recognition › ask › explain-the-lean-theorem-cos-satisfies-regularity-in-module-00d475d0

Explain the Lean theorem `cos_satisfies_regularity` in module `IndisputableMonolith.Measurement.RecognitionAngle.AngleFunctionalEquation`. 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.

permalink: https://pith.science/recognition/ask/explain-the-lean-theorem-cos-satisfies-regularity-in-module-00d475d0 · first asked 2026-05-10 · browse all asks

confidence: low outside recognition cached

The supplied source contains the module IndisputableMonolith.Measurement.RecognitionAngle.AngleFunctionalEquation, which includes theorems establishing that cosine satisfies various regularity hypotheses for the negative branch of the d'Alembert functional equation (e.g., continuity, differentiability, and bootstrap to C²). However, the exact declaration cos_satisfies_regularity does not appear verbatim anywhere in the provided Lean modules. No formal statement, dependencies, or proof for this specific name can be extracted from the canon.

outside recognition

Aspects Recognition does not yet address:

The declaration cos_satisfies_regularity
Its formal statement in Lean
Any direct proof or certificate for this named theorem

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.