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Explain the Lean lemma `Jcost_zero_iff_one` 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 source does not contain module IndisputableMonolith.Cost or any declaration named Jcost_zero_iff_one. The question therefore cannot be answered from the canon. Related but distinct material on cost-zero conditions appears in other modules (e.g., self_recognition_zero_cost and recognition_is_cost_structure in IndisputableMonolith.Foundation.RecognitionForcing, which use LedgerForcing.J and establish that ratio = 1 iff cost = 0 for RecognitionEvent). These are not the requested declaration and reside in a different module.

outside recognition

Aspects Recognition does not yet address:

  • Module IndisputableMonolith.Cost
  • Declaration Jcost_zero_iff_one

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.