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.
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.
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- 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
IndisputableMonolith.Foundation.AlexanderDualityIndisputableMonolith.Mathematics.LanglandsFromRecognitionCostIndisputableMonolith.Foundation.RealityFromDistinctionIndisputableMonolith.Measurement.RSNative.Calibration.SingleAnchorIndisputableMonolith.Unification.RecognitionBandGeometryIndisputableMonolith.Unification.RecognitionBandwidthIndisputableMonolith.Cost.AczelClassIndisputableMonolith.Cost.FunctionalEquation