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Explain the Lean def `ode_regularity_continuous_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_regularity_continuous_hypothesis (without the _neg suffix) in module IndisputableMonolith.Cost.FunctionalEquation. The provided slice of IndisputableMonolith.Cost.FunctionalEquation is truncated and contains no such definition. A closely analogous declaration ode_regularity_continuous_hypothesis_neg appears in IndisputableMonolith.Measurement.RecognitionAngle.AngleFunctionalEquation and is used to package the assumption that a continuous solution to the ODE H'' = -H satisfies the regularity needed for uniqueness proofs. This declaration is a hypothesis (not a theorem) and does not prove any result by itself; it is consumed as an input by ode_cos_uniqueness and dAlembert_cos_solution.

outside recognition

Aspects Recognition does not yet address:

  • Exact declaration `ode_regularity_continuous_hypothesis` in `IndisputableMonolith.Cost.FunctionalEquation`
  • Any positive-branch counterpart in the truncated Cost.FunctionalEquation module

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.