IndisputableMonolith.Meta.Homogenization
This module supplies a local non-sealed metric interface for homogenization scaffolding atop the simplicial ledger. It bridges the coordinate-free sheaf representation of the ledger to the foundation summary certificate. The module consists of sibling definitions for metric tensors, determinants, densities and homogenization limits with no sealed proofs.
claimThe module introduces a metric tensor $g$ on a simplicial 3-complex together with its determinant and a homogenization limit $H$ in the coordinate-free sheaf setting.
background
The upstream SimplicialLedger module formalizes the ledger as a simplicial 3-complex rather than a coordinate-fixed cubic lattice. It supplies a coordinate-free sheaf representation that unifies local and global J-cost variations. The present meta module adds a non-sealed metric interface used by homogenization scaffolding.
proof idea
this is a definition module, no proofs
why it matters in Recognition Science
This module feeds the SimplicialFoundationSummary certificate that the ledger structure is moving toward a coordinate-free simplicial sheaf representation. It supplies the metric scaffolding layer required for homogenization steps in the Recognition framework.
scope and limits
- Does not seal any metric definitions or theorems.
- Does not import or use coordinate-fixed cubic lattices.
- Does not compute explicit numerical homogenization values.
- Does not contain proofs of J-cost unification.