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Explain the Lean theorem `cosh_second_deriv_eq` 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_second_deriv_eq. The module defines helpers such as G, H, CoshAddIdentity, DirectCoshAdd, Jcost_G_eq_cosh_sub_one, Jcost_cosh_add_identity, dAlembert_even, dAlembert_double, dAlembert_product, dAlembert_diff_square, HasLogCurvature, and several ODE lemmas (ode_diagonalization, deriv_neg_self_zero, deriv_pos_self_zero), but the requested theorem is absent. No material in the provided slice directly addresses or defines cosh_second_deriv_eq.

outside recognition

Aspects Recognition does not yet address:

  • declaration cosh_second_deriv_eq 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.