Fractional Jacobian topology loss / results.json

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  1{
  2  "device": "cuda",
  3  "N": 32,
  4  "math_check": {
  5    "frequency_ks": [
  6      1,
  7      2,
  8      4,
  9      8
 10    ],
 11    "fractional_energies": [
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 13      0.6690105199813843,
 14      1.8922576904296875,
 15      5.5801615715026855
 16    ],
 17    "loglog_slope_expected_1_plus_s": 1.5,
 18    "loglog_slope_observed": 1.518062619226667,
 19    "target_winding": {
 20      "count": 2,
 21      "plaquettes": [
 22        [
 23          11,
 24          10,
 25          0.9999999403953552
 26        ],
 27        [
 28          20,
 29          20,
 30          -1.0
 31        ]
 32      ]
 33    },
 34    "initial_winding": {
 35      "count": 2,
 36      "plaquettes": [
 37        [
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 39          10,
 40          1.0
 41        ],
 42        [
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 44          20,
 45          -1.0000001192092896
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 47      ]
 48    },
 49    "target_integer_defect_count": 2,
 50    "jacobian_loss_at_constant_field": 0.0019531248835846782,
 51    "jacobian_gradient_norm_at_constant_field": 6.9156295273709034e-12
 52  },
 53  "baseline_tv": {
 54    "task_mse": 0.0001623212592676282,
 55    "fractional_energy": 1.8164335489273071,
 56    "tv_energy": 0.9250288009643555,
 57    "winding_mse": 6.575653088900082e-17,
 58    "winding_defects": {
 59      "count": 2,
 60      "plaquettes": [
 61        [
 62          11,
 63          10,
 64          1.0
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 66        [
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 68          20,
 69          -1.0
 70        ]
 71      ]
 72    },
 73    "integer_defect_count": 2,
 74    "high_frequency_spectrum": 0.01178131066262722,
 75    "final_winding_range": [
 76      -1.0,
 77      1.0
 78    ]
 79  },
 80  "idea_fractional_jacobian": {
 81    "task_mse": 0.0003124744107481092,
 82    "fractional_energy": 1.627249002456665,
 83    "tv_energy": 0.9465042352676392,
 84    "winding_mse": 4.345112590675315e-17,
 85    "winding_defects": {
 86      "count": 2,
 87      "plaquettes": [
 88        [
 89          11,
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 91          1.0
 92        ],
 93        [
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 95          20,
 96          -1.0
 97        ]
 98      ]
 99    },
100    "integer_defect_count": 2,
101    "high_frequency_spectrum": 0.00849775318056345,
102    "final_winding_range": [
103      -1.0,
104      1.0
105    ]
106  }
107}