{
 "counts": {
  "argument": 1,
  "computed": 6,
  "failed": 0,
  "receipt": 0,
  "symbolic": 1
 },
 "kernel": "s1177_omega_support_certificate",
 "rows": {
  "6": {
   "chi_over_pi": "0",
   "k_with_zero": [
    0,
    3
   ],
   "min_sin2": "0",
   "min_sin2_float": 0.0,
   "strict": false
  },
  "7": {
   "chi_over_pi": "-4/5",
   "k_with_zero": [],
   "min_sin2": "sin(pi/35)**2",
   "min_sin2_float": 0.008035205700685171,
   "strict": true
  },
  "8": {
   "chi_over_pi": "2/5",
   "k_with_zero": [],
   "min_sin2": "(-sqrt(2)*sqrt(5/8 - sqrt(5)/8)/2 + sqrt(2)*(1/4 + sqrt(5)/4)/2)**2",
   "min_sin2_float": 0.024471741852423214,
   "strict": true
  },
  "9": {
   "chi_over_pi": "-2/5",
   "k_with_zero": [],
   "min_sin2": "sin(2*pi/45)**2",
   "min_sin2_float": 0.01936915203084057,
   "strict": true
  },
  "10": {
   "chi_over_pi": "4/5",
   "k_with_zero": [],
   "min_sin2": "sin(2*pi/25)**2",
   "min_sin2_float": 0.06184665997806821,
   "strict": true
  }
 },
 "verdict": "Omega_n^(2) >= min_k sin^2((chi+2 pi k)/n) > 0 at n = 7,8,9,10 under P1-P3; bound 0 at n = 6 (scalar control)"
}
sha256 021a958c0118798abe6f0f11033c953f910aada528bc5f15c3f9b1810e3a3c88
s1177: 6 computed + 1 symbolic PASS-able, 1 argument, 0 failed
