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Explain the Lean theorem `ode_regularity_bootstrap_of_smooth` 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 contains module IndisputableMonolith.Cost.FunctionalEquation with supporting material for T5 (J-cost uniqueness), including definitions of G, H, CoshAddIdentity, DirectCoshAdd, lemmas such as G_even_of_reciprocal_symmetry, Jcost_G_eq_cosh_sub_one, Jcost_cosh_add_identity, even_deriv_at_zero, dAlembert_even, dAlembert_double, dAlembert_product, dAlembert_diff_square, HasLogCurvature, dAlembert_continuous_of_log_curvature, ode_diagonalization, deriv_neg_self_zero, and deriv_pos_self_zero. However, the declaration ode_regularity_bootstrap_of_smooth is absent from the provided code. No formal statement, proof, or explanation of this specific theorem can be extracted from the canon slice.

outside recognition

Aspects Recognition does not yet address:

  • ode_regularity_bootstrap_of_smooth 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.