Explanation of the all declaration

(1) In plain English, all is a constant list that enumerates the seven ore classes in the model: silicate, carbonate, oxide, sulfide, metallic_Fe, metallic_Ni, and platinoid. Each class is assigned a rung (0 through 6) that indexes its characteristic spectral peak on the φ-ladder.

(2) In Recognition Science this enumeration matters because the asteroid-ore spectroscopy track uses φ-ladder phonon resonance to identify minerals. The list supplies the complete set of classes whose peaks are strictly monotonic powers of φ, enabling the discrimination bounds and the one-statement certificate that seven distinct classes exist with adjacent ratios exactly equal to φ.

(3) The formal statement reads def all : List OreClass := [.silicate, .carbonate, .oxide, .sulfide, .metallic_Fe, .metallic_Ni, .platinoid]. In Lean this defines a named constant of type List OreClass whose value is the explicit finite list of the inductive type's constructors. The surrounding namespace OreClass makes the full name OreClass.all.

(4) Visible dependencies and certificates in the supplied source are all_length (proves length = 7), all_nodup (proves the list has no duplicates), asteroidOreSpectroscopyCert (bundles the list into the master certificate), and ore_spectroscopy_one_statement (uses the list to state the complete claim about seven classes and φ-ratios). The definition also depends on the inductive OreClass and the rung function.

(5) The declaration itself does not prove any physical or mathematical properties of the peaks. It supplies only the enumeration; positivity of frequencies, strict monotonicity, and the exact φ-ratio between adjacent classes are proved separately by peakFrequency_pos, peakFrequency_strict_mono, and adjacent_class_ratio.