# Эксперимент: Monotone CDT autoencoder bottleneck (#426)

{
  "worked": true,
  "confidence": 8,
  "verdict": "Built a reproducible monotone CDT bottleneck prototype with cumulative softplus increments, conservative quantile push-forward, invariant checks, and a shared-data POD comparison. The mechanism manifested: monotonicity was 100% across all logit temperatures, the fixed final endpoint error was 4.4e-15, the epsilon-derived increment lower bound held across the sweep, and push-forward mass error was 3.3e-16 with no negative cells. In the toy comparison, CDT-space reconstruction had lower Wasserstein proxy error at d=2, 4, and 8 while eliminating negative outputs, although this is a POD prototype rather than a trained neural autoencoder.",
  "metrics": {
    "baseline": "d=2/4/8 physical L1 = 0.6491/0.3795/0.2102; Wasserstein proxy = 0.05450/0.02316/0.01119; negative-cell fraction = 30.9%/29.8%/26.8%; mass error approximately 1e-16.",
    "idea": "d=2/4/8 physical L1 = 0.1147/0.0974/0.0925; Wasserstein error = 0.001228/0.0002744/0.0000711; negative-cell fraction = 0%; monotone fraction = 100%; mass error = 3.97e-4/7.94e-5/1.29e-16."
  },
  "how_to_run": "/home/maxwelhelp/main/bin/python3 experiment.py",
  "files": [
    "experiment.py",
    "results.json"
  ],
  "limitations": "The experiment uses POD projections and cumulative-maximum repair rather than training an encoder/decoder neural network. It tests synthetic 1D Gaussian mixtures only, and does not test square pulses, CUDA, optimization speed, learned bottlenecks, or higher-dimensional transport. The physical push-forward is a simple piecewise-uniform discretization."
}