# Эксперимент: Nullspace-coordinate constrained operator blocks (#1135)

{
  "worked": true,
  "confidence": 9,
  "verdict": "Built a weighted nullspace-coordinate adapter and deterministic constrained linear rollout in experiment.py. The algebraic claims were verified numerically: ||Cu_p-b||=5.6e-17, ||CV||=5.0e-17, and ||VᵀMV-I||=4.6e-15; reduced and M-metric projected one-step updates differed by only 2.7e-16. The exact-invariance effect is real, but no stability advantage over projection was observed: both had identical large Euler energy drift, while soft penalties retained substantial residuals and unconstrained evolution violated the constraints severely.",
  "metrics": {
    "baseline": "M-metric projection: max constraint residual 1.49e-15; max relative mass-norm drift 43.27. Soft penalty λ=30: residual 2.47; unconstrained ambient: residual 2.12e3.",
    "idea": "Reduced coordinates: max constraint residual 4.46e-15; max relative mass-norm drift 43.27. One-step difference from M-metric projection 2.74e-16."
  },
  "how_to_run": "/home/maxwelhelp/main/bin/python3 experiment.py",
  "files": [
    "experiment.py",
    "results.json"
  ],
  "limitations": "Only a small deterministic linear toy system was tested; no neural operator, learned frozen mechanism blocks, unseen geometries, FLOP/runtime comparison, or PDE accuracy experiment was performed. Explicit Euler was unstable for the chosen skew dynamics, so the test does not establish long-horizon stability benefits beyond exact constraint preservation."
}