IndisputableMonolith.Cost.Ndim.Uniqueness
The Cost.Ndim.Uniqueness module establishes that the N-dimensional reciprocal cost F factors through the weighted aggregate via a scalar profile G. Researchers extending the scalar J-cost to multi-component systems cite it for the uniqueness step. The module imports the core lifting definitions and derives the factorization from the scalar case via its sibling theorems.
claimThe N-dimensional cost function $F$ factors through the weighted log aggregate via some scalar profile $G$.
background
This module belongs to the Cost domain and imports IndisputableMonolith.Cost.Ndim.Core. The upstream module defines the multi-component reciprocal cost by lifting the scalar kernel through a weighted log aggregate. The uniqueness module then isolates the factorization property that any such $F$ must satisfy.
proof idea
This is a module collecting uniqueness results rather than a single proof. It organizes the factorization argument through its sibling declarations FactorsThrough, forced_of_scalar_uniqueness, and forced_of_factorization, each relying on the imported core definitions.
why it matters in Recognition Science
The module supplies the uniqueness foundation for the N-dimensional extension of the reciprocal cost. It supports higher-level results that apply the weighted aggregate in the Recognition Science framework, completing the step from scalar J-cost to the multi-component case.
scope and limits
- Does not define the underlying scalar J kernel or its functional equation.
- Does not treat time-dependent or dynamic cost extensions.
- Does not compute explicit values of G for particular dimension counts.