Parity fractions and multi-band plasma lensing of noncommutative regular Schwarzschild–AdS black holes: Theory and EHT compatibility

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We present photon propagation and gravitational lensing in a Regular Schwarzschild-Anti-de Sitter spacetime produced by a finite width Gaussian source inspired by noncommutative geometry, which removes the central singularity, yields a de Sitter-like core, and preserves AdS asymptotics. Within geometric optics we model uniform and radially stratified dispersive plasmas and track their impact on strong and weak field observables. In the strong field regime, stronger dispersion and larger |Λ| drive the photon sphere inward and shrink the shadow; mass effects at those radii are subleading. In the weak field regime we obtain analytic deflection laws: a uniform plasma acts as a global refractive rescaling, a singular isothermal sphere adds b − 2 and b − 3 terms, and a 1/ r profile yields a persistent b − 1 term degenerate with the vacuum 4 M / b , motivating multi-frequency constraints. Image observables ( θ E , μ tot , parity fractions) reflect these trends: plasma generally increases θ E and μ tot , whereas Λ < 0 mildly suppresses them, and parity helps break the mass plasma degeneracy. A comparison with Event Horizon Telescope size estimates for M87* and Sgr A* via the shadow deviation diagnostic reveals the parameter space compatible with current observations. The allowed plasma domains shrink for larger |Λ| and smaller M . Joint shadow-lensing analyses with multi-band data thus offer a practical test of noncommutative-geometry-inspired regular black holes in plasma-rich environments.