peak_pos
plain-language theorem explainer
The theorem establishes that the spectral peak frequency for any asteroid ore class is strictly positive. Mineral identification models relying on phi-ladder resonances would cite it to ensure all assigned frequencies remain positive. The proof is a one-line wrapper applying the positivity result for the underlying peakFrequency function at the class rung.
Claim. For every ore class $c$, the peak frequency satisfies $0 < peak(c)$, where $peak(c) = omega_0 phi^{r(c)}$ and $r(c)$ is the rung of $c$.
background
Asteroid Ore Spectroscopy models mineral identification via phi-ladder phonon resonance. The OreClass inductive type lists seven classes with assigned rungs: silicate at 0, carbonate at 1, oxide at 2, sulfide at 3, metallic_Fe at 4, metallic_Ni at 5, platinoid at 6. Peak frequency is defined by peakFrequency(k) = omega_0 * phi^k for rung k, and peak(c) extracts this value at c.rung.
proof idea
The proof is a one-line wrapper that applies the peakFrequency_pos lemma, which states 0 < peakFrequency k by mul_pos omega_0_pos (pow_pos phi_pos _).
why it matters
This result guarantees positive frequencies throughout the asteroid ore spectroscopy model, supporting class discrimination by phi-powered peak ratios. It completes a basic positivity step in the engineering derivation of the module, consistent with Recognition Science use of phi for self-similar scaling. No downstream theorems are recorded yet.
Switch to Lean above to see the machine-checked source, dependencies, and usage graph.