IndisputableMonolith.Cost.Ndim.DAlembert
This module extends the N-dimensional reciprocal cost framework by defining d'Alembert variants of the J-cost. Researchers modeling multi-component wave propagation or higher-dimensional cost minimization in Recognition Science would cite these definitions. The module consists of targeted definitions that lift the scalar kernel from the imported Core module without introducing new theorems.
claimIntroduces the N-dimensional d'Alembert cost $J_{cost,N}^{d'Alembert}$ and the submultiplicative variant $J_{cost,N}^{submult}$, obtained by lifting the scalar kernel $J(x)=(x+x^{-1})/2-1$ through a weighted log aggregate in $N$ dimensions.
background
The module resides in the Cost domain and imports IndisputableMonolith.Cost.Ndim.Core. That core module defines the multi-component reciprocal cost by lifting the scalar kernel through a weighted log aggregate, providing the base for N-dimensional extensions. The d'Alembert construction adds the second-order wave operator structure, aligning with the framework's eight-tick octave and spatial dimension D=3.
proof idea
This is a definition module, no proofs.
why it matters in Recognition Science
These definitions supply the N-dimensional cost objects required by the Recognition Composition Law and feed the parent cost hierarchy that supports mass formulas on the phi-ladder. They close the lifting step from scalar J to multi-component costs used in downstream calculations of constants such as alpha and G.
scope and limits
- Does not contain any theorems or proofs.
- Does not specify numerical values for N or explicit examples.
- Does not derive connections to the phi-ladder mass formula or Berry threshold.