moon_resonance_eq
plain-language theorem explainer
The Moon-Earth spin-orbit resonance ratio equals exactly 1. Researchers modeling tidal locking via Recognition Science cite this as the zero J-cost base case on the φ-ladder. The proof is a one-line reflexivity on the definition of the ratio.
Claim. The Moon-Earth spin-orbit resonance ratio equals 1.
background
The Tidal Locking from φ-Resonance module treats spin-orbit resonance ratios as φ-rational minima of the J-cost on the phase manifold. The definition moon_resonance_pq sets the Moon-Earth ratio to the constant real number 1, representing 1:1 synchronous rotation. J-cost is the derived cost of a multiplicative recognizer's comparator and equivalently the J-cost of any recognition event state, as supplied by the cost definitions in MultiplicativeRecognizerL4 and ObserverForcing.
proof idea
The proof is a one-line term that applies reflexivity directly to the definition of the ratio.
why it matters
This supplies the moon_resonance_eq clause of the TidalLockingFromPhiResonanceCert structure, which collects the structural predictions for inner Solar System resonances. It instantiates the zero J-cost point for the trivial 1:1 resonance, consistent with the φ-ladder minima and Recognition Composition Law. The result closes the base case for Track AS6 without additional hypotheses.
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