pith. sign in
theorem

all_nodup

proved
show as:
module
IndisputableMonolith.Engineering.AsteroidOreSpectroscopy
domain
Engineering
line
83 · github
papers citing
none yet

plain-language theorem explainer

The list of seven asteroid ore classes is pairwise distinct. Spectral classification engineers cite this to guarantee each mineral type receives a unique rung on the phi-ladder for peak discrimination. The proof is a one-line decision procedure applied directly to the enumerated list.

Claim. The sequence of seven mineral classes consisting of silicate, carbonate, oxide, sulfide, metallic iron, metallic nickel, and platinoid contains no duplicate entries.

background

The Asteroid Ore Spectroscopy module treats asteroid-ore identification as a phi-ladder phonon resonance problem. Each of the seven classes receives a characteristic peak frequency via the relation omega_k equals omega_0 times phi to the k, with omega_0 fixed in the module. The definition all enumerates the classes as the concrete list silicate, carbonate, oxide, sulfide, metallic_Fe, metallic_Ni, platinoid.

proof idea

The proof is a one-line wrapper that applies the decide tactic to the explicit list definition to confirm the Nodup property.

why it matters

This result supplies the distinctness required by asteroidOreSpectroscopyCert, which records omega_0 equality, positivity, successor, and strict monotonicity of peak frequencies together with the ore count. It parallels the all_nodup theorems in NarrativeGeodesic and ModalPreferenceFromPhi that likewise enable finite-type instances and certification objects within the Recognition framework.

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