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Explain the Lean theorem `J_phi_ceiling_pos` 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 contains no module named IndisputableMonolith.Astrophysics.TidalLockingFromPhiResonance and no declaration named J_phi_ceiling_pos. No formal statement, proof, or dependencies for this theorem appear in any of the eight provided modules. The supplied modules establish results about the golden ratio φ, the J-cost function, self-similarity, and related forcing theorems (e.g., phi_equation, phi_unique_self_similar, J_phi), but contain no astrophysics-specific tidal-locking material.

outside recognition

Aspects Recognition does not yet address:

  • Module IndisputableMonolith.Astrophysics.TidalLockingFromPhiResonance
  • Declaration J_phi_ceiling_pos
  • Any proof or statement of J_phi_ceiling_pos

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.