Explain the Lean theorem `hasDerivAt_Jcost` 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 source contains no module IndisputableMonolith.Cost and no declaration hasDerivAt_Jcost. Imported references appear in IndisputableMonolith.Mathematics.LanglandsFromRecognitionCost (which uses Jcost and Jcost_symm) and IndisputableMonolith.Foundation.RecognitionForcing (which uses LedgerForcing.J), but these modules supply only symmetry and positivity facts, not differentiability. (1) No plain-English statement of the declaration exists here. (2) No RS-specific role for differentiability of J-cost can be extracted. (3) No formal statement is available to parse. (4) Visible dependencies are limited to the imported Jcost_symm and positivity lemmas already present; no certificates for derivatives appear. (5) The declaration is absent, so it proves nothing within this slice. The question therefore lies outside the provided canon slice.