f_Schumann_RS_above_seven_point_five
plain-language theorem explainer
The theorem establishes that the BIT carrier frequency for the Schumann resonance exceeds 7.5 Hz. Geophysicists and plasma physicists modeling the Earth-ionosphere cavity would cite this lower bound when aligning the Recognition Science prediction with observed ELF data. The proof is a one-line wrapper that extracts the left conjunct of the band theorem for 5 phi and closes the inequality via linear arithmetic.
Claim. $7.5 < 5 phi$ where $phi$ is the golden ratio and the left-hand side is expressed in Hz.
background
In the Recognition Science framework the Schumann fundamental is identified with the BIT carrier $f_{Schumann,RS} := 5 phi$ Hz. The module proves this frequency lies in (8.05, 8.10) Hz and supplies supporting bounds including positivity and the 7.5 Hz floor. The upstream theorem f_Schumann_RS_band states 8.05 < f_Schumann_RS ∧ f_Schumann_RS < 8.10, obtained directly from the interval 1.61 < phi < 1.62 via unfolding and linarith.
proof idea
The proof is a one-line wrapper. It obtains the left conjunct of f_Schumann_RS_band via projection and invokes linarith to deduce 7.5 < 5 phi from the known numerical lower bound 8.05.
why it matters
This bound is assembled into the master certificate schumannResonanceCert and the one-statement theorem schumann_one_statement. It confirms that the BIT carrier 5 phi Hz (derived from the 8-tick octave of T7 and the phi-ladder) sits above the empirical threshold 7.5 Hz, consistent with the structural identification of the Earth-ionosphere mode. The result closes one of the four numerical claims required for the full Schumann resonance certificate.
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