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Explain the Lean def `IsReciprocalCost` 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 contains definitions including G, H, CoshAddIdentity, DirectCoshAdd, HasLogCurvature and theorems such as Jcost_G_eq_cosh_sub_one, Jcost_cosh_add_identity, G_even_of_reciprocal_symmetry, even_deriv_at_zero, dAlembert_even, dAlembert_double, dAlembert_product, dAlembert_diff_square, tendsto_H_one_of_log_curvature, dAlembert_continuous_of_log_curvature, ode_diagonalization, deriv_neg_self_zero, and deriv_pos_self_zero. These establish properties of the J-cost function, reciprocal symmetry lemmas, d'Alembert functional equations, and ODE uniqueness infrastructure. However, the declaration IsReciprocalCost is not present in the supplied text for this module or any other module in the canon source. The question cannot be answered from the canon because the specific definition is absent.

outside recognition

Aspects Recognition does not yet address:

  • The Lean definition IsReciprocalCost
  • Its plain English interpretation
  • Its role in Recognition Science
  • How to read its formal statement
  • Visible dependencies or certificates for IsReciprocalCost
  • What IsReciprocalCost does not prove

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.