Explain the Lean module `IndisputableMonolith.Cost.Ndim.Metric`. Write a module-level guide for a reader arriving from Pith. Cover the module's purpose, the main declarations, how it fits into the Recognition Science forcing chain or runtime, and what remains outside this module. Cite only declarations present in the supplied Recognition source.

The supplied Lean source slice does not contain the module IndisputableMonolith.Cost.Ndim.Metric. Because I can only cite declarations that appear verbatim in the provided text, I cannot write a guide covering the specific purpose, main declarations, or runtime fit of this exact module.

However, I can explain how the concept of cost fits into the Recognition Science (RS) framework based on the provided primer and the modules that are in the slice:

1. Core Cost Theorem: The wider framework establishes as a THEOREM that $J(x) = (x + x^{-1})/2 - 1$ is the unique reciprocal-symmetric cost function (t5_holds, via washburn_uniqueness_aczel in IndisputableMonolith.Cost.FunctionalEquation, which is not in this slice but referenced by AxiomDischargePlan).
2. Recognition Cost: In the supplied IndisputableMonolith.Foundation.RecognitionForcing module, the framework defines recognition_cost and proves as a THEOREM that non-trivial recognition events carry strictly positive cost while self-recognition has zero cost.
3. Analytic Foundations: The supplied IndisputableMonolith.Foundation.AxiomDischargePlan module provides the rigorous ODE-uniqueness proofs required to discharge the classical axioms underlying the Aczél–Kannappan classification of the d'Alembert functional equation, which formalizes the cost derivation.

To see the specific multi-dimensional metric declarations from Ndim.Metric, the source for that specific module would need to be included in the canon slice.