pith. sign in

Explain the Lean def `mercury_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.

Big AI job. Grok 4.3 reads the canon and writes a Lean-grounded derivation; usually 20 seconds to 2 minutes. Your answer will appear below.
confidence: low outside recognition cached

The supplied Lean source does not contain the module IndisputableMonolith.Astrophysics.TidalLockingFromPhiResonance or any declaration named mercury_resonance_pq. No formal statement, dependencies, or certificates for this definition are present. The source includes related material on phi forcing and resonances in other modules (e.g., self-similar ratios and phi-harmonics), but the specific astrophysics definition is absent. This prevents any direct explanation or citation from the canon.

outside recognition

Aspects Recognition does not yet address:

  • The definition mercury_resonance_pq
  • The module IndisputableMonolith.Astrophysics.TidalLockingFromPhiResonance
  • Any theorems or dependencies specific to tidal locking from phi 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.