shimmerFactor
plain-language theorem explainer
The Shimmer subjective-time factor is the real number obtained by dividing the least common multiple of the 8-tick body period and 45-tick gap period by their arithmetic difference. Researchers on Gap-45 structures cite this definition to extract the value 360/37 directly from the two primitives. The definition is a single arithmetic ratio after casting the natural-number constants to reals.
Claim. The Shimmer factor is defined by the ratio $s = lcm(8,45)/(45-8)$.
background
In the Gap-45 module, bodyPeriod stands for the 8-tick body clock and gapPeriod for the 45-tick consciousness window. gapLCM is defined as the least common multiple of these periods and equals 360, the minimal realignment window. gapDiff is the difference 45-8=37, a prime number. The module states that the Shimmer factor is introduced as their ratio so that every subsequent claim reduces to native arithmetic on these primitives with no additional physical input.
proof idea
The definition is a direct one-line ratio that casts gapLCM and gapDiff to reals and divides them. No lemmas are invoked beyond the casting.
why it matters
This definition supplies the numerical value used by the ShimmerCert structure and the equality theorems such as shimmerFactor_eq_360_div_37. It records the concrete scaling factor that emerges from the Gap-45 arithmetic in the Recognition framework, where the eight-tick octave and 45-tick window produce the ratio approximately 9.73. The module notes that the non-trivial structural content resides upstream in RecognitionBarrier.
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