AsteroidOreSpectroscopyCert
AsteroidOreSpectroscopyCert defines a record structure that bundles the assertions omega_0 equals 1, peak frequencies omega_k equal phi to the power k are positive and strictly monotone, exactly seven distinct ore classes exist on the phi-ladder, and adjacent-rung classes satisfy the exact phi ratio. Engineers validating asteroid mineral identification via phonon resonances would cite this certificate to confirm their spectral assignments match the Recognition Science phi-ladder. As a plain structure definition it records the properties without
claimA structure certifying that the reference frequency satisfies $omega_0 = 1$, that the peaks $omega_k = phi^k$ obey $0 < omega_k$, $omega_{k+1} = omega_k phi$, and strict monotonicity in $k$, that the list of seven ore classes is duplicate-free, and that any two classes differing by one rung satisfy peak$(c_2) =$ peak$(c_1) phi$.
background
The module models asteroid-ore identification by assigning each of seven mineral classes a characteristic spectral peak on the phi-ladder. peakFrequency is defined by $omega_k = omega_0 phi^k$ with the reference $omega_0$ fixed at 1; OreClass is the inductive type whose constructors are silicate (rung 0) through platinoid (rung 6). Upstream results supply the length-7 list of all classes together with the positivity, recurrence, and strict-monotonicity lemmas for peakFrequency.
proof idea
The declaration is a structure definition whose fields are simply the required propositions; there is no proof body. The downstream construction asteroidOreSpectroscopyCert populates the fields by direct reference to the already-proved lemmas peakFrequency_pos, peakFrequency_succ, peakFrequency_strict_mono and OreClass.all_length.
why it matters in Recognition Science
The structure supplies the engineering certificate for Track J3 of Plan v5, confirming that asteroid spectroscopy can be read off the phi-ladder with exactly seven classes and exact phi ratios between adjacent rungs. It is instantiated by asteroidOreSpectroscopyCert and aligns with the self-similar fixed point phi (T6) and the eight-tick octave. The module states an explicit falsifier: any sample exhibiting more than five distinct peaks whose ratios lie outside the interval $[1/(2phi), 2phi]$.
scope and limits
- Does not derive the numerical value of phi from the forcing chain.
- Does not incorporate measurement noise or instrumental resolution limits.
- Does not claim these seven classes exhaust all possible asteroid minerals.
- Does not link the spectral peaks to the mass formula or G, alpha constants.
formal statement (Lean)
100structure AsteroidOreSpectroscopyCert where
101 omega_0_eq : omega_0 = 1
102 peak_freq_pos : ∀ k, 0 < peakFrequency k
103 peak_freq_succ : ∀ k, peakFrequency (k + 1) = peakFrequency k * phi
104 peak_freq_strict_mono : ∀ {k₁ k₂ : ℕ}, k₁ < k₂ →
105 peakFrequency k₁ < peakFrequency k₂
106 ore_count : OreClass.all.length = 7
107 ore_distinct : OreClass.all.Nodup
108 adjacent_ratio : ∀ (c₁ c₂ : OreClass), c₂.rung = c₁.rung + 1 →
109 OreClass.peak c₂ = OreClass.peak c₁ * phi
110