pith. sign in

Why is J(x) the unique reciprocal-symmetric cost?

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 modules contain no definition of J(x), no functional equation for cost, and no proof of uniqueness for any reciprocal-symmetric cost function. PreTemporalForcingOrder lists jCost as stage 6 in the forcing order (with theorems such as rcl_before_jCost and jCost_before_arithmetic) but provides only the ordering, not the explicit form or uniqueness. No other module derives or cites a cost functional equation. The question therefore lies outside the supplied canon slice.

outside recognition

Aspects Recognition does not yet address:

  • Definition or theorem establishing J(x) = (x + x^{-1})/2 - 1
  • Uniqueness proof for reciprocal-symmetric cost
  • Module IndisputableMonolith.Cost.FunctionalEquation or any equivalent

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.