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    "P1": "At T=1, rank(J)<=2m; m<8 cannot have rank 16, while m=8 is only a necessary counting threshold.",
    "P2": "At m=4, rank 16 is first possible at T=3 because 4(T+1)>=16.",
    "P3": "A log-det regularizer should increase finite-horizon Gramian logdet, but cannot overcome structural rank loss."
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      "smin": 4.431030782110014e-16,
      "logdet": -29.503028869628906
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    {
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    {
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    {
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      "rank": 16,
      "smin": 0.03132854402065277
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    {
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    {
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