fibonacci_connection_explained

formal source

 225
 226This explains why the Fibonacci derivation "works" — it's actually
 227computing T(9) in a different form. -/
 228def fibonacci_connection_explained : String :=
 229  "5 = (9+1)/2 from the triangular formula T(9) = 9 × 10 / 2. " ++
 230  "The Fibonacci interpretation is algebraically equivalent but " ++
 231  "the triangular number is the fundamental origin."
 232
 233/-! ## Complete Physical Derivation Chain -/
 234
 235/-- **THE COMPLETE DERIVATION**
 236
 2371. The 8-tick cycle comes from 2^D with D=3 (ledger coverage)
 2382. To close the cycle, you need 8+1 = 9 steps (fence-post principle)
 2393. Cumulative phase over n steps is T(n) = n(n+1)/2 (linear accumulation)
 2404. For the closed 8-tick cycle: T(9) = 45
 2415. Synchronization: lcm(8, 45) = 360 forces D = 3
 242
 243This is a complete, physically motivated derivation of 45. -/
 244structure PhysicalDerivationCert where
 245  /-- 8 comes from 2^3 -/
 246  eight_from_dimension : 2^3 = 8
 247  /-- 9 = 8 + 1 (closure) -/
 248  nine_from_closure : closure_number = 9
 249  /-- 45 = T(9) (triangular) -/
 250  fortyfive_from_triangular : triangular 9 = 45
 251  /-- T(9) = 9 × 5 (algebraic identity) -/
 252  triangular_factorization : triangular 9 = 9 * 5
 253  /-- lcm(8, 45) = 360 -/
 254  synchronization : Nat.lcm 8 45 = 360
 255  /-- 360 = 2^3 × 45 (D=3 forced) -/
 256  dimension_forced : ∀ D : ℕ, D ≤ 10 → (Nat.lcm (2^D) 45 = 360 ↔ D = 3)
 257
 258/-- The physical derivation certificate is verified. -/