Topological invisibility in altermagnetic skyrmion magnonics.

In this work, we demonstrate a geometric selection rule for magnons in compensated altermagnetic skyrmions. In the leading circular- and exchange-domain-odd channel, the response probes the symmetric-traceless pullback metric of the Néel texture rather than skyrmion density. Calibrating the covariant derivative transfer isolates the local source UQ = QijGij, where Qij is the altermagnetic exchange quadrupole. A Belavin-Polyakov skyrmion is thus a conformal null: it carries finite winding and emergent flux while UQ vanishes pointwise. Smooth fixed-topology deformations break conformality and restore the response linearly, separating topology from geometric shear. Starting from a two-sublattice exchange model, we derive the gauge-covariant circular-magnon operator and establish the controlled long-wavelength/WKB hierarchy. Split-step propagation benchmarks the Born-eikonal reduction, while a lattice audit tests the continuum limit. The angular node and exchange/polarization sign reversals provide differential tests of real-space magnon quantum geometry.