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Explain the Lean lemma `Jcost_prod_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 does not contain the module IndisputableMonolith.Cost or any declaration named Jcost_prod_bound. Modules such as IndisputableMonolith.Mathematics.LanglandsFromRecognitionCost import IndisputableMonolith.Cost and reference Jcost and Jcost_symm, but the actual definitions, lemmas, or proofs from the Cost module are absent. No material bearing on Jcost_prod_bound is present, so the requested explanation (plain-English meaning, RS relevance, formal reading, dependencies, and limitations) cannot be produced from the canon.

outside recognition

Aspects Recognition does not yet address:

  • The lemma Jcost_prod_bound
  • Any formal statement or proof of Jcost_prod_bound
  • Dependencies or certificates specific to the 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.