lag_q
plain-language theorem explainer
Researchers working on Gap45 beat synchronization cite this lemma to normalize the lag quotient 45/(8*120). It asserts the rational equality to 3/64 and supplies a simp rule for downstream time-lag reductions. The proof is a one-line wrapper that invokes norm_num on the arithmetic.
Claim. $45/(8*120)=3/64$ holds as an equality of rational numbers.
background
The Gap45 module encodes the gating rule that experience is required exactly when the plan period is not a multiple of 8, capturing the policy that 8-beat alignment disables Gap45 gating. Sibling definitions include beats, lcm_8_45_eq_360, and cycles_of_8, which track synchronization between 8-beat cycles and 45-unit periods. The present lemma normalizes the lag expression appearing in TimeLag calculations.
proof idea
This is a one-line wrapper that applies norm_num to discharge the equality.
why it matters
The lemma supplies a simp attribute used by the parent TimeLag.lag_q and supports beat-alignment steps in Gap45. It fixes the rational value of the 8-beat divisor that appears in the eight-tick octave (T7) and feeds into Recognition Composition Law reductions for period synchronization.
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