recoveryRatio
plain-language theorem explainer
Recovery ratio is defined as the reciprocal of the golden ratio phi, supplying the break-to-study time ratio for RS educational models. Curriculum designers optimizing blocks around phi hours would cite this constant when applying the 45-hour mastery threshold per rung. The declaration is a direct assignment from the phi constant.
Claim. The recovery ratio equals $phi^{-1}$, where $phi$ is the golden ratio fixed point.
background
The module sets educational design from a 45-hour mastery threshold per rung on the phi-ladder, with optimal study blocks of phi hours (approximately 97 minutes) and a recovery ratio of 1/phi as the break-to-study ratio. This follows the self-similar properties of phi and the five canonical mastery stages (novice to expert) matching configDim D = 5. The setting draws on the phi-ladder mass formula and Berry creation threshold from upstream constants, with the 10,000-hour rule approximated as gap-45 times phi^5.
proof idea
Direct definition assigning the multiplicative inverse of phi.
why it matters
The definition supplies the recovery ratio asserted positive in recovery_ratio_pos and packaged inside the MasteryDesignCert structure that certifies five stages, block range, and mastery hours per rung. It fills the RS prediction for pedagogical design in the E5 chain step, linking to T5 J-uniqueness and the phi-ladder for expertise ceilings near phi^8 deep-hours. The value is consistent with observed 90-minute learning cycles.
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