{
  "base_case": {
    "det": "1"
  },
  "factors": [
    {
      "type": "Phi1",
      "aux": "a1",
      "monomial": "x**3*y",
      "block_det": "1",
      "pass": true
    },
    {
      "type": "Phi1",
      "aux": "a2",
      "monomial": "y**2*z",
      "block_det": "1",
      "pass": true
    },
    {
      "type": "Phi1",
      "aux": "a3",
      "monomial": "x**3",
      "block_det": "1",
      "pass": true
    },
    {
      "type": "Phi1",
      "aux": "a4",
      "monomial": "x**2*y",
      "block_det": "1",
      "pass": true
    },
    {
      "type": "Phi1",
      "aux": "a5",
      "monomial": "y**3",
      "block_det": "1",
      "pass": true
    },
    {
      "type": "Phi1",
      "aux": "a6",
      "monomial": "y**2",
      "block_det": "1",
      "pass": true
    },
    {
      "type": "Phi1",
      "aux": "a7",
      "monomial": "a2*y",
      "block_det": "1",
      "pass": true
    },
    {
      "type": "Phi1",
      "aux": "a8",
      "monomial": "y*z",
      "block_det": "1",
      "pass": true
    },
    {
      "type": "Phi1",
      "aux": "a9",
      "monomial": "x**2",
      "block_det": "1",
      "pass": true
    },
    {
      "type": "Phi1",
      "aux": "a10",
      "monomial": "x*z",
      "block_det": "1",
      "pass": true
    },
    {
      "type": "Phi1",
      "aux": "a11",
      "monomial": "a2*x",
      "block_det": "1",
      "pass": true
    },
    {
      "type": "Phi1",
      "aux": "a12",
      "monomial": "a6*y",
      "block_det": "1",
      "pass": true
    },
    {
      "type": "Phi1",
      "aux": "a13",
      "monomial": "a3*z",
      "block_det": "1",
      "pass": true
    },
    {
      "type": "Phi1",
      "aux": "a14",
      "monomial": "a7*x",
      "block_det": "1",
      "pass": true
    },
    {
      "type": "Phi1",
      "aux": "a15",
      "monomial": "a5*y",
      "block_det": "1",
      "pass": true
    },
    {
      "type": "Phi1",
      "aux": "a16",
      "monomial": "a8*y",
      "block_det": "1",
      "pass": true
    },
    {
      "type": "Phi1",
      "aux": "a17",
      "monomial": "x*y",
      "block_det": "1",
      "pass": true
    },
    {
      "type": "Phi1",
      "aux": "a18",
      "monomial": "a4*y",
      "block_det": "1",
      "pass": true
    },
    {
      "type": "Phi1",
      "aux": "a19",
      "monomial": "a1*z",
      "block_det": "1",
      "pass": true
    }
  ],
  "steps": [
    {
      "step": 1,
      "phi2_block_det": "1",
      "composition_identity": true,
      "pass": true
    },
    {
      "step": 2,
      "phi2_block_det": "1",
      "composition_identity": true,
      "pass": true
    },
    {
      "step": 3,
      "phi2_block_det": "1",
      "composition_identity": true,
      "pass": true
    },
    {
      "step": 4,
      "phi2_block_det": "1",
      "composition_identity": true,
      "pass": true
    },
    {
      "step": 5,
      "phi2_block_det": "1",
      "composition_identity": true,
      "pass": true
    },
    {
      "step": 6,
      "phi2_block_det": "1",
      "composition_identity": true,
      "pass": true
    },
    {
      "step": 7,
      "phi2_block_det": "1",
      "composition_identity": true,
      "pass": true
    },
    {
      "step": 8,
      "phi2_block_det": "1",
      "composition_identity": true,
      "pass": true
    },
    {
      "step": 9,
      "phi2_block_det": "1",
      "composition_identity": true,
      "pass": true
    },
    {
      "step": 10,
      "phi2_block_det": "1",
      "composition_identity": true,
      "pass": true
    },
    {
      "step": 11,
      "phi2_block_det": "1",
      "composition_identity": true,
      "pass": true
    },
    {
      "step": 12,
      "phi2_block_det": "1",
      "composition_identity": true,
      "pass": true
    },
    {
      "step": 13,
      "phi2_block_det": "1",
      "composition_identity": true,
      "pass": true
    },
    {
      "step": 14,
      "phi2_block_det": "1",
      "composition_identity": true,
      "pass": true
    },
    {
      "step": 15,
      "phi2_block_det": "1",
      "composition_identity": true,
      "pass": true
    },
    {
      "step": 16,
      "phi2_block_det": "1",
      "composition_identity": true,
      "pass": true
    },
    {
      "step": 17,
      "phi2_block_det": "1",
      "composition_identity": true,
      "pass": true
    },
    {
      "step": 18,
      "phi2_block_det": "1",
      "composition_identity": true,
      "pass": true
    }
  ],
  "ALL_PASS": true,
  "conclusion": "det J_final = (prod of factor dets) * det J_base = 1 * 1 = 1 identically, by the chain rule over the verified factorization. Every factor det and every composition identity verified symbolically in exact arithmetic.",
  "elapsed_sec": 0.43
}