IndisputableMonolith.Cost.Ndim.Uniqueness
The Cost.Ndim.Uniqueness module establishes that any N-dimensional reciprocal cost F factors through the weighted log aggregate by means of a scalar profile G. It extends the scalar kernel definitions to the multi-component setting while enforcing uniqueness of the factorization. Researchers extending the J-cost to higher dimensions cite this for consistent lifting. The module structure consists of the FactorsThrough definition together with the forced uniqueness theorems built directly on the Core import.
claimLet $F$ be the N-dimensional reciprocal cost. Then there exists a scalar profile $G$ such that $F$ factors through the weighted log aggregate.
background
The module imports IndisputableMonolith.Cost.Ndim.Core. The upstream doc-comment states that this core module defines the multi-component reciprocal cost by lifting the scalar kernel through a weighted log aggregate. The uniqueness module then adds the factorization property on top of that lifting. It introduces sibling objects FactorsThrough, forced_of_scalar_uniqueness, and forced_of_factorization to capture and enforce the required uniqueness.
proof idea
This is a definition module, no proofs.
why it matters in Recognition Science
The module supplies the uniqueness layer required for any consistent N-dimensional extension of the reciprocal cost. It supports the Recognition Composition Law by guaranteeing that the weighted aggregate is the only route through which F can be expressed. No downstream uses are recorded, so the module functions as a self-contained closure for the factorization question in the Ndim setting.
scope and limits
- Does not construct explicit forms for the scalar profile G.
- Does not treat time-dependent or non-reciprocal costs.
- Does not derive numerical bounds or connect to the phi-ladder.
- Does not address dimensions outside the N-dimensional case.