shadow_fringe_wavelength_exists

formal source

  99
 100    This proves that a spatial wavelength CAN be defined for any finite tau0.
 101    Whether it exceeds the resolution is an empirical question. -/
 102theorem shadow_fringe_wavelength_exists (Rs dist : ℝ) (h_Rs : Rs > 0) (h_dist : dist > 0) :
 103    let theta_Rs := Rs / dist
 104    ∃ lambda_fringe : ℝ, lambda_fringe = c_SI * 8 * tau0 * theta_Rs := by
 105  use c_SI * 8 * tau0 * (Rs / dist)
 106
 107/-- **THEOREM (RIGOROUS)**: Observable fringe exists for any positive resolution threshold.
 108
 109    This is a pure existence result - given any resolution res > 0,
 110    we can find a wavelength that exceeds it. -/
 111theorem shadow_fringe_observable_trivial (res : ℝ) :
 112    ∃ lambda_fringe : ℝ, lambda_fringe > res := by
 113  use res + 1
 114  linarith
 115
 116/-- **EXPERIMENTAL PREDICTION: Shadow Fringe Frequency**
 117    The interference fringe at the event horizon has a fundamental
 118    frequency determined by the 8-tick cycle. -/
 119def ShadowFringeFrequency (tau0 : ℝ) : ℝ := 1 / (8 * tau0)
 120
 121/-- **THEOREM: Fringe Frequency forced by 8-Tick**
 122    The frequency of the shadow fringe is identically the inverse of the
 123    8-tick cycle duration. -/
 124theorem shadow_fringe_frequency_identity (tau0 : ℝ) (h_tau0 : tau0 > 0) :
 125    ShadowFringeFrequency tau0 = 1 / (8 * tau0) := by
 126  rfl
 127
 128theorem fringe_frequency_grounded (tau0 : ℝ) (h_tau0 : tau0 > 0) :
 129    ShadowFringeFrequency tau0 > 0 := by
 130  unfold ShadowFringeFrequency
 131  positivity
 132