files / problems / simon-ionization-excess / compute / q13 / certs / sharper_cut.json

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{
  "status": "residue",
  "reason": "Chebyshev D\u00b7M_{-1}\u22651 (since D\u00b7M_{-1}\u2265M_1\u22651) on the endpoint identities shrinks the (Q,D) slab. At R<=9 the new cut is still below 0.908265, so R<=9 stays dead against printed 1.1010. At R=9.5 the Chebyshev cut 0.91029 would sit above that floor; that is a probe, not a wired lift. The cheap live line stays the proven R=10 split.",
  "need_gamma": 0.9082652134423251,
  "reopens_R_le_9": false,
  "rows": [
    {
      "R": 8.0,
      "positivity_cut": 0.8888888888888888,
      "chebyshev_cut": 0.8967368888891145,
      "need_vs_1.1010": 0.9082652134423251,
      "chebyshev_beats_1.1010": false,
      "positivity_beats_1.1010": false
    },
    {
      "R": 9.0,
      "positivity_cut": 0.9,
      "chebyshev_cut": 0.9061720000001775,
      "need_vs_1.1010": 0.9082652134423251,
      "chebyshev_beats_1.1010": false,
      "positivity_beats_1.1010": false
    },
    {
      "R": 9.5,
      "positivity_cut": 0.9047619047619048,
      "chebyshev_cut": 0.9102929047620638,
      "need_vs_1.1010": 0.9082652134423251,
      "chebyshev_beats_1.1010": true,
      "positivity_beats_1.1010": false
    },
    {
      "R": 9.8,
      "positivity_cut": 0.9074074074074074,
      "chebyshev_cut": 0.9126014074075568,
      "need_vs_1.1010": 0.9082652134423251,
      "chebyshev_beats_1.1010": true,
      "positivity_beats_1.1010": false
    },
    {
      "R": 9.9,
      "positivity_cut": 0.908256880733945,
      "chebyshev_cut": 0.9133448807340913,
      "need_vs_1.1010": 0.9082652134423251,
      "chebyshev_beats_1.1010": true,
      "positivity_beats_1.1010": false
    },
    {
      "R": 10.0,
      "positivity_cut": 0.9090909090909091,
      "chebyshev_cut": 0.9140769090910524,
      "need_vs_1.1010": 0.9082652134423251,
      "chebyshev_beats_1.1010": true,
      "positivity_beats_1.1010": true
    }
  ]
}