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Explain the Lean theorem `washburn_uniqueness_aczel` in module `IndisputableMonolith.Cost.FunctionalEquation`. 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 the declaration washburn_uniqueness_aczel (or any theorem by that name) in module IndisputableMonolith.Cost.FunctionalEquation. The module supplies supporting lemmas and theorems for the T5 cost-uniqueness argument, including Jcost_G_eq_cosh_sub_one, Jcost_cosh_add_identity, dAlembert_continuous_of_log_curvature, even_deriv_at_zero, and several d'Alembert functional-equation helpers such as dAlembert_even and dAlembert_double. These establish that the J-cost satisfies the cosh-add identity and that continuous solutions to the associated d'Alembert equation are smooth. The specific uniqueness theorem referenced in docstrings of other modules (e.g., LogicAsFunctionalEquation) is absent from this slice.

outside recognition

Aspects Recognition does not yet address:

  • washburn_uniqueness_aczel declaration and its proof
  • Full Aczél-based classification that isolates J(x) = (x + x⁻¹)/2 − 1 as the unique continuous reciprocal-symmetric cost

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.