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Explain the Lean def `ode_linear_regularity_bootstrap_hypothesis` 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 does not contain the declaration ode_linear_regularity_bootstrap_hypothesis (or any verbatim match) inside module IndisputableMonolith.Cost.FunctionalEquation. That module supplies ODE infrastructure such as ode_diagonalization, deriv_pos_self_zero and deriv_neg_self_zero for the cosh branch, but the named regularity-bootstrap hypothesis appears only in the parallel negative (cosine) branch as ode_linear_regularity_bootstrap_hypothesis_neg inside IndisputableMonolith.Measurement.RecognitionAngle.AngleFunctionalEquation.

outside recognition

Aspects Recognition does not yet address:

  • Exact declaration ode_linear_regularity_bootstrap_hypothesis in IndisputableMonolith.Cost.FunctionalEquation
  • Its formal statement and any certificates attached to the positive (cosh) branch

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.