Structural Predictions of Magnetic Exchange Coupling Signs from Compact-Fiber Geometry

This paper develops a compact-fiber structural classification of magnetic exchange-coupling signs in selected local materials geometries. Starting from the finite compact-fiber carrier F ≅ Z/4Z × Z/4Z × Z/8Z, magnetic exchange pathways are treated as sector- and channel-readout problems.

The central result is a theorem-grade near-90° edge-sharing split/shared channel decomposition: the local geometry separates into a split σ channel and a shared-like π channel, carrying opposite half-filled exchange-sign tendencies. This recovers familiar Goodenough–Kanamori–Anderson sign behavior at the channel-topology level and identifies additional compact-fiber branch structure involving direct-exchange gates, magnetic-sector half-filling, bridge-Π efficiency, and mediator-pathway diagnostics.

The paper predicts and classifies exchange-coupling sign structure. It does not claim exchange magnitudes, ordering temperatures, propagation vectors, or complete magnetic phase diagrams. Empirical compounds are used as validation, boundary, and diagnostic cases for the structural readout framework.