gapDiff_prime
plain-language theorem explainer
The declaration proves that the Gap-45 beat difference equals 37 and is therefore prime. A researcher formalizing the Recognition Barrier would cite it to establish that the 37-tick frequency shares no common factors with the 360-tick window. The proof reduces the claim to the already-decided primality of 37 via a single rewrite.
Claim. Let $d := 45 - 8$. Then $d$ is a prime number.
background
In the Gap-45 module the two primitives are the 8-tick body period and the 45-tick consciousness window. Their least common multiple is 360 and their difference is defined as gapDiff := gapPeriod - bodyPeriod. The upstream result beat_is_prime states that 37 is prime, and gapDiff_eq shows that gapDiff equals 37. This local arithmetic sits inside the larger claim that the shimmer factor 360/37 arises purely from these two periods without external calibration.
proof idea
The proof is a one-line wrapper. It rewrites gapDiff using the equality gapDiff = 37 and then applies the theorem that 37 is prime.
why it matters
This result supplies the primality needed for the coprimality hypothesis in the Recognition Barrier. The module doc-comment notes that the beat is prime and therefore coprime with every proper divisor of the 360-tick window. It closes the arithmetic foundation for the subjective-time factor 360/37 before any physical interpretation is attached.
Switch to Lean above to see the machine-checked source, dependencies, and usage graph.