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module: IndisputableMonolith.Engineering.AsteroidOreSpectroscopy
domain: Engineering
line: 11 · github
papers citing: none yet

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IndisputableMonolith.Engineering.AsteroidOreSpectroscopy on GitHub at line 11.

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   8## Status: THEOREM (engineering derivation)
   9
  10Asteroid-ore identification via φ-ladder phonon resonance. Each ore
  11class has a characteristic spectral peak `ω_k = ω_0 · φ^k`. We rank
  12seven mineral classes by their k-rung and bound the discrimination
  13floor.
  14
  15## Falsifier
  16
  17Asteroid spectroscopy on a sample with > 5 distinct ore-class peaks
  18where peak ratios fall outside `[1/(2φ), 2φ]` of φ.
  19-/
  20
  21namespace IndisputableMonolith
  22namespace Engineering
  23namespace AsteroidOreSpectroscopy
  24
  25open Constants
  26
  27noncomputable section
  28
  29/-! ## §1. Ore class ladder -/
  30
  31/-- Reference spectral peak `ω_0` (silicate baseline). -/
  32def omega_0 : ℝ := 1
  33
  34theorem omega_0_pos : 0 < omega_0 := by unfold omega_0; norm_num
  35
  36/-- Peak frequency at φ-rung `k`. -/
  37def peakFrequency (k : ℕ) : ℝ := omega_0 * phi ^ k
  38
  39theorem peakFrequency_pos (k : ℕ) : 0 < peakFrequency k :=
  40  mul_pos omega_0_pos (pow_pos phi_pos _)
  41

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