asteroidOreSpectroscopyCert
plain-language theorem explainer
Engineers modeling asteroid mineral identification via phonon resonance cite the asteroid ore spectroscopy certificate to establish that seven ore classes exhibit spectral peaks on the phi-ladder with base frequency one and adjacent ratios exactly phi. The certificate guarantees positivity, strict monotonicity, and distinctness of the classes. Its construction directly instantiates the structure using pre-established lemmas for frequency properties and list invariants.
Claim. The certificate asserts that the base angular frequency equals one, that the peak frequency at natural number rung $k$ is positive, that successive peaks multiply by the golden ratio phi, that the frequency sequence is strictly increasing, that exactly seven ore classes exist and are distinct, and that peaks of adjacent classes differ by exactly phi.
background
The module derives asteroid ore identification from the phi-ladder in Recognition Science. Peak frequency at rung k is defined as base frequency times phi to the power k. OreClass enumerates seven mineral types ranked by rung, with peaks computed from that definition. The local setting is track J3 of plan v5, an engineering derivation that ranks mineral classes by k-rung and bounds the discrimination floor for spectral data.
proof idea
The definition constructs the certificate record by reflexivity on the base frequency equation and by direct reference to the positivity theorem, the successor relation theorem, the strict monotonicity theorem, the length theorem for the ore list, the nodup theorem, and the adjacent ratio theorem.
why it matters
This supplies the engineering certificate for track J3 of plan v5, asserting the seven-class phi-ladder structure for ore spectroscopy. It completes the master certificate section in the module and provides the concrete object for the falsifier test on peak ratios outside the phi band. In the broader framework it instantiates the self-similar fixed point phi through the ladder construction.
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