Эксперимент: Dilation-Matched Metropolized Dynamics (#967)

{ "worked": true, "confidence": 8, "verdict": "Built a scalar dilation-matched kick-drift-kick sampler with exact Metropolis correction and numerical checks. Closure error stayed below 6.5e-9; the classical derivative grew geometrically while the quotient remained bounded, and fixed-step acceptance stayed high for the quotient but collapsed for classical dynamics at high resolution. This demonstrates a real stability signal, but not a fully validated sampling-quality improvement because short-chain quotient posterior means and ESS were unstable.", "metrics": { "baseline": "Classical derivative max magnitude: 6.28 at N=0, 1.19e4 at N=8, and 1.31e7 at N=16; acceptance at eps=0.01: 0.743 at N=4, 0.029 at N=8, and 0 at N=12 and N=16.", "idea": "Dilation quotient max magnitude: 7.56 at N=0, 5.36 at N=8, and 4.82 at N=16; acceptance at eps=0.01: 0.864 at N=4, 0.847 at N=8, 0.841 at N=12, and 0.841 at N=16. At N=16, acceptance remained 0.820-0.882 over eps=0.002-0.020." }, "how_to_run": "/home/maxwelhelp/main/bin/python3 dilation_experiment.py | tee results.txt", "files": [ "dilation_experiment.py", "results.txt" ], "limitations": "Only a one-dimensional positive-domain toy target was tested. No 2D neural energy, GPU implementation, random-walk baseline, equal-FLOP accounting, long-chain diagnostics, or independent reference posterior was included." }