J_phi_Hz_pos
plain-language theorem explainer
J_phi_Hz_pos establishes that the golden-section J-cost ceiling J(phi) = phi - 3/2 is strictly positive in Hz units. Researchers modeling the Schumann resonance via the BIT carrier cite it to anchor the predicted frequency band above the empirical lower threshold. The proof is a term-mode one-liner that unfolds the definition and applies the lemma phi > 1.61 via linear arithmetic.
Claim. $0 < phi - 3/2$ where $phi$ is the golden ratio.
background
The module identifies the Schumann fundamental with the BIT carrier 5 phi Hz. J_phi_Hz is defined as phi - 3/2 and supplies the canonical J-cost ceiling in frequency units that enters the band estimates separating the predicted resonance near 8.07 Hz from the observed 7.83 Hz. The local setting is the structural theorem that the Earth-ionosphere cavity supports a transverse electromagnetic mode at the BIT frequency derived from the gauge-boson scaffolding and the eight-tick octave.
proof idea
The proof is a term-mode one-liner. It unfolds the definition J_phi_Hz := phi - 3/2, obtains the hypothesis phi > 1.61 from the Constants module, and closes with linarith.
why it matters
This positivity result supplies the lower-bound component required by the master certificate schumannResonanceCert. It supports the BIT carrier identification consistent with J-uniqueness and the eight-tick octave of the Recognition framework. The certificate in turn certifies that the empirical value lies within J(phi) of the predicted band after the canonical K-gate suppression.
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