Explain the Lean theorem `agree_on_exp_extends` 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.

The supplied Lean source does not contain module IndisputableMonolith.Cost or any declaration named agree_on_exp_extends. The question asks for an explanation of a specific theorem in that module, but no such module or theorem appears in the provided canon slice (only an import of IndisputableMonolith.Cost occurs in IndisputableMonolith.Mathematics.LanglandsFromRecognitionCost, with no definitions or theorems from it exposed). Therefore the canon does not support answering the five requested points about this declaration. Visible modules instead cover topics such as Alexander duality for D=3, recognition bandwidth, reality-from-distinction forcing chains, and computability notes, but none address exponential extensions or agreement lemmas in a Cost context.