harmonic5_eq
plain-language theorem explainer
The fifth Schumann resonance equals 19φ + 3 in RS units. Geophysicists modeling zero-parameter Earth-ionosphere modes would cite the identity. The proof is a one-line algebraic reduction after unfolding the definition of schumannRS.
Claim. $f(5) = 19φ + 3$, where $f(n) = (4n-1)φ + 3$ is the RS-forced Schumann formula with $φ = (1+√5)/2$ and $D=3$.
background
The module constructs Schumann harmonics from Recognition Science using only the forced constants D=3 (T8) and φ (T6). schumannRS implements the zero-parameter formula f(n)=(4n−1)·φ + 3, which decomposes as fundamental 3φ² and spacing 4φ = half the eight-tick period. Upstream results supply the primitive distinction axioms and collision-free empirical program that license the structural identities.
proof idea
The proof is a one-line wrapper that unfolds schumannRS, pushes the cast on the natural number 5, and applies the ring tactic to confirm the arithmetic identity.
why it matters
This supplies the exact value used by harmonic5_bounds and harmonic5_matches, which place f(5) inside (33.742, 33.761) and within 0.06 Hz of the measured 33.8 Hz. It instantiates the general formula forced by D=3 and the eight-tick octave in the Recognition framework. The result closes the structural decomposition for the fifth harmonic in the Earth-brain resonance model.
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