sessionCount
The declaration fixes the per-rung session count at eight to realize the eight-tick octave structure inside the 45-hour mastery rung. Pedagogy researchers and learning-schedule optimizers cite the constant when converting total rung time into distributed sessions that match empirical spacing data. It is supplied as a direct natural-number constant with no further computation.
claimThe number of sessions per rung is defined to be $8$.
background
The module deepens the 45-hour per-rung mastery threshold by distributing those hours into an 8-tick pattern. Session count therefore equals eight, per-session length equals 45/8 hours, and the spacing ratio between consecutive sessions is required to lie near the golden ratio. This arrangement is presented as the Recognition-Science-native realization of distributed practice that outperforms massed practice.
proof idea
The definition is a direct constant assignment of the natural number 8.
why it matters in Recognition Science
The constant supplies the session_count field of the PedagogyOptimalCert structure and is used to prove both per_session_eq and total_eq_session_times_count. It instantiates the eight-tick octave (T7) of the forcing chain, where the period-2^3 structure governs rung acquisition and forces the optimal spacing ratio to lie inside the phi band. The module thereby closes the gap between the gap-45 mastery threshold and the empirical SuperMemo/Anki spacing literature.
scope and limits
- Does not derive the integer 8 from any prior Recognition axiom inside this file.
- Does not vary the count with learner age, prior knowledge, or subject domain.
- Does not constrain session lengths outside the fixed 45-hour rung total.
- Does not prove optimality of the phi spacing ratio; that is left to sibling declarations.
formal statement (Lean)
56def sessionCount : ℕ := 8
proof body
Definition body.
57
58/-- Per-session length in hours (rational). -/