder framework.
Switch to Lean above to see the machine-checked source, dependencies, and usage graph.