files / problems / hilbert16-limit-cycles / compute / q3 / ii-complex-cube / certs / arithmetic.json

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{
  "N_formula": "3n+2",
  "rows": [
    {
      "n": 1,
      "N": 5,
      "sheet_ceiling_bezout": 9,
      "actual_complex": 3,
      "chebyshev_m": 3,
      "chebyshev_sheets": 9,
      "ratio": [
        3,
        1
      ],
      "complex_eq_(N+1)/(n+1)": true
    },
    {
      "n": 2,
      "N": 8,
      "sheet_ceiling_bezout": 9,
      "actual_complex": 3,
      "chebyshev_m": 3,
      "chebyshev_sheets": 9,
      "ratio": [
        3,
        1
      ],
      "complex_eq_(N+1)/(n+1)": true
    },
    {
      "n": 3,
      "N": 11,
      "sheet_ceiling_bezout": 9,
      "actual_complex": 3,
      "chebyshev_m": 3,
      "chebyshev_sheets": 9,
      "ratio": [
        3,
        1
      ],
      "complex_eq_(N+1)/(n+1)": true
    }
  ],
  "conclusion": {
    "beats_T3": false,
    "weaker_than_T3": true,
    "attains_bezout": false,
    "actual_complex_growth": "linear",
    "complex_sheets_formula": "(N+1)/(n+1)",
    "bezout_ceiling_growth": "quadratic",
    "answers_remark4": "negative_for_holomorphic_cube",
    "do_not_claim_9_sheets": true,
    "do_not_claim_252_1080_1380_2012": true
  }
}