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Explain the Lean lemma `cosh_minus_one_eq` 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 canon source does not contain the module IndisputableMonolith.Cost or any declaration named cosh_minus_one_eq. No Lean source for that module is provided, so the requested explanation of its formal statement, dependencies, or role cannot be given from the canon. The question asks specifically for an explanation of a lemma in a module absent from the supplied Recognition source.

outside recognition

Aspects Recognition does not yet address:

  • Module IndisputableMonolith.Cost
  • Declaration cosh_minus_one_eq
  • Any formal statement, proof, or dependencies for cosh_minus_one_eq

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.