{
  "seed": 584,
  "model": "two-layer scalar linear network f(x)=(a*b)x, x=1, target=4",
  "constraint": "loss(theta(s)) <= loss(theta(0)) + 1e-10",
  "core_check": {
    "start_loss": 0.0,
    "end_loss": 0.0,
    "endpoint_max_loss": 0.0,
    "dense_max_loss": 5.0625,
    "dense_peak_s": 0.5,
    "interior_violation": 5.0624999999,
    "analytic_midpoint_output": 6.25
  },
  "K_comparison": {
    "4": {
      "endpoint_only_accepts": true,
      "envelope_accepts": false,
      "sampled_max_violation": 5.0624999999,
      "sampled_max_loss": 5.0625,
      "sampled_peak_s": 0.5
    },
    "8": {
      "endpoint_only_accepts": true,
      "envelope_accepts": false,
      "sampled_max_violation": 5.0624999999,
      "sampled_max_loss": 5.0625,
      "sampled_peak_s": 0.5
    },
    "16": {
      "endpoint_only_accepts": true,
      "envelope_accepts": false,
      "sampled_max_violation": 5.0624999999,
      "sampled_max_loss": 5.0625,
      "sampled_peak_s": 0.5
    },
    "32": {
      "endpoint_only_accepts": true,
      "envelope_accepts": false,
      "sampled_max_violation": 5.0624999999,
      "sampled_max_loss": 5.0625,
      "sampled_peak_s": 0.5
    }
  },
  "largest_feasible_fraction": {
    "8": 1.1166540900831023e-06,
    "16": 1.1166540900831023e-06,
    "32": 1.1166540900831023e-06
  },
  "50_identical_candidate_trials": {
    "endpoint_only_accepted": 50,
    "robust_envelope_accepted": 0
  },
  "interpretation": "Endpoint rule accepts the weight swap, while every envelope grid detects its interior loss spike; K=8,16,32 agree on rejection and similar halving threshold."
}