harmonic3_eq
plain-language theorem explainer
The third Schumann resonance harmonic equals exactly 11 phi plus 3 under the Recognition Science formula. Researchers modeling ionosphere cavity modes or EEG band alignments would cite this specialization. The proof is a one-line wrapper that unfolds the schumannRS definition and reduces the resulting expression with the ring tactic.
Claim. $f(3) = 11 phi + 3$, where $f(n) = (4n-1) phi + 3$ is the RS-predicted nth Schumann harmonic frequency, $phi = (1 + sqrt(5))/2$, and $n$ is a positive integer.
background
Recognition Science forces the golden ratio phi via T6 self-similarity and spatial dimension D=3 via T8. The module defines schumannRS(n) as (4n-1) phi + 3 to encode the fundamental 3 phi squared and the spacing 4 phi. This matches the measured harmonics 7.83, 14.3, 20.8, 27.3, 33.8 Hz within 0.4 percent using zero free parameters.
proof idea
One-line wrapper that unfolds schumannRS, casts the natural number argument to real, and applies the ring tactic to confirm the polynomial identity.
why it matters
The equality is invoked directly by harmonic3_bounds and harmonic3_matches to place f(3) inside (20.798, 20.809) and within 0.01 Hz of the measured 20.8 Hz. It instantiates the general RS formula at n=3, confirming the structural decomposition that uses D=3 from T8 and phi from T6.
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