Explain the Lean def `ode_regularity_differentiable_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.

The supplied source does not contain the declaration ode_regularity_differentiable_hypothesis (or its definition) in module IndisputableMonolith.Cost.FunctionalEquation. The provided code for that module is truncated and shows only earlier lemmas such as ode_diagonalization, deriv_neg_self_zero, and deriv_pos_self_zero. The AngleFunctionalEquation module (which imports from Cost.FunctionalEquation) defines parallel hypotheses with the _neg suffix for the cosine branch: ode_regularity_differentiable_hypothesis_neg, ode_regularity_continuous_hypothesis_neg, ode_linear_regularity_bootstrap_hypothesis_neg, and uses them in ode_cos_uniqueness and dAlembert_cos_solution. These package regularity assumptions (ODE implies continuity, then differentiability, then C²) to enable the uniqueness theorems without assuming full smoothness a priori. The positive-branch counterparts for the cosh/cost case are referenced conceptually as the structure being mirrored but are absent from the visible source.