IndisputableMonolith.Cost.Ndim.Bridge
The Cost.Ndim.Bridge module supplies quadratic approximations to the N-dimensional reciprocal cost. It defines additive, multiplicative, and compensatory forms that approximate the lifted scalar kernel for small defects. Researchers extending Recognition Science cost models to multiple dimensions cite these when analyzing the J-cost expansion. The module achieves its purpose through direct definitions that import and build on the core weighted log aggregate.
claimQuadratic additive approximation to the N-dimensional reciprocal cost: $1/2 sum_i epsilon_i^2$.
background
This module resides in the Cost domain and extends the scalar J-cost to N dimensions. It imports the core module, which defines the multi-component reciprocal cost by lifting the scalar kernel through a weighted log aggregate, as stated in the upstream documentation.
proof idea
This is a definition module, no proofs. It organizes the content as a collection of direct definitions for the quadratic forms, drawing the underlying cost structure from the imported core module.
why it matters in Recognition Science
This module supplies the quadratic bridge needed for N-dimensional cost analysis in the Recognition framework. It supports the broader development of cost decompositions that connect to the forcing chain steps T5 through T8 and the phi-ladder mass formulas.
scope and limits
- Does not prove error bounds on the quadratic approximation.
- Does not treat non-quadratic terms or higher-order expansions.
- Does not fix a specific value for the dimension N.