Meaning
A finite-window zero-cost normalizer is an internal unitary change that preserves all the declared comparison data on that window.
It preserves source and destination corners, the canonical marking algebra, physical graph data, and every spatial and refinement face map. Comparisons related by its action count as zero-cost equivalent in the stated comparison problem.
Example (illustrative)
If a common scalar phase preserves every corner, marking, graph datum, and face map in a particular window, it is an elementary candidate for such a normalization. A unitary swapping distinct fixed branch labels is not allowed merely because it preserves norms.
Scope and limits
“Zero cost” refers to the declared comparison equivalence. It is not permission to discard sector labels or arbitrary physical distinctions.
Source
GAT I — Grassmannian Gluing, Spectral Trichotomy, and Conditional Sectorial Type II. GAT I, Definition 5.67.