# Эксперимент: First-Hit Interacting Optimizer (#513)

{
  "worked": true,
  "confidence": 8,
  "verdict": "Built a reproducible exact 1-D first-passage MVP comparing independent, normalized bounded, unnormalized coherent, and pair-kick regimes. The mechanism manifested: normalized coupling remained approximately logarithmic, coherent coupling approached the predicted N^-1 scaling with high-N slope -0.876, and pair kicks showed approximately 1/(N log N) behavior with high-N slope -1.232 and near-constant N log(N) E[T]. This is a toy verification rather than evidence for a neural-network optimization win.",
  "metrics": {
    "baseline": "Independent particles: mean T(128)=0.06591; log-log slope versus N=-0.281 and slope versus log(log N)=-1.445.",
    "idea": "Normalized coupling slope versus log(log N)=-1.095; unnormalized coherent high-N log-log slope=-0.876; pair-kick high-N log-log slope=-1.232, with N log(N) E[T] at N=64,128,256 equal to 1.562, 1.552, 1.535 versus predicted asymptotic constant 1.25."
  },
  "how_to_run": "/home/maxwelhelp/main/bin/python3 first_hit_toy.py",
  "files": [
    "first_hit_toy.py",
    "results.json",
    "results_run.json",
    "REPORT.md"
  ],
  "limitations": "No MNIST or neural-network optimizer experiment was run. Pairwise kicks were represented using the paper's exact effective marginal diffusivity rather than explicit shared antisymmetric Brownian trajectories, so cross-particle correlations were not independently validated. The tested N range is finite and the coherent exponent remains affected by Brownian-to-drift crossover."
}