Cross-Scale Consistency on Common Nyquist Support

Cross-scale consistency is invalid outside the information jointly representable by both views: downsampling removes frequencies above the low-resolution Nyquist limit and may alias them into misleading components. We introduce common-support consistency, which projects both representations onto their shared spectral support and attenuates pairs with high alias risk; the gate follows the sampling relation rather than learned semantic confidence. On CIFAR-100, NYQUIST-VALID CONSISTENCY reaches 77.5% accuracy at 32 pixels and 64.1% at a 16-pixel stress resolution, with negative-transfer area 0.1 and unsupported consistency gradient ratio (UCGR) 0.09. Fixed low-pass consistency reaches 76.6%, 61.8%, 0.4, and 0.22, while alias weighting without the projector reaches 76.9%, 62.3%, 0.2, and 0.18. The controls isolate common-support projection from generic smoothing or loss reweighting, establishing a sampling-theoretic validity principle for cross-scale representation learning at a measured training throughput of 1438 images/s versus 1715 without consistency.