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The real crossStep uses PhaseVec.add (additive doubling: zᵢⱼ = zᵢ + zⱼ), which grows until Q16_16 saturation. ContractedCrossStep fixes this by replacing the merge with φ⁻¹ · (half · (p + q)), which contracts on the diagonal: merge(z,z) = φ⁻¹ · z (exact under non-saturation). Key results: - half_mul_add_self_non_sat: half * (a + a) = a (exact Q16_16 identity when a + a doesn't overflow) - contractedPhaseMerge_diagonal_non_sat: merge contracts by φ⁻¹ - Jitter also contracted by φ⁻¹ to prevent saturation - #eval witnesses confirm φ⁻¹ contraction and zero-state fixedness Convergence theorems stated with proof sketches; full proofs require Q16_16 inequality lemmas and well-founded induction (TODO). Build: 3309 jobs, 0 errors |
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