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Local shattering, global growth, Sauer deletion and conditional pair-swapping are distinct objects. Statistical bounds state their ghost-sample conditions and are sufficient bounds, not observed errors or minimax 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finite restriction families on integer points; each affine label has an integer strict-separator or Radon obstruction certificate. Local shattering, global growth, Sauer deletion and conditional pair-swapping are distinct objects. 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finite restriction families on integer points; each affine label has an integer strict-separator or Radon obstruction certificate. Local shattering, global growth, Sauer deletion and conditional pair-swapping are distinct objects. Statistical bounds state their ghost-sample conditions and are sufficient bounds, not observed errors or minimax claims."}}]}