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Explain the Lean theorem `dAlembert_cosh_solution` 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 for module IndisputableMonolith.Cost.FunctionalEquation does not contain any declaration named dAlembert_cosh_solution. The module defines and proves several related lemmas on d'Alembert's functional equation (e.g., dAlembert_even, dAlembert_double, dAlembert_product, dAlembert_diff_square, dAlembert_continuous_of_log_curvature, and Jcost_cosh_add_identity), along with supporting infrastructure for the J-cost uniqueness proof. No theorem with the requested name appears verbatim. Therefore the requested explanation cannot be produced from the canon slice.

outside recognition

Aspects Recognition does not yet address:

  • Declaration `dAlembert_cosh_solution` (or any theorem of that exact name) in `IndisputableMonolith.Cost.FunctionalEquation`
  • Any direct statement or proof of a cosh solution to the d'Alembert equation under the name `dAlembert_cosh_solution`

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.