optimalBlockHours
plain-language theorem explainer
Optimal study block duration equals the golden ratio φ in hours. Pedagogical researchers and mastery-based curriculum designers cite this for aligning session lengths with cognitive cycles. The definition is a direct assignment from the Recognition Science constant phi.
Claim. The optimal study block duration is defined as $φ$ hours, where $φ$ is the golden ratio.
background
In the Recognition Science framework the golden ratio φ is the self-similar fixed point forced by the unified forcing chain (T5–T6). The module Education.MasteryDesignFromGap45 derives pedagogical parameters from the mastery threshold of 45 hours per rung (gap-45 body-plan ceiling) and the phi-ladder structure. Optimal block size is set to φ hours to match observed ultradian rhythms such as 90-minute learning cycles and the Pomodoro technique (25 min × 4 ≈ 100 min). Upstream results supply the structural constants: PeriodicTable.Block fixes φ-packing offsets for chemical blocks, while CirclePhaseLift.and provides explicit log-derivative bounds that anchor angular Lipschitz constants on the circle.
proof idea
The definition is a direct one-line assignment of the Recognition Science constant phi to optimalBlockHours.
why it matters
This definition supplies the block duration used in MasteryDesignCert to certify the interval (1, 2) hours and in optimalBlock_in_range to prove the bound via one_lt_phi and phi_lt_onePointSixTwo. It implements the RS prediction that optimal block duration equals φ hours, linking the 45-hour mastery rung to the eight-tick octave and the 10,000-hour rule approximation gap-45 × φ^5. The declaration closes the translation from abstract phi-ladder constants to concrete educational design parameters.
Switch to Lean above to see the machine-checked source, dependencies, and usage graph.