mercury_resonance_pq
plain-language theorem explainer
Mercury-Sun spin-orbit resonance ratio is assigned the value 3/2. Researchers deriving tidal locking from the Recognition Science phi-ladder cite this constant when checking alignment with J(phi) on the phase manifold. The definition is a direct rational assignment.
Claim. The Mercury-Sun spin-orbit resonance ratio is $3/2$.
background
Recognition Science treats spin-orbit resonances as phi-rational minima of the J-cost on the phase manifold. The J-cost obeys the Recognition Composition Law J(xy) + J(x/y) = 2 J(x) J(y) + 2 J(x) + 2 J(y), with phi the self-similar fixed point where J(phi) equals 1. The upstream period definition supplies the phi-ladder via period(k) := phi^k.
proof idea
One-line definition that directly assigns the rational 3/2.
why it matters
This supplies the ratio for mercury_deviation_eq_J_phi, mercury_deviation_in_J_phi_band, and the TidalLockingFromPhiResonanceCert structure. It realizes the structural claim that inner-solar-system resonances sit within J(phi) of a phi-power, linking to T5 J-uniqueness and T6 phi fixed point in the forcing chain.
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