perRungHours
plain-language theorem explainer
Recognition Science sets the mastery threshold per rung at 45 hours. Pedagogists cite this constant when deriving optimal session distributions that maximize retention through distributed practice over the eight-tick octave. The declaration is a direct constant assignment in natural numbers that sibling results unfold to obtain per-session lengths and total equality.
Claim. The hours allocated to each rung for mastery acquisition equal $45$.
background
The module deepens the gap-45 mastery threshold by deriving optimal time distribution within each rung. It relies on the eight-tick octave structure, where session count equals 8, and the fundamental tick as the RS time quantum set to 1. Upstream results include definitions of rung in mass anchors, fermion classifications, and asteroid ore spectroscopy, plus the tick constant in RS-native units.
proof idea
The declaration is a direct definition assigning the constant 45. It requires no lemmas or tactics and serves as the base value unfolded in sibling theorems such as per_session_eq and total_eq_session_times_count.
why it matters
This definition supplies the per-rung value in the PedagogyOptimalCert structure, which also records session count 8 and per-session hours 45/8. It completes the gap-45 step in the education module, linking to the eight-tick period from the forcing chain. The falsifier is any prospective pedagogy trial showing optimal spacing-ratio outside the phi band.
Switch to Lean above to see the machine-checked source, dependencies, and usage graph.