The pipeline runs SLOS (K=2) to compute ONE number (Omega) from the
full M_n-state distribution. The other 4 queries (Sidon check, GCCL
gate, QR rank, collision count) don't need SLOS at all — they use
integer arithmetic or eigenvalue decomposition.
The shortcut: skip SLOS for 4/5 queries. 5x speedup from not running
expensive quantum simulations for queries that only need O(n²) or O(n³)
classical computation.
The Omega computation itself still needs full SLOS (K=2). The K=2
interference pattern IS the irreducible residual — the part the K=1
spectrum can't predict. Conservation law: spectrum (model) + K=2
interference (residual) = full distribution. Can't predict Omega from
spectrum alone.
This is the honest quantum advantage: SLOS computes something the
spectrum can't recover. Not quantum speedup — information content.
The K=2 correlations are fundamentally denser than the K=1 spectrum.
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