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Explain the Lean def `moon_resonance_pq` in module `IndisputableMonolith.Astrophysics.TidalLockingFromPhiResonance`. Write for an educated reader who knows science and programming but may not know Lean. Cover: (1) what the declaration says in plain English, (2) why it matters in Recognition Science, (3) how to read the formal statement, (4) visible dependencies or certificates in the supplied source, and (5) what this declaration does not prove. Cite only declarations present in the supplied Recognition source.

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The declaration moon_resonance_pq appears in module IndisputableMonolith.Astrophysics.TidalLockingFromPhiResonance inside a noncomputable section.

(1) In plain English it is a constant that sets the Moon-Earth spin-orbit resonance ratio to exactly 1 (one rotation per orbit, i.e., synchronous tidal locking).

(2) In Recognition Science it supplies the baseline trivial resonance whose J-cost is zero; the surrounding theorems then locate the Mercury 3:2 and Venus 4:1 ratios inside the canonical J(φ) band, showing that observed Solar-System resonances occupy φ-rational positions on the recognition lattice.

(3) The formal statement is simply def moon_resonance_pq : ℝ := 1. It is a non-computable definition of type whose value is the literal numeral 1; no computation or proof obligation is attached to the definition itself.

(4) Visible dependencies and certificates: the module imports IndisputableMonolith.Constants and IndisputableMonolith.Cost. The definition is immediately used by moon_resonance_eq (proved by rfl) and moon_J_cost_zero (proved via Cost.Jcost_unit0). It is also referenced inside the master certificate tidalLockingFromPhiResonanceCert and the one-statement summary tidal_locking_one_statement.

(5) The declaration itself does not prove the physical mechanism that produces the 1:1 lock, does not derive the integer 1 from the forcing chain or from J-cost minimisation, and does not address stability or tidal-evolution dynamics; those remain outside the supplied module.

cited recognition theorems

outside recognition

Aspects Recognition does not yet address:

  • Derivation of the numerical value 1 from the Universal Forcing chain or from first-principles J-cost minimisation
  • Physical tidal-evolution dynamics that realise the resonance

recognition modules consulted

The Recognition library is at github.com/jonwashburn/shape-of-logic. The model is restricted to the supplied Lean source and instructed not to invent theorem names. Treat output as a starting point, not a verified proof.