Эксперимент: Flip-Bifurcation Spectral Guard (#773)

{ "worked": false, "confidence": 9, "verdict": "Built and numerically verified the scalar flip normal form. The predicted boundary mu=0 was observed between 0.000 and 0.005, period-two amplitude matched sqrt(mu/a) with 8.1e-16 mean relative error, and cubic-coefficient scaling matched 1/sqrt(a) with 2.9e-16 error. However, the displayed loss has the wrong sign: for lambda=-1.1 it is zero, so the literal guard converged to the unstable lambda=-1.15 just like baseline; only a corrected lower-bound penalty/projection produced lambda=-0.95 and suppressed the cycle. Therefore the idea as specified does not work without fixing its formula.", "metrics": { "baseline": "mu=0.1500, lambda=-1.1500, two-cycle amplitude=0.27386; literal displayed penalty also gave mu=0.1500, lambda=-1.1500, amplitude=0.27386", "idea": "Corrected lower-bound guard: mu=-0.0500, lambda=-0.9500, two-cycle amplitude approximately 7.7e-60; predicted/observed boundary 0.0/0.0025, square-root scaling relative error 8.1e-16, cubic scaling relative error 2.9e-16" }, "how_to_run": "/home/maxwelhelp/main/bin/python3 flip_guard_experiment.py", "files": [ "flip_guard_experiment.py", "results.json" ], "limitations": "Only a scalar normal-form toy and scalar gain-training comparison were tested; no tanh RNN, sequential MNIST, graph task, multidimensional Arnoldi/JVP estimator, runtime/FLOP comparison, or noisy finite-sample training study was performed. The reported A_K metric is zero on an exact period-two orbit because h_K equals h_{K-2}, so cycle amplitude is the meaningful instability diagnostic here." }