schumannMeasured
plain-language theorem explainer
The measured Schumann resonance harmonics supply the five observed frequencies in hertz as a finite map. Researchers validating the Recognition Science zero-parameter formula against experimental cavity data would cite these values to quantify the reported agreement within 0.4 percent. The definition proceeds by direct assignment to each index in the five-element set.
Claim. The measured Schumann resonance harmonics are the function $m :$ Fin $5$ $to$ $mathbb{R}$ given by $m(0) = 7.83$, $m(1) = 14.3$, $m(2) = 20.8$, $m(3) = 27.3$, $m(4) = 33.8$ in units of hertz.
background
The module develops the connection between Earth's Schumann cavity resonances and brain EEG bands using only Recognition Science constants. The golden ratio $phi = (1 + sqrt{5})/2$ is the self-similar fixed point forced at T6, while the spatial dimension $D = 3$ is forced at T8. The upstream result supplies the RS-predicted n-th Schumann harmonic frequency as $f(n) = (4n - 1)phi + 3$ for natural numbers n at least 1.
proof idea
The definition is realized by pattern matching on the index in the finite set of five elements, returning the corresponding measured frequency in each case.
why it matters
This definition anchors the empirical comparison in the Earth-Brain Resonance module. It allows verification that the formula using the golden ratio and spatial dimension matches the observed harmonics to within 0.4 percent. The module links these frequencies to EEG band boundaries, illustrating how the eight-tick octave structure (T7) and dimension forcing (T8) appear in geophysical data.
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