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Explain the Lean def `IsCalibrated` 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 and lemmas such as G, H, CoshAddIdentity, DirectCoshAdd, Jcost_G_eq_cosh_sub_one, Jcost_cosh_add_identity, even_deriv_at_zero, dAlembert_even, dAlembert_double, dAlembert_product, dAlembert_diff_square, HasLogCurvature, sub_one_eq_mul_ratio, tendsto_H_one_of_log_curvature, dAlembert_continuous_of_log_curvature, deriv_exp_neg, ode_diagonalization, deriv_neg_self_zero, and deriv_pos_self_zero. No declaration named IsCalibrated appears in the provided text for this module or any other module in the source. The module focuses on functional equation helpers for T5 cost uniqueness, including reparametrizations and d'Alembert identities, but does not define or reference IsCalibrated.

outside recognition

Aspects Recognition does not yet address:

  • The Lean definition `IsCalibrated`
  • Any explanation of its plain English meaning, role in Recognition Science, formal reading, dependencies, or what it 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.