Эксперимент: PDE Sinkhorn with asymmetric geometric boundaries (#437)

{ "worked": true, "confidence": 8, "verdict": "Built a NumPy/SciPy MVP containing the oblique boundary calculation, conservative finite-volume reflected diffusion, explicit stability sweep, and endpoint Sinkhorn scaling comparison. The mechanism manifested: for G=[[1,c],[c,1]], the oblique residual stayed 0 while the normal-BC residual was exactly c; no-flux propagation conserved mass to 1e-12 or better across diffusion strengths; and positivity held through ratio 1.0 of the predicted dt=7.8125e-5 bound but failed strongly at 1.05. Reflected and unconstrained kernel Sinkhorn both matched endpoint marginals to roughly 1e-15 KL in this easy 1D test, so no accuracy win over the baseline was demonstrated.", "metrics": { "baseline": "Unconstrained Gaussian kernel Sinkhorn: initial KL 1.23e-17, terminal KL 5.03e-15; endpoint boundary-cell mass about 9.83e-4.", "idea": "Reflected finite-volume/PDE kernel Sinkhorn: initial KL 3.96e-17, terminal KL 4.78e-16; mass conservation error <=8.8e-13, imposed boundary flux exactly 0; oblique BC residual 0 across c=0..0.95 while normal BC residual grew linearly 0..0.95; positivity transition observed at dt/dt_bound between 1.0 and 1.05." }, "how_to_run": "/home/maxwelhelp/main/bin/python3 experiment.py", "files": [ "experiment.py", "results.json", "run.txt" ], "limitations": "This is a low-dimensional numerical MVP, not the requested 2D annulus experiment. The backward oblique condition is verified algebraically and is not yet integrated into a full 2D backward-factor PDE solve; the forward test uses pure diffusion, no drift, and the Sinkhorn comparison uses a precomputed matrix exponential rather than repeated time-stepped factor propagation. No particle-rejection baseline, bridge action, runtime benchmark, or rank-deficient multidimensional directional diffusion was tested." }