f_Schumann_RS_below_eight_point_one
plain-language theorem explainer
The theorem establishes that the BIT carrier frequency 5 phi Hz lies strictly below 8.10 Hz. Researchers comparing Recognition Science predictions for the Earth-ionosphere cavity mode against ELF observations would cite this upper bound when validating the structural identification. The proof is a one-line extraction of the second conjunct from the band theorem f_Schumann_RS_band.
Claim. Let $f = 5 phi$ denote the BIT carrier frequency in hertz. Then $f < 8.10$.
background
In this module the Schumann resonance fundamental is identified with the BIT carrier $f = 5 phi$ Hz, where phi is the self-similar fixed point of the Recognition Composition Law. The module proves that this frequency occupies the open interval (8.05, 8.10) Hz, consistent with the eight-tick octave of T7 and the gauge-boson-mass scaffolding. Upstream, the definition unfolds directly to $5 * phi$, while the band theorem establishes the full interval from the bounds $1.61 < phi < 1.62$ via linear arithmetic.
proof idea
The proof is a one-line wrapper that applies the second conjunct of the conjunction proved by f_Schumann_RS_band. No further unfolding or arithmetic is performed; the band result already supplies the required upper bound.
why it matters
This upper bound completes the predicted interval for the Schumann fundamental and is included in the master certificate schumannResonanceCert. It supports the structural claim that the empirical 7.83 Hz mode lies within J(phi) of the BIT carrier derived from the phi-ladder. The result touches the open question of how the canonical 1/45 K-gate suppression explains the small deficit relative to the upper edge.
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