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Explain the Lean lemma `Jcost_submult` 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 the declaration Jcost_submult. Modules that import Cost (LanglandsFromRecognitionCost, RecognitionBandwidth) reference related cost concepts such as Jcost but provide no definitions, statements, or proofs of Jcost_submult. The question specifically requests an explanation of that lemma, which is absent from the canon slice.

outside recognition

Aspects Recognition does not yet address:

  • The lemma Jcost_submult in module IndisputableMonolith.Cost
  • Any submultiplicativity or related properties of Jcost

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.