Logical operations

conjugate periodic plane Pauli pair for odd L transversal verified

Level: logical Pauli · Cost: one parallel physical-Pauli layer on a constructor-derived periodic plane; the displayed X and Z representatives each have area scaling and anticommute for odd L, while special even periods require a separately tracked logical basis

boundary creation, condensation, and defect manipulation switching claimed

Level: geometry-changing code operation · Cost: replace the periodic block by a boundary or defect geometry, specify which excitations condense, measure the changed checks, decode the transition, and track the resulting logical frame

References: aitchison2023boundaries

ungauging to a fractal-symmetry model switching claimed

Level: representation and phase transformation · Cost: introduce the ungauging constraints and change the model's degrees of freedom and symmetry description; this is not a universal gate on the original fixed periodic code block

References: williamson2016fractal