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.
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.
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outside recognition
- The declaration `cosh_quadratic_lower_bound` in module `IndisputableMonolith.Cost`
- Any content, dependencies, or certificates from the `IndisputableMonolith.Cost` module
recognition modules consulted
IndisputableMonolith.Foundation.AlexanderDualityIndisputableMonolith.Mathematics.LanglandsFromRecognitionCostIndisputableMonolith.Foundation.RealityFromDistinctionIndisputableMonolith.Measurement.RSNative.Calibration.SingleAnchorIndisputableMonolith.Unification.RecognitionBandGeometryIndisputableMonolith.Unification.RecognitionBandwidthIndisputableMonolith.Foundation.RecognitionForcingIndisputableMonolith.Meta.ConstructiveNote