perf(row-reduce): complete Phase 4 evidence - #9865
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August 31, 2026 04:46
Cost-model derivation: fixed-aspect Gauss-Jordan visits cubic matrix work; prepared span operations traverse quadratic data; prepared nullspace construction materializes quadratic output while linearly scanning pivot columns, giving cubic work. Add exact-hash informational fmpq_mat RREF and canonical-nullspace anchors.
Promote HexRowReduce through Phase 4 with clean scientific, comparator, and profile evidence for every advertised executable operation.
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Cost-model derivation: echelonCoeffs constructs n output entries in linear work; freeCols tests n columns against n/2 sorted pivots in quadratic work. Their controlled ladders stop below the runtime allocation transitions.
Cost-model derivation: echelonCoeffs constructs n output entries in linear work; freeCols tests n columns against n/2 sorted pivots in quadratic work. Their controlled ladders stop below the runtime allocation transitions.
kim-em
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Closing after premise validation found asymptotic implementation gaps that make the proposed Phase-4 claims unsound. The concrete source and measurement evidence is recorded on #9811. This PR must not merge by weakening the models or tolerances. |
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Summary
Complexity contract
All ten direct registrations use the strongest ordered evidence mode. The public RREF, rank, span, and nullspace wrappers declare cubic fixed-aspect Gauss--Jordan cost; prepared echelon span queries declare quadratic matrix--vector work; prepared reduced-nullspace construction declares the documented cubic loose bound while profiling separates it from elimination. These models and input dimensions match the HexRowReduce SPEC, and each registration passes the mode-1 normalized-constant/slope checks.
Verification
lake build(10,506 jobs)lake build hexrowreduce_bench.lake/build/bin/hexrowreduce_bench verify(39/39)python3 scripts/check_phase4.pyCloses #9811