# Эксперимент: Delay-Aware Frequency-Preserving Recurrent Coupling (#450)

{
  "worked": true,
  "confidence": 9,
  "verdict": "Built and ran a delayed modal recurrent-coupling MVP with ordinary delayed feedback and a two-tap phase-lead predictor. The three mechanism predictions were confirmed: delay phase slope was -1.000 versus -1.000 predicted, the lambda=0 mode was exactly delay-invariant while a nonzero mode changed by relative RMS 0.825, and the small-gain frequency-shift slope differed from perturbation theory by 3.9%. In the four-branch ring toy experiment, compensation reduced mean nonzero-mode frequency error from 0.03425 rad/time to 0.000563 rad/time, a 98.4% reduction; this is a real signal for the stated mechanism, though not evidence of a general ML-training win.",
  "metrics": {
    "baseline": "Delayed coupling: mean nonzero-mode frequency error 0.0342477 rad/time; lambda=2 error 0.0251704; lambda=4 error 0.0524022.",
    "idea": "Two-tap predictor compensation: mean nonzero-mode frequency error 0.0005633 rad/time; lambda=2 error 0.0007321; lambda=4 error 0.0002257; relative reduction 98.36%. Phase slope -1.000 predicted/observed; frequency-shift slope 0.31074 observed vs 0.29909 predicted, a 3.90% relative error."
  },
  "how_to_run": "/home/maxwelhelp/main/bin/python3 delay_coupling_experiment.py",
  "files": [
    "delay_coupling_experiment.py",
    "results.json"
  ],
  "limitations": "Only a deterministic complex single-mode Euler DDE and a four-branch ring modal equivalent were tested. No learned GRU/SSM, synthetic readout training, multi-frequency mixture, broad delay/gain stability-boundary sweep, wall-clock comparison, or GPU experiment was included; FFT output-spectrum evaluation was replaced by a continuous phase-slope estimator."
}