IndisputableMonolith.Meta.Homogenization
The Meta.Homogenization module supplies a local non-sealed metric interface for homogenization scaffolding on the simplicial ledger. Researchers extending coordinate-free sheaf models of the ledger topology would cite it when adding metric limits to J-cost unification. The module contains only definitions for tensors, densities, and limit objects with no theorems or proofs.
claimThe module defines the metric tensor $g$ on the simplicial 3-complex together with its determinant, the simplicial density function, and the homogenization limit operator $H$ used for local metric scaffolding.
background
The module sits inside the Recognition Science meta layer and imports the simplicial ledger topology. That upstream module formalizes the ledger as a simplicial 3-complex rather than a coordinate-fixed cubic lattice and supplies a coordinate-free sheaf representation that unifies local and global J-cost variations.
proof idea
This is a definition module, no proofs. It declares the metric interface objects (MetricTensor, metric_det, SimplicialDensity, H_HomogenizationLimit, homogenization_limit) that downstream modules apply directly.
why it matters in Recognition Science
The module feeds the SimplicialFoundationSummary certificate, which records progress toward a coordinate-free simplicial sheaf representation of the ledger. It supplies the local metric scaffolding required for homogenization steps in the meta layer while remaining unsealed.
scope and limits
- Does not seal the metric globally.
- Does not contain any theorems or proofs.
- Does not construct the underlying simplicial complex.
- Does not reference the forcing chain or phi-ladder constants.