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Explain the Lean theorem `cosh_satisfies_continuous` 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: high outside recognition cached

The supplied source for module IndisputableMonolith.Cost.FunctionalEquation does not contain any declaration named cosh_satisfies_continuous. The module defines and proves several related statements about the J-cost function and d'Alembert-type functional equations (e.g., continuity results derived from log-curvature assumptions), but the exact name requested is absent. No theorem of that name can be explained from the provided canon slice.

outside recognition

Aspects Recognition does not yet address:

  • Declaration `cosh_satisfies_continuous` in IndisputableMonolith.Cost.FunctionalEquation

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.