Эксперимент: Wedge-Positive Tangent Dynamics (#369)

{ "worked": true, "confidence": 8, "verdict": "Built and ran a NumPy/SciPy MVP for second additive compounds, wedge transitions, positivity, and Hilbert projective contraction. The mechanism manifested: the compound identity had observed O(h^2) error slope 1.992, the six-cycle worst-entry scaling had observed alpha^3 slope 3.000 as predicted, and stronger irreducible coupling reduced the Birkhoff bound from 0.99996 at alpha=0.05 to 0.87525 at alpha=0.8. This validates the toy mathematical mechanism, but does not establish a neural-network accuracy win.", "metrics": { "baseline": "Signed/non-Metzler cycle: minimum finite-window transition entry -0.1463; among positive-output samples, maximum Hilbert ratio 2.492, so uniform positive-cone contraction was absent.", "idea": "Metzler irreducible cycle: all finite-window entries were positive; sampled maximum Hilbert ratios decreased from 0.9904 to 0.6799 as alpha increased from 0.05 to 0.8, while exact Birkhoff bounds decreased from 0.99996 to 0.87525. Compound identity slope was 1.992 versus predicted 2.0; path scaling slope was 3.000 versus predicted 3.0." }, "how_to_run": "/home/maxwelhelp/main/bin/python3 wedge_experiment.py", "files": [ "wedge_experiment.py", "results.json", "run_output.txt" ], "limitations": "This is a controlled linear compound-dynamics toy experiment, not a trained neural ODE or residual RNN. It does not test prediction loss, rollout accuracy, FLOPs, learned regularization, time-varying generators, sign-gauge learning, or downstream task performance. Hilbert ratios are random-sample estimates and the Birkhoff bound can be loose." }