Эксперимент: Lipschitz-Inflated Conformal Trajectory Tube (#1067)

{ "worked": true, "confidence": 8, "verdict": "Built a readable Lipschitz-inflated split-conformal trajectory-tube wrapper and numerical verifier. The triangle-inequality bound had zero measured violation, radius slope matched the predicted Gamma (0.9210526) to numerical precision, and the conditional coverage transition occurred exactly at multiplier 1.0; a 0.75 multiplier failed immediately after the largest observation gap. Marginal coverage at the estimated slope quantile was 0.988 versus the predicted slope-event coverage of 0.9, showing the mechanism but also conservatism from the grid/test construction.", "metrics": { "baseline": "Constant observed-time conformal radius q=0; dense-grid coverage on the boundary test trajectory was 0.75025.", "idea": "At Gamma=Lhat, boundary trajectory coverage was 1.000; iid test-slope marginal coverage was 0.98826, versus 1.000 with a 1.1 safety multiplier. Radius slope predicted/observed was 0.9210526/0.9210526; maximum triangle-bound violation was 0." }, "how_to_run": "/home/maxwelhelp/main/bin/python3 run_experiment.py", "files": [ "trajectory_tube.py", "run_experiment.py", "article.md", "idea_context.json" ], "limitations": "This was a deterministic synthetic piecewise-linear toy study with a zero predictor, scalar trajectories, and no neural ODE/GRU training or noisy pendulum experiment. It did not test finite-sample behavior across many independent calibration splits, predictor slope estimation error, multidimensional norms, or irregular observation processes beyond the fixed sparse grid." }