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Explain the Lean theorem `ode_regularity_continuous_of_smooth` 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 contains the module IndisputableMonolith.Cost.FunctionalEquation with lemmas including ode_diagonalization, deriv_neg_self_zero, deriv_pos_self_zero, dAlembert_continuous_of_log_curvature, and Jcost_cosh_add_identity, but does not contain any declaration named ode_regularity_continuous_of_smooth. The question therefore cannot be answered from the canon slice.

outside recognition

Aspects Recognition does not yet address:

  • ode_regularity_continuous_of_smooth

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.