MolecularEnergyLevel
plain-language theorem explainer
MolecularEnergyLevel enumerates five molecular energy levels as an inductive type with automatic Fintype structure. Molecular spectroscopists building RS-derived state counts or energy ladders would cite it to fix the base enumeration before applying phi ratios. The declaration is a direct inductive definition deriving decidable equality and finite cardinality without lemmas or tactics.
Claim. The molecular energy levels form the inductive type whose constructors are electronic, vibrational, rotational, translational, and spin, equipped with decidable equality and finite cardinality five.
background
Recognition Science treats each molecular energy level as a rung on the phi-ladder, with adjacent levels related by the fixed ratio phi. The module documentation sets configDim D equal to five for these levels and notes that five levels times two polarizations yields ten total states. This inductive definition is imported from the CrossDomain.QuantumMolecularBound module and supplies the enumeration used by downstream cardinality and certificate results.
proof idea
The definition lists the five constructors explicitly and attaches the deriving clause for DecidableEq, Repr, BEq, and Fintype. No tactics or lemmas are invoked; the Fintype instance is generated automatically to support later cardinality statements such as energyCount.
why it matters
The definition supplies the five-level enumeration required by MolecularPhysicsCert, which asserts both the cardinality five and the phi-ratio property for adjacent rungs, plus the total of ten states. It realizes the configDim D equals five stated in the module documentation and is referenced by energyCount, gate_surj, and molecularQuantumStateClasses. The construction sits inside the Recognition Composition Law framework and the phi-ladder structure that follows from T5 J-uniqueness and T6 phi fixed point.
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