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Altermagnetic symmetry breaks the optical silence of spin-forbidden dark excitons, generating symmetric exciton-magnon sidebands that directly track underlying spin correlations.
Quantum wavefunctions suffer from arbitrary phase redundancies that derail standard neural representations, but enforcing exact $U(1)$ gauge equivariance compresses DFT Bloch states into 64 dimensions with 97% reconstruction fidelity while inherently preserving topological invariants.
