Эксперимент: Spectral-gap adaptive polynomial filtering (#535)

{ "worked": true, "confidence": 8, "verdict": "Built a readable toy MVP for Fejer and Jackson-type polynomial filtering on exact rotation spectra, including coefficient validation, explicit iterate equivalence, adaptive selection, and a 10% residual safeguard. The mechanism manifested: the critical residual matched 1/(K+1) to approximately 1e-6 or better, while fixed sK=8 produced nearly constant K^2sresidual around 3.4, consistent with O(1/(K^2 s)). The nominal sK=2 switch was too aggressive on this spectrum, but the safeguard rejected the approximately 1.45x degradation; Jackson became beneficial around sK=3.5 and was substantially better by sK=8.", "metrics": { "baseline": "Fejer critical residual*(K+1) = 0.9999998 mean, 0.9999999993 maximum; plain degree-K iteration residual ratio = 1.0 on the rotation-envelope measurement.", "idea": "Jackson fixed-sK=8 residualK^2s = 3.36, 3.41, 3.37, 3.39, 3.41 for K=7,15,31,63,127; at sK=8 it reduced residual by roughly 2.3x-2.5x versus Fejer. At sK=2 its residual was about 1.45x Fejer and was rejected by the 10% safeguard." }, "how_to_run": "/home/maxwelhelp/main/bin/python3 spectral_gap_filter.py", "files": [ "spectral_gap_filter.py", "results.json", "analyze.py", "report.json", "REPORT.md" ], "limitations": "Only synthetic diagonal rotation spectra were tested; no matrix-free Jacobian estimation, DEQ/recurrent model, CIFAR-10 task accuracy, wall-clock evaluation budget, Anderson baseline, noisy gap estimation, or nonlinear operator behavior was tested. The Jackson construction is a simple squared-Fejer polynomial approximation rather than a full paper-derived coefficient implementation." }