bodyPeriod
plain-language theorem explainer
The body period is defined as the natural number 8, anchoring the 8-tick body-clock cycle in Gap-45 arithmetic. Researchers deriving the shimmer factor from lcm and difference operations on the two Gap-45 periods would cite this constant to fix the numerator window at 360. The assignment follows directly from the eight-tick octave forced by spatial dimension D=3.
Claim. Let $b$ denote the body period. Then $b := 8$, where 8 is the period of the body clock arising as $2^D$ for spatial dimension $D=3$.
background
The Gap-45 module constructs the shimmer subjective-time factor from two primitives: bodyPeriod and gapPeriod=45. BodyPeriod supplies the 8-tick cycle, matching the fundamental octave in RS-native units where the tick is the base time quantum τ₀=1. Upstream results establish the tick as the RS time quantum and note that one octave equals 8 ticks.
proof idea
This is a direct definition that assigns the constant 8. No lemmas or tactics are invoked; it is a one-line definition supplying the value for all downstream gap arithmetic.
why it matters
This definition supplies the body-clock period that enters the Gap-45 barrier. It is used to form gapLCM = lcm(8,45)=360 and gapDiff=37, which certify the shimmer factor via the master statement shimmer_is_gap45_arithmetic. It realizes the T7 eight-tick octave from the forcing chain (T6 phi fixed point, T8 D=3).
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