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Explain the Lean theorem `cosh_quadratic_lower_bound` in module `IndisputableMonolith.Cost`. 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 Lean source contains eight modules but does not include the module IndisputableMonolith.Cost or any declaration named cosh_quadratic_lower_bound. No theorem with that name or in that module appears verbatim in the provided source. The question therefore cannot be answered from the canon slice.

outside recognition

Aspects Recognition does not yet address:

  • The declaration `cosh_quadratic_lower_bound` in module `IndisputableMonolith.Cost`
  • Any content, dependencies, or certificates from the `IndisputableMonolith.Cost` 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.