structure
definition
def or abbrev
EarthBrainResonanceCert
show as:
view Lean formalization →
formal statement (Lean)
302structure EarthBrainResonanceCert where
303 -- FORCED (from RCL alone: T6 forces φ, T8 forces D=3)
304 formula_zero_params : ∀ n, schumannRS n = (4 * (n : ℝ) - 1) * phi + 3
305 fundamental_is_3phi2 : schumannRS 1 = 3 * phi ^ 2
306 fundamental_is_phi4p1 : schumannRS 1 = phi ^ 4 + 1
307 harmonic_spacing : ∀ n, schumannRS (n + 1) - schumannRS n = 4 * phi
308 strictly_increasing : ∀ m n : ℕ, m < n → schumannRS m < schumannRS n
309 forced_label : Provenance
310 -- EMPIRICAL PREDICTIONS (Earth's radius is contingent)
311 match_h1 : |schumannRS 1 - 7.83| < 0.03
312 match_h2 : |schumannRS 2 - 14.3| < 0.04
313 match_h3 : |schumannRS 3 - 20.8| < 0.01
314 match_h4 : |schumannRS 4 - 27.3| < 0.03
315 match_h5 : |schumannRS 5 - 33.8| < 0.06
316 worst_case_bound : |schumannRS 1 - 7.83| < 0.06 ∧
317 |schumannRS 2 - 14.3| < 0.06 ∧
318 |schumannRS 3 - 20.8| < 0.06 ∧
319 |schumannRS 4 - 27.3| < 0.06 ∧
320 |schumannRS 5 - 33.8| < 0.06
321 eeg_coverage : inFreqBand (schumannRS 1) 4 8 ∧
322 inFreqBand (schumannRS 2) 13 30 ∧
323 inFreqBand (schumannRS 3) 13 30 ∧
324 inFreqBand (schumannRS 4) 13 30 ∧
325 inFreqBand (schumannRS 5) 30 100
326 empirical_label : Provenance
327
328/-- **MASTER THEOREM**: Earth-Brain Resonance is forced and matches observation.
329
330From the Recognition Composition Law alone:
3311. φ forced (T6: x² = x + 1)
3322. D = 3 forced (T8: linking + sync)
3333. f(n) = (4n−1)φ + 3 (zero free parameters)
3344. f(1) = 3φ² = φ⁴ + 1 ≈ 7.854 Hz
3355. Spacing = 4φ ≈ 6.472 Hz
3366. All 5 harmonics match measured Schumann within 0.06 Hz
3377. Harmonics span theta, beta, and gamma EEG bands
338
339The Earth's electromagnetic cavity and the human brain operate on
340the same φ-structured frequency ladder forced by the RCL. -/