module module high

`IndisputableMonolith.Physics.EarthBrainResonance`

The EarthBrainResonance module supplies the Recognition Science formula for the n-th Schumann harmonic frequency as f(n) = (4n - 1) φ + 3. Researchers comparing RS predictions to observed Earth-ionosphere cavity modes would cite these expressions. The module consists of direct definitions and equalities for the harmonics together with auxiliary bounds on φ.

claimThe RS-predicted frequency of the n-th Schumann harmonic is $f(n) = (4n-1)φ + 3$ for integers $n ≥ 1$, where $φ$ is the golden-ratio fixed point.

background

Recognition Science obtains all physical relations from the forcing chain that terminates in three spatial dimensions and the self-similar fixed point φ. The upstream Constants module fixes the fundamental time quantum as τ₀ = 1 tick. This module applies those foundations to Schumann resonances, the standing electromagnetic waves trapped in the Earth-ionosphere cavity, by writing each harmonic frequency as a linear function of φ.

proof idea

This is a definition module, no proofs.

why it matters in Recognition Science

The module supplies explicit, testable frequency predictions that instantiate the Recognition Science claim that φ governs self-similar structure at geophysical scales. It connects the phi-ladder and eight-tick octave of the forcing chain to measured cavity resonances, although no downstream theorems currently depend on it.

scope and limits

Does not derive the linear coefficient structure from the Recognition Composition Law.
Does not include damping, ionospheric height variation, or propagation losses.
Applies only to the fundamental Schumann series for n ≥ 1.
States frequencies in RS-native units without conversion factors to Hertz.
Does not address any Earth-brain coupling beyond the module name.

depends on (1)

Lean names referenced from this declaration's body.

IndisputableMonolith.Constants module_import

declarations in this module (42)

lemma phi_gt_1618 L71
lemma phi_lt_1619 L79
def schumannRS L96
def schumannMeasured L99
theorem harmonic1_eq L110
theorem harmonic2_eq L113
theorem harmonic3_eq L116
theorem harmonic4_eq L119
theorem harmonic5_eq L122
abbrev D L130
theorem fundamental_eq_D_phi_sq L133
theorem three_phi_sq_eq_phi4_plus_1 L138
theorem fundamental_eq_phi4_plus_1 L142
theorem spacing_eq L146
theorem spacing_pos L151
theorem schumannRS_strictMono L155
theorem harmonic1_bounds L170
theorem harmonic1_matches L174
theorem harmonic2_bounds L179
theorem harmonic2_matches L183
theorem harmonic3_bounds L188
theorem harmonic3_matches L192
theorem harmonic4_bounds L197
theorem harmonic4_matches L201
theorem harmonic5_bounds L206
theorem harmonic5_matches L210
theorem all_harmonics_match L215
def inFreqBand L234
theorem harmonic1_in_theta L238
theorem fundamental_near_theta_alpha_boundary L243
theorem harmonic2_in_beta L248
theorem harmonic3_in_beta L253
theorem harmonic4_in_beta L258
theorem harmonic5_in_gamma L263
theorem schumann_spans_eeg_bands L269
theorem alpha_beta_ratio_near_phi L284
theorem spacing_bounds L289
inductive Provenance L297
structure EarthBrainResonanceCert L302
def earthBrainResonance_forced L341
structure FalsificationCriteria L359
def falsification L372