harmonic4_eq
plain-language theorem explainer
The fourth Schumann harmonic in Recognition Science equals exactly 15 times the golden ratio plus 3. Researchers modeling zero-parameter planetary resonances or EEG band alignments would cite this to anchor the n=4 case of the general formula. The proof is a one-line wrapper that unfolds the definition of the harmonic function and reduces the arithmetic via the ring tactic.
Claim. The Recognition Science prediction for the fourth Schumann resonance frequency satisfies $f(4) = 15 phi + 3$, where $phi = (1 + sqrt(5))/2$ is the golden ratio.
background
The Earth-Brain Resonance module defines schumannRS as the RS-predicted n-th Schumann harmonic frequency via the zero-parameter expression f(n) = (4n - 1) phi + 3 for n a natural number at least 1. This rests on the spatial dimension D = 3 forced by the eight-tick octave at T8 together with the self-similar fixed point phi fixed at T6, where the factor 4 equals D + 1. The upstream definition supplies the general closed form that the present theorem specializes at n = 4.
proof idea
The proof is a one-line wrapper that unfolds the definition of schumannRS, pushes the natural-number cast into the reals, and applies the ring tactic to obtain the simplified arithmetic expression 15 phi + 3.
why it matters
This supplies the exact algebraic value required by the downstream results harmonic4_bounds and harmonic4_matches, which place the prediction inside (27.270, 27.285) and show agreement with the measured 27.3 Hz to within 0.03 Hz. It instantiates the general Schumann formula for the specific index n = 4, confirming the RS structural claims that 3 equals D and 4 equals half the eight-tick period. The step completes one concrete case in the zero-parameter matching of the Earth's cavity spectrum to observed EEG boundaries.
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