Perovskite Spin-Structure Classifier

quick_mag/classify_spin_structure.py classifies common collinear perovskite B-site spin patterns from an existing B-site grid. It expects the caller to provide the perovskite site roles through PerovskiteSiteIndexing, preferably from site_indexing_from_perovskite_build(build) for generated structures or from the B-site matching workflow for imported structures.

Descriptors

sigma_a, sigma_b, sigma_c: average normalized spin dot product to the two periodic B-site neighbors along each pseudocubic axis.
axis_signs: snapped signs of each sigma, where +1 is ferromagnetic, -1 is antiferromagnetic, 0 is mixed, and None is unresolved.
kappa: 1 - mean(dot_ij ** 2) over resolved nearest-neighbor bonds. This is near zero for collinear states and grows for non-collinear states.
confidence: average closeness of resolved sigmas to their snapped targets.
notes: audit flags such as single-layer periodic axes or inactive B-site moments.

Rule Table

Label	Axis signs
`F`	`+ + +`
`G`	`- - -`
`A`	two `+`, one `-`
`C`	one `+`, two `-`
`E`	in-plane `a-b` plaquette has a `++--` rotation and `c` is single-layer constrained or ferromagnetically stacked
`CE`	`E` plus mixed oxidation-state variance when `site_oxidation_states` are supplied
`noncollinear`	no canonical match and large `kappa`
`canted`	collinear-like but intermediate axis sigmas
`unknown`	insufficient or ambiguous data