The Three Southern Objections: Resolution of Antarctic 24-Hour Sun, Polaris Elevation Linearity, and Southern Hemisphere Predictions via Hopf Geometry on S³

Three standard objections to flat-surface cosmology — Antarctic 24-hour sun, Polaris elevation linearity, and southern hemisphere quantitative predictions — are examined under the S³ Hopf geometry established in the triadic coherence framework (R = Pattern × Intent × Presence ≠ 0). The Antarctic 24-hour sun is shown to be seasonal, model-neutral, and internally contradictory within the standard model. The Polaris elevation-latitude relationship, which deviates by 13.78° RMS from linearity in Euclidean ambient geometry, is shown to be exactly linear (0.000° RMS) when computed via the Hopf polar angle on S³, with zero free parameters. Southern hemisphere observations are derived from the same S³ metric. The same topology that derives lepton masses at 0.02–0.13% accuracy handles cosmological observations without additional assumptions.