Repaired exact-rational defect checker

justification. Every real endpoint is rounded outward using exact integer floor or ceiling. Mixed complex arithmetic is implemented by rectangular promotion. Elementary functions use the rational remainder bounds stated in Section sec:defect. Validation cells refine the original piecewise-linear grid, so endpoint extrema enclose each interpolant component on each cell.

Theorems thm:cell and thm:defect justify the bound-producing algorithm. Integer square roots include endpoint-modulus uncertainty. Startup self-tests address dispatch and selected exact identities, not completeness of a formal software verification.

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