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closure_interpretation
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IndisputableMonolith.Gap45.Derivation on GitHub at line 200.
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197/-- The closure factor represents the "wrap-around" of the eight-tick cycle.
198 To return to the initial state after traversing 8 ticks, you need 8+1=9 steps
199 (like needing 9 fence posts for 8 fence sections). -/
200def closure_interpretation : String :=
201 "closure_factor = 8 + 1 = 9: one full eight-tick cycle plus return to start"
202
203/-- The Fibonacci factor comes from the golden ratio φ.
204 5 is Fibonacci(5), the smallest Fibonacci number > 1 that is coprime with 8.
205 This ensures the gap creates a non-trivial synchronization structure. -/
206def fibonacci_interpretation : String :=
207 "fibonacci_factor = 5 = Fib(4): smallest Fibonacci > 1 coprime with 8"
208
209/-- Summary of the derivation. -/
210def derivation_summary : String :=
211 "45 = (8+1) × 5 = closure × fibonacci\n" ++
212 "360 = lcm(8, 45) = full synchronization period\n" ++
213 "D = 3 because 2^3 = 8 and lcm(8, 45) = 360"
214
215end Derivation
216end Gap45
217end IndisputableMonolith