1{
  2  "seed": 2843,
  3  "device": "cuda",
  4  "autograd_max_abs_error": 9.5367431640625e-07,
  5  "predictions": {
  6    "P1": "At T=1, rank(J)<=2m; m<8 cannot have rank 16, while m=8 is only a necessary counting threshold.",
  7    "P2": "At m=4, rank 16 is first possible at T=3 because 4(T+1)>=16.",
  8    "P3": "A log-det regularizer should increase finite-horizon Gramian logdet, but cannot overcome structural rank loss."
  9  },
 10  "boundary_T1": [
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 12      "m": 2,
 13      "counting_max_rank": 4,
 14      "rank": 4,
 15      "smin": 0.6200574636459351,
 16      "logdet": -221.71067810058594
 17    },
 18    {
 19      "m": 4,
 20      "counting_max_rank": 8,
 21      "rank": 7,
 22      "smin": 0.0,
 23      "logdet": -168.34890747070312
 24    },
 25    {
 26      "m": 6,
 27      "counting_max_rank": 12,
 28      "rank": 11,
 29      "smin": 0.0,
 30      "logdet": -94.81372833251953
 31    },
 32    {
 33      "m": 7,
 34      "counting_max_rank": 14,
 35      "rank": 13,
 36      "smin": 0.0,
 37      "logdet": -63.804290771484375
 38    },
 39    {
 40      "m": 8,
 41      "counting_max_rank": 16,
 42      "rank": 15,
 43      "smin": 4.431030782110014e-16,
 44      "logdet": -29.503028869628906
 45    },
 46    {
 47      "m": 9,
 48      "counting_max_rank": 16,
 49      "rank": 16,
 50      "smin": 0.057427044957876205,
 51      "logdet": -11.292519569396973
 52    },
 53    {
 54      "m": 12,
 55      "counting_max_rank": 16,
 56      "rank": 16,
 57      "smin": 0.2517799437046051,
 58      "logdet": -0.29802656173706055
 59    },
 60    {
 61      "m": 16,
 62      "counting_max_rank": 16,
 63      "rank": 16,
 64      "smin": 1.0,
 65      "logdet": 8.08195972442627
 66    }
 67  ],
 68  "horizon_m4": [
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 70      "T": 0,
 71      "counting_max_rank": 4,
 72      "rank": 4,
 73      "smin": 1.0
 74    },
 75    {
 76      "T": 1,
 77      "counting_max_rank": 8,
 78      "rank": 8,
 79      "smin": 0.2869236469268799
 80    },
 81    {
 82      "T": 2,
 83      "counting_max_rank": 12,
 84      "rank": 12,
 85      "smin": 0.08652034401893616
 86    },
 87    {
 88      "T": 3,
 89      "counting_max_rank": 16,
 90      "rank": 15,
 91      "smin": 3.1279455022355457e-15
 92    },
 93    {
 94      "T": 4,
 95      "counting_max_rank": 16,
 96      "rank": 16,
 97      "smin": 0.019547194242477417
 98    },
 99    {
100      "T": 5,
101      "counting_max_rank": 16,
102      "rank": 16,
103      "smin": 0.03132854402065277
104    },
105    {
106      "T": 6,
107      "counting_max_rank": 16,
108      "rank": 16,
109      "smin": 0.03403342142701149
110    },
111    {
112      "T": 7,
113      "counting_max_rank": 16,
114      "rank": 16,
115      "smin": 0.034734711050987244
116    },
117    {
118      "T": 8,
119      "counting_max_rank": 16,
120      "rank": 16,
121      "smin": 0.035113878548145294
122    }
123  ],
124  "regularizer_m9": {
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127      "smin": 6.862334034352102e-10,
128      "smax": 1.7604278326034546,
129      "logdet": -25.529905319213867,
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149    "final": {
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151      "smin": 2.5555253913012166e-08,
152      "smax": 5.717824459075928,
153      "logdet": -17.043895721435547,
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169        1.2184311515284207e-07,
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172    }
173  },
174  "fixed_control_m9": {
175    "initial": {
176      "rank": 15,
177      "smin": 6.862334034352102e-10,
178      "smax": 1.7604278326034546,
179      "logdet": -25.529905319213867,
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199    "final": {
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201      "smin": 6.862334034352102e-10,
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222    }
223  }
224}