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Explain the Lean theorem `cosh_satisfies_differentiable` 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 cosh_satisfies_differentiable. The module defines related results including Jcost_G_eq_cosh_sub_one (equating the reparametrized J-cost function to cosh(t) - 1), Jcost_cosh_add_identity (the cosh-add functional equation), dAlembert_even, dAlembert_double, dAlembert_product, dAlembert_diff_square, dAlembert_continuous_of_log_curvature, and even_deriv_at_zero, along with infrastructure for ODE uniqueness and log-curvature conditions. It also imports and uses AczelSmoothnessPackage from IndisputableMonolith.Cost.AczelClass (with theorem aczel_dAlembert_smooth). The requested declaration is absent.

outside recognition

Aspects Recognition does not yet address:

  • cosh_satisfies_differentiable declaration 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.