theorem
proved
gap_45_factorization
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IndisputableMonolith.Foundation.DimensionForcing on GitHub at line 326.
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323/-! ## The Gap-45 Synchronization -/
324
325/-- Gap-45 factorization: 45 = 9 × 5 = 3² × 5. -/
326theorem gap_45_factorization : gap_45 = 9 * 5 := rfl
327
328/-- Gap-45 has factor 9 = 3². -/
329theorem gap_45_has_factor_9 : 9 ∣ gap_45 := ⟨5, rfl⟩
330
331/-- The sync period 360 = 8 × 45 / gcd(8,45) = 360. -/
332theorem sync_factorization : sync_period = 8 * 45 := by
333 unfold sync_period eight_tick gap_45
334 -- lcm(8, 45) = 8 * 45 / gcd(8, 45) = 360 / 1 = 360
335 -- But actually gcd(8, 45) = 1, so lcm = 8 * 45 = 360
336 rfl
337
338/-- 360 = 2³ × 3² × 5. -/
339theorem sync_prime_factorization : sync_period = 2^3 * 3^2 * 5 := by
340 unfold sync_period eight_tick gap_45; rfl
341
342/-- 360 degrees in a circle relates to SO(3). -/
343theorem rotation_period : sync_period = 360 := sync_period_eq_360
344
345/-- The 2³ factor in 360 corresponds to D = 3. -/
346theorem sync_implies_D3 : 2^3 ∣ sync_period := by
347 rw [sync_period_eq_360]
348 use 45; rfl
349
350/-! ## Combined Forcing -/
351
352/-- A dimension is RS-compatible if it satisfies all forcing conditions:
353 1. Supports non-trivial linking (ledger conservation)
354 2. 2^D = 8 (eight-tick synchronization)
355 3. Compatible with gap-45 sync -/
356structure RSCompatibleDimension (D : Dimension) : Prop where