1{
 2  "seed": 584,
 3  "model": "two-layer scalar linear network f(x)=(a*b)x, x=1, target=4",
 4  "constraint": "loss(theta(s)) <= loss(theta(0)) + 1e-10",
 5  "core_check": {
 6    "start_loss": 0.0,
 7    "end_loss": 0.0,
 8    "endpoint_max_loss": 0.0,
 9    "dense_max_loss": 5.0625,
10    "dense_peak_s": 0.5,
11    "interior_violation": 5.0624999999,
12    "analytic_midpoint_output": 6.25
13  },
14  "K_comparison": {
15    "4": {
16      "endpoint_only_accepts": true,
17      "envelope_accepts": false,
18      "sampled_max_violation": 5.0624999999,
19      "sampled_max_loss": 5.0625,
20      "sampled_peak_s": 0.5
21    },
22    "8": {
23      "endpoint_only_accepts": true,
24      "envelope_accepts": false,
25      "sampled_max_violation": 5.0624999999,
26      "sampled_max_loss": 5.0625,
27      "sampled_peak_s": 0.5
28    },
29    "16": {
30      "endpoint_only_accepts": true,
31      "envelope_accepts": false,
32      "sampled_max_violation": 5.0624999999,
33      "sampled_max_loss": 5.0625,
34      "sampled_peak_s": 0.5
35    },
36    "32": {
37      "endpoint_only_accepts": true,
38      "envelope_accepts": false,
39      "sampled_max_violation": 5.0624999999,
40      "sampled_max_loss": 5.0625,
41      "sampled_peak_s": 0.5
42    }
43  },
44  "largest_feasible_fraction": {
45    "8": 1.1166540900831023e-06,
46    "16": 1.1166540900831023e-06,
47    "32": 1.1166540900831023e-06
48  },
49  "50_identical_candidate_trials": {
50    "endpoint_only_accepted": 50,
51    "robust_envelope_accepted": 0
52  },
53  "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."
54}