Эксперимент: Second-order fusion prior for point-set diffusion (#1177)

{ "worked": true, "confidence": 8, "verdict": "Built a reproducible analytic prior and toy point-set Langevin experiment. The beta=2 determinantal Sine-kernel expansion matched the theorem’s kappa to relative errors of 5.4e-10 for m=2 and 3.0e-9 for m=3, while the implemented coordinate score matched finite differences within 1.45e-10. The prior reduced normalized short-gap collisions from 9.11% baseline to 0.27% with the full correction, but the second-order correction itself did not improve collision rate over repulsion-only, so its incremental benefit remains unproven.", "metrics": { "baseline": "collision rate 0.0911; gap standard deviation 0.9454; 5th-percentile normalized gap 0.0531", "idea": "full second-order prior: collision rate 0.00271; gap standard deviation 0.4516; 5th-percentile normalized gap 0.3308; theorem kappa relative errors 5.4e-10 (m=2) and 3.0e-9 (m=3)" }, "how_to_run": "/home/maxwelhelp/main/bin/python3 run_experiment.py", "files": [ "run_experiment.py", "results.json" ], "limitations": "This is not a trained diffusion network or Sine-beta simulator; it is a small Langevin proxy with global rather than randomly selected local subsets, no Wasserstein or pair-correlation evaluation, and no systematic tuning or multi-seed confidence intervals. The correction was evaluated at fixed beta=2 and its incremental effect versus repulsion-only was not a demonstrated win." }