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Explain the Lean theorem `reciprocal_comp_reciprocal` in module `IndisputableMonolith.Algebra.CostAlgebra`. 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: high outside recognition cached

The supplied source for module IndisputableMonolith.Algebra.CostAlgebra does not contain any declaration named reciprocal_comp_reciprocal. Visible content in this module includes the J-cost definition, theorems such as J_reciprocal, J_at_one, RCL_holds, costCompose_comm, costCompose_assoc_defect, H_dAlembert, defectDist_symm, and structures for the shifted monoid on [1/2, ∞). No theorem with the requested name appears verbatim. As a result, none of the requested explanations (plain-English meaning, RS relevance, formal-statement reading, dependencies, or unproved aspects) can be provided from the canon for this specific declaration.

outside recognition

Aspects Recognition does not yet address:

  • declaration `reciprocal_comp_reciprocal` in IndisputableMonolith.Algebra.CostAlgebra

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.