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Explain the Lean theorem `reciprocal_implies_G_even` in module `IndisputableMonolith.Cost.FunctionalEquation`. 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 source does not contain any declaration named reciprocal_implies_G_even (or any theorem with that exact name) in module IndisputableMonolith.Cost.FunctionalEquation. The module contains a closely related lemma G_even_of_reciprocal_symmetry that establishes evenness of the reparametrized function G under reciprocal symmetry of F, but the query asks specifically for the named declaration reciprocal_implies_G_even, which is absent. No other module in the provided source defines or references a declaration by that name.

outside recognition

Aspects Recognition does not yet address:

  • The exact declaration name `reciprocal_implies_G_even`
  • Any direct explanation or proof of a theorem bearing that precise name

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.