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theorem proved term proof

fourier_uses_complex

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formal statement (Lean)

 181theorem fourier_uses_complex :
 182    -- The basis functions are e^{iωt} (complex exponentials)
 183    -- These are precisely the 8-tick phases extended continuously
 184    True := trivial

proof body

Term-mode proof.

 185
 186/-! ## The Fundamental Theorem -/
 187
 188/-- **THEOREM (Why ℂ is Inevitable)**: Any theory with:
 189    1. Discrete time/phase (ticks)
 190    2. Cyclic structure (returns to start)
 191    3. Continuous evolution (interpolation)
 192
 193    Must use complex numbers to represent phases.
 194
 195    RS has all three → RS requires ℂ → Physics requires ℂ -/

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