totalStates_10
plain-language theorem explainer
The declaration establishes that the total number of molecular states in the Recognition Science model equals 10. Researchers deriving molecular energy spectra from the phi-ladder would cite this result when certifying the five-level structure with polarization. The proof reduces directly to evaluating the definition of total molecular states as five multiplied by two via the decide tactic.
Claim. The total number of molecular states, defined as the product of five canonical energy levels and two polarizations, equals 10: $5 × 2 = 10$.
background
The Molecular Physics from RS module sets five canonical molecular energy levels (electronic, vibrational, rotational, translational, spin) equal to configDim D = 5. Recognition Science places each level on a phi-rung of recognition energy with adjacent ratios φ, yielding the phi-ladder structure. The upstream definition totalMolecularStates computes the product 5 * 2 to count states including polarization.
proof idea
The proof is a one-line wrapper that invokes the decide tactic on the equality totalMolecularStates = 10, which holds by direct evaluation of the definition totalMolecularStates := 5 * 2.
why it matters
This result supplies the total_10 field in the molecularPhysicsCert definition, completing the certification of molecular physics parameters. It instantiates the five-level structure and 2 × configDim D = 10 relation from the module documentation, linking to the phi-ladder in the Recognition Science framework. No open questions are addressed; it closes a basic counting step in the certification chain.
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