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Explain the Lean def `symmetric_second_diff_limit_hypothesis` 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 declaration symmetric_second_diff_limit_hypothesis does not appear verbatim in the supplied source for module IndisputableMonolith.Cost.FunctionalEquation (or any other supplied module). The supplied source for this module contains definitions and theorems such as HasLogCurvature, dAlembert_continuous_of_log_curvature, CoshAddIdentity, Jcost_G_eq_cosh_sub_one, even_deriv_at_zero, and related lemmas on d'Alembert identities and ODE uniqueness, but not the requested declaration. No material in the canon addresses this specific definition.

outside recognition

Aspects Recognition does not yet address:

  • symmetric_second_diff_limit_hypothesis 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.