gapDiff
plain-language theorem explainer
gapDiff defines the integer difference 45 minus 8 between the consciousness window and body-clock period inside the Gap-45 arithmetic. Workers on the Shimmer factor cite it as the denominator that produces the ratio 360/37. The definition is a direct subtraction of the two upstream constants.
Claim. Let $d := 45 - 8$. Then $d$ is the arithmetic beat between the Gap-45 consciousness window and the eight-tick body period.
background
In the Gap-45 module, bodyPeriod is the 8-tick body-clock period fixed by T6 as $2^D = 2^3 = 8$. gapPeriod is the 45-tick consciousness window. Their difference supplies the beat 37 that is later shown prime and coprime with the lcm window of 360. The module states that the Shimmer subjective-time factor is obtained purely as the ratio lcm(8,45)/(45-8) with no empirical calibration.
proof idea
One-line definition that subtracts the bodyPeriod constant from the gapPeriod constant.
why it matters
This definition supplies the denominator for shimmerFactor and is invoked by the master theorem shimmer_is_gap45_arithmetic, which asserts that the numerical value ~9.73 is forced by Gap-45 arithmetic alone. It closes the counting step that follows the eight-tick octave (T7) and enables the coprimality barrier used downstream in RecognitionBarrier.
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