Certified rational-anchor filtering for exact GPU scans of power-residue runs

We study exact longest monochromatic runs of power-residue colourings, including neutral prefixes and least canonical witnesses. A certified rational cover represents every relevant interval inside a short signed character table. A reflection-compatible schedule retains an anchor; conservative filters reject only known contradictions, bilateral completion recovers the full run, and tie-preserving reduction selects its least witness. We prove this exact-success contract and describe its CUDA realization with separate arithmetic domains below \(2^{32}\) and \(2^{33}\). On one RTX 5090, two reserved cohorts give ratios \(24.00\) and \(10.95\) of sums of hot per-prime medians against the identified historical dense engine. A separate batch study gives throughput factors \(1.23\)-\(2.58\) against an already optimized reference. The experiments have different timing boundaries and their factors are reported separately. Short-table multiplicative extraction has close algorithmic antecedents in cryptanalysis; our contribution is its certified organization for exhaustive maxima and witnesses and its measured implementation. Square-root-sized cover parameters do not give a general \(O(\sqrt p)\) running-time bound.