fundamental_near_theta_alpha_boundary
plain-language theorem explainer
The Recognition Science prediction for the fundamental Schumann frequency sits 0.143 to 0.146 Hz below the 8 Hz theta/alpha EEG boundary. Geophysicists and neuroscientists examining zero-parameter matches between planetary cavity modes and brain rhythms would cite this bound. The proof is a one-line term that applies linear arithmetic directly to the closed interval already established for the first harmonic.
Claim. Let $f_1 = 3φ + 3$ be the Recognition Science formula for the fundamental Schumann resonance frequency. Then $0 < 8 - f_1 < 0.15$.
background
The EarthBrainResonance module constructs Schumann harmonics from Recognition Science primitives only. The function schumannRS(n) is defined as (4n − 1)φ + 3, where φ is the golden ratio forced by T6 self-similarity and the coefficient 4 arises from D + 1 with D = 3 from T8. The sibling theorem harmonic1_bounds supplies the tight interval 7.854 < schumannRS(1) < 7.857, obtained by rewriting the closed-form expression and applying the rational bounds on φ.
proof idea
The proof is a term-mode exact that packages two linear-arithmetic goals. The left conjunct 8 − schumannRS(1) < 0.15 follows from the upper bound on schumannRS(1) supplied by harmonic1_bounds.1; the right conjunct 0 < 8 − schumannRS(1) follows from the lower bound supplied by harmonic1_bounds.2. No further rewriting or case analysis is required.
why it matters
This places the RS fundamental inside the 0.15 Hz window immediately below the theta/alpha boundary, confirming the module claim that f(1) lands at the EEG transition. It supports the larger structural decomposition in the module documentation that links D = 3, φ² self-similarity, and the eight-tick octave to observed brain frequencies. Although no downstream theorems currently depend on it, the result closes one concrete numerical check in the zero-parameter Schumann–EEG correspondence.
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