{
 "lemma": "L5 has no right factor of order 1, 2, 3, or 4 over Q(xi)",
 "rates": "(A,B,C) = (2,3,5)",
 "inputs": {
  "data/L5_theta.txt": "58eb063ae8c40b5485d76bd5f4b0a8a41d6396abdb12b8689c6e44dda4d73fe2",
  "data/L5_dform.json": "795ed945b383b7582ccac83f2890e1d8073c97b72d95b468de703620c94445a5",
  "data/exterior_powers.json": "a336d26aff30f38db7e0473bdb94bf590844baa0ec8533de0a47b337d3dc90cc"
 },
 "software": {
  "python": "3.12.3",
  "sympy": "1.14.0",
  "python-flint": "0.8.0"
 },
 "stage0": {
  "degrees": [
   6,
   7,
   8,
   9,
   10,
   11
  ],
  "lc_factored": "x**5*(216*x**2 + 20*x + 3)*(576*x**4 - 960*x**3 + 352*x**2 - 40*x + 1)"
 },
 "stage1": {
  "sweep": {
   "operator": "L5_r1",
   "order": 5,
   "ncombos_solved": 0,
   "candidates": [],
   "flags": [],
   "seconds": 0.2
  },
  "exponent_options": [
   {
    "factor": "x",
    "deg": 1,
    "options": [
     "0"
    ],
    "complete": "True"
   },
   {
    "factor": "216*x**2 + 20*x + 3",
    "deg": 2,
    "options": [
     "0"
    ],
    "complete": "True"
   },
   {
    "factor": "576*x**4 - 960*x**3 + 352*x**2 - 40*x + ",
    "deg": 4,
    "options": [
     "0",
     "1/2"
    ],
    "complete": "True"
   }
  ],
  "lam_options": [
   "1/2",
   "1",
   "3/2",
   "5/2",
   "7/2"
  ],
  "root_census": [
   {
    "factor": "x",
    "deg": 1,
    "indicial_degree": 5,
    "roots_found": 5,
    "roots": [
     "0",
     "1",
     "2"
    ],
    "status": "all roots found"
   },
   {
    "factor": "216*x**2 + 20*x + 3",
    "deg": 2,
    "indicial_degree": 5,
    "roots_found": 5,
    "roots": [
     "0",
     "1",
     "2",
     "3",
     "5"
    ],
    "status": "all roots found"
   },
   {
    "factor": "576*x**4 - 960*x**3 + 352*x**2 - 40*x + ",
    "deg": 4,
    "indicial_degree": 5,
    "roots_found": 5,
    "roots": [
     "0",
     "1",
     "1/2",
     "2",
     "3"
    ],
    "status": "all roots found"
   }
  ]
 },
 "stage2": {
  "M_2": {
   "order": 10,
   "max_degree": 76,
   "max_bits": 233,
   "annihilates_all_wedges": true
  },
  "M_3": {
   "order": 10,
   "max_degree": 90,
   "max_bits": 277,
   "annihilates_all_wedges": true
  },
  "M_4": {
   "order": 5,
   "max_degree": 29,
   "max_bits": 90,
   "annihilates_all_wedges": true
  }
 },
 "stage3": {
  "M_2": {
   "sweep": {
    "operator": "Lambda2",
    "order": 10,
    "ncombos_solved": 1,
    "candidates": [],
    "flags": [],
    "seconds": 3.1
   },
   "exponent_options": [
    {
     "factor": "x",
     "deg": 1,
     "options": [
      "-1",
      "0"
     ],
     "complete": "True"
    },
    {
     "factor": "576*x**4 - 960*x**3 + 352*x**2 - 40*x + ",
     "deg": 4,
     "options": [
      "-1/2",
      "0",
      "1/2",
      "3/2",
      "5/2"
     ],
     "complete": "True"
    },
    {
     "factor": "1085399347739004949329827995538603069197",
     "deg": 53,
     "options": [
      "0"
     ],
     "complete": "True"
    }
   ],
   "lam_options": [
    "5/2",
    "3",
    "7/2",
    "4",
    "9/2",
    "5",
    "11/2",
    "6",
    "7",
    "8"
   ],
   "root_census": [
    {
     "factor": "x",
     "deg": 1,
     "indicial_degree": 10,
     "roots_found": 10,
     "roots": [
      "-1",
      "0",
      "1",
      "2"
     ],
     "status": "all roots found"
    },
    {
     "factor": "576*x**4 - 960*x**3 + 352*x**2 - 40*x + ",
     "deg": 4,
     "indicial_degree": 10,
     "roots_found": 10,
     "roots": [
      "-1/2",
      "0",
      "1",
      "1/2",
      "2",
      "3",
      "3/2",
      "4",
      "5",
      "5/2"
     ],
     "status": "all roots found"
    },
    {
     "factor": "1085399347739004949329827995538603069197",
     "deg": 53,
     "indicial_degree": 10,
     "roots_found": 10,
     "roots": [
      "0",
      "1",
      "10",
      "2",
      "3",
      "4",
      "5",
      "6",
      "7",
      "8"
     ],
     "status": "all roots found"
    }
   ]
  },
  "M_3": {
   "sweep": {
    "operator": "Lambda3",
    "order": 10,
    "ncombos_solved": 10,
    "candidates": [],
    "flags": [],
    "seconds": 6.9
   },
   "exponent_options": [
    {
     "factor": "x",
     "deg": 1,
     "options": [
      "-3",
      "-2",
      "-1",
      "0"
     ],
     "complete": "True"
    },
    {
     "factor": "576*x**4 - 960*x**3 + 352*x**2 - 40*x + ",
     "deg": 4,
     "options": [
      "-3/2",
      "-1/2",
      "0",
      "1/2",
      "3/2",
      "5/2",
      "7/2"
     ],
     "complete": "True"
    },
    {
     "factor": "5516242843094979012163712437755335615048",
     "deg": 57,
     "options": [
      "0"
     ],
     "complete": "True"
    }
   ],
   "lam_options": [
    "6",
    "7",
    "15/2",
    "8",
    "17/2",
    "9",
    "19/2",
    "10",
    "21/2",
    "11"
   ],
   "root_census": [
    {
     "factor": "x",
     "deg": 1,
     "indicial_degree": 10,
     "roots_found": 10,
     "roots": [
      "-1",
      "-2",
      "-3",
      "0"
     ],
     "status": "all roots found"
    },
    {
     "factor": "576*x**4 - 960*x**3 + 352*x**2 - 40*x + ",
     "deg": 4,
     "indicial_degree": 10,
     "roots_found": 10,
     "roots": [
      "-1/2",
      "-3/2",
      "0",
      "1",
      "1/2",
      "2",
      "3",
      "3/2",
      "5/2",
      "7/2"
     ],
     "status": "all roots found"
    },
    {
     "factor": "5516242843094979012163712437755335615048",
     "deg": 57,
     "indicial_degree": 10,
     "roots_found": 10,
     "roots": [
      "0",
      "1",
      "10",
      "2",
      "3",
      "4",
      "5",
      "6",
      "7",
      "8"
     ],
     "status": "all roots found"
    }
   ]
  },
  "M_4": {
   "sweep": {
    "operator": "Lambda4",
    "order": 5,
    "ncombos_solved": 2,
    "candidates": [],
    "flags": [],
    "seconds": 0.2
   },
   "exponent_options": [
    {
     "factor": "x",
     "deg": 1,
     "options": [
      "-5",
      "-4",
      "-3",
      "0"
     ],
     "complete": "True"
    },
    {
     "factor": "216*x**2 + 20*x + 3",
     "deg": 2,
     "options": [
      "0"
     ],
     "complete": "True"
    },
    {
     "factor": "576*x**4 - 960*x**3 + 352*x**2 - 40*x + ",
     "deg": 4,
     "options": [
      "-5/2",
      "-3/2",
      "-1/2",
      "0",
      "1/2"
     ],
     "complete": "True"
    }
   ],
   "lam_options": [
    "23/2",
    "25/2",
    "27/2",
    "14",
    "29/2"
   ],
   "root_census": [
    {
     "factor": "x",
     "deg": 1,
     "indicial_degree": 5,
     "roots_found": 5,
     "roots": [
      "-3",
      "-4",
      "-5"
     ],
     "status": "all roots found"
    },
    {
     "factor": "216*x**2 + 20*x + 3",
     "deg": 2,
     "indicial_degree": 5,
     "roots_found": 5,
     "roots": [
      "0",
      "2",
      "3",
      "4",
      "5"
     ],
     "status": "all roots found"
    },
    {
     "factor": "576*x**4 - 960*x**3 + 352*x**2 - 40*x + ",
     "deg": 4,
     "indicial_degree": 5,
     "roots_found": 5,
     "roots": [
      "-1/2",
      "-3/2",
      "-5/2",
      "0",
      "1/2"
     ],
     "status": "all roots found"
    }
   ]
  }
 },
 "checks": [
  {
   "check": "Stage 0: D-form of data/L5_theta.txt at (2,3,5) == data/L5_dform.json",
   "pass": true,
   "detail": ""
  },
  {
   "check": "Stage 0: leading coefficient c_5 = xi^5 (216 xi^2+20 xi+3)(576 xi^4-960 xi^3+352 xi^2-40 xi+1)",
   "pass": true,
   "detail": ""
  },
  {
   "check": "Stage 0: L5_dform.json has order 5 and integer coefficient lists",
   "pass": true,
   "detail": ""
  },
  {
   "check": "Stage 0: certificate operators agree (L5 of prove_wedge == L5_dform.json)",
   "pass": true,
   "detail": ""
  },
  {
   "check": "Stage 1: engine finds no exponent combination with a nonnegative integer degree (0 combinations, 0 candidates)",
   "pass": true,
   "detail": ""
  },
  {
   "check": "Stage 1: no completeness flag raised by the enumeration",
   "pass": true,
   "detail": ""
  },
  {
   "check": "Stage 1: every finite exponent option >= 0 and every lam > 0, so deg P = -lam - sum e_F deg F < 0 for every combination",
   "pass": true,
   "detail": ""
  },
  {
   "check": "Stage 1: roots at infinity are those of the printed P_6: {1/2, 1, 3/2, 5/2, 7/2}",
   "pass": true,
   "detail": ""
  },
  {
   "check": "Stage 1: root census -- at every factor of c_5 the indicial polynomial has constant coefficients and all roots found over Q",
   "pass": true,
   "detail": ""
  },
  {
   "check": "Stage 2: M_2 has order 10 with integer coefficients",
   "pass": true,
   "detail": "order 10, max coefficient degree 76, max 233 bits"
  },
  {
   "check": "Stage 2: exact wedge annihilation identity for r = 2 (row identity zero in Z[xi])",
   "pass": true,
   "detail": ""
  },
  {
   "check": "Stage 2: M_3 has order 10 with integer coefficients",
   "pass": true,
   "detail": "order 10, max coefficient degree 90, max 277 bits"
  },
  {
   "check": "Stage 2: exact wedge annihilation identity for r = 3 (row identity zero in Z[xi])",
   "pass": true,
   "detail": ""
  },
  {
   "check": "Stage 2: M_4 has order 5 with integer coefficients",
   "pass": true,
   "detail": "order 5, max coefficient degree 29, max 90 bits"
  },
  {
   "check": "Stage 2: exact wedge annihilation identity for r = 4 (row identity zero in Z[xi])",
   "pass": true,
   "detail": ""
  },
  {
   "check": "Stage 3: M_2 has no hyperexponential solution (0 candidates; every combination NOSOL by full column rank)",
   "pass": true,
   "detail": "1 admissible combinations"
  },
  {
   "check": "Stage 3: no completeness flag for M_2",
   "pass": true,
   "detail": ""
  },
  {
   "check": "Stage 3: root census for M_2 -- all indicial roots found at every factor; infinity complete",
   "pass": true,
   "detail": ""
  },
  {
   "check": "Stage 3: M_3 has no hyperexponential solution (0 candidates; every combination NOSOL by full column rank)",
   "pass": true,
   "detail": "10 admissible combinations"
  },
  {
   "check": "Stage 3: no completeness flag for M_3",
   "pass": true,
   "detail": ""
  },
  {
   "check": "Stage 3: root census for M_3 -- all indicial roots found at every factor; infinity complete",
   "pass": true,
   "detail": ""
  },
  {
   "check": "Stage 3: M_4 has no hyperexponential solution (0 candidates; every combination NOSOL by full column rank)",
   "pass": true,
   "detail": "2 admissible combinations"
  },
  {
   "check": "Stage 3: no completeness flag for M_4",
   "pass": true,
   "detail": ""
  },
  {
   "check": "Stage 3: root census for M_4 -- all indicial roots found at every factor; infinity complete",
   "pass": true,
   "detail": ""
  }
 ],
 "npass": 24,
 "nfail": 0,
 "verdict": "PASS",
 "seconds": 14.1
}