IndisputableMonolith.Cost.Ndim.Connections
This module defines the Kronecker delta on Fin n together with flat and pulled connection structures that extend the N-dimensional reciprocal cost. Researchers extending the scalar cost kernel to multi-index settings would cite these objects. The module contains only definitions and no proofs.
claimThe Kronecker delta $\delta_{ij}$ on the finite index set $\mathrm{Fin}\,n$, together with the flat connection on the $x$-component and the pulled connection on the $t$-component of the weighted log-aggregate cost.
background
The imported Core module defines the multi-component reciprocal cost by lifting the scalar kernel through a weighted log aggregate. The present module adds the standard basis object (Kronecker delta on Fin n) and the auxiliary connection maps needed to handle projective equivalence and diagonal/off-diagonal components in that aggregate.
The local theoretical setting is the cost domain, where these structures prepare the ground for N-dimensional extensions of the J-cost without yet invoking the phi-ladder or the forcing chain.
proof idea
this is a definition module, no proofs
why it matters in Recognition Science
Supplies the connection and delta objects required by any parent theorem that lifts the scalar reciprocal cost to N dimensions. It fills the geometric layer between the Core kernel and later multi-component calculations in the cost domain, even though no downstream uses are yet recorded.
scope and limits
- Does not contain any theorems or proofs.
- Does not define the underlying scalar J-cost kernel.
- Does not reference the phi-ladder, forcing chain, or Recognition constants.
- Does not treat projective equivalence beyond the listed connection maps.