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Replicates the codec cross-runtime KAT pattern across the rest of the math substrate. Each package now ships: * kat.go — KATEntry/KATBundle aliases pointing at codec.KATEntry/ codec.KATBundle (one schema for the whole substrate). * cmd/emit_*_kat/main.go — Go-side emitter that produces the canonical bundle. * kat_test.go — Go replay test (TestKATBundle_RoundTrip*). * testdata/*_kat.json — emitted bundle, byte-stable across runs. modarith/cmd/emit_modarith_kat: ~300 entries - 100 MontMulMod cross-checked against MulMod - 100 AddMod across deterministic random pairs - 100 MontgomeryRoundTrip (ToMontgomery -> FromMontgomery) - Multiple moduli (PulsarQ, NTT998). ntt/cmd/emit_ntt_kat: ~50 entries - input: 256 random uint64 mod PulsarQ - output: NTT(input) byte-stream + SHA-256 commitment - Pulsar N=256 ring. sample/cmd/emit_sample_kat: ~30 entries - Uniform / Ternary / CenteredBinomial across param sweeps - Each entry records the seed + first 64 sampled values. Tests: GOWORK=off go test ./modarith/ ./ntt/ ./sample/ -> all PASS. C++ replay tests follow in luxcpp/crypto commit on this same branch.