{
  "status": "Certified finite inner family; not asserted maximal or minimum",
  "members": [
    {
      "position": 1,
      "index": 598,
      "lambda": "1",
      "list": 1,
      "formula": "1/(a**2 - 2*b**2 - 2*c**2)",
      "rational": true,
      "source": "https://faculty.evansville.edu/ck6/encyclopedia/ETC.html#X598",
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      "sharp_outward_centroidal_ray": true,
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      "certificate": "refined/entry_8.json",
      "group": "previous-current-base",
      "label": "F(1,X598)",
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    },
    {
      "position": 3,
      "index": 4193,
      "lambda": "1",
      "list": 1,
      "formula": "(a - b - c)*(a*b**2 - a*b*c + a*c**2 + b**3 - b**2*c - b*c**2 + c**3)",
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      "source": "https://faculty.evansville.edu/ck6/encyclopedia/ETCPart3.html#X4193",
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      "sharp_outward_centroidal_ray": true,
      "status": "Proved attractive",
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      "merge_position": 2,
      "current_base_position": 2,
      "necessity_status": "proved necessary in B41",
      "family_role": "retained B36 rational map",
      "b46_position": 2
    },
    {
      "position": 4,
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      "source": "https://faculty.evansville.edu/ck6/encyclopedia/ETCPart6.html#X10523",
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      "sharp_outward_centroidal_ray": true,
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      "certificate": "proofs/entry_20.json",
      "group": "previous-current-base",
      "label": "F(1,X10523)",
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      "current_base_position": 3,
      "necessity_status": "proved necessary in B41",
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      "b46_position": 3
    },
    {
      "position": 6,
      "index": 12877,
      "lambda": "1",
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      "formula": "(-a + b + c)*(3*a**6 - a**4*(5*b**2 + 5*c**2) - 4*a**3*b*c*(b + c) + a**2*(b**4 - b*c*(2*b**2 - b*c + 2*c**2) + c**4) + (b - c)**2*(b**2 - c**2)**2)",
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      "sharp_outward_centroidal_ray": true,
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      "current_base_position": 4,
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      "family_role": "retained B36 rational map",
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    {
      "position": 12,
      "index": 27277,
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      "source": "supplied candidate38-first-pass.json",
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      "group": "previous-current-base",
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      "necessity_status": "proved necessary in B41",
      "family_role": "retained B36 rational map",
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      "position": 13,
      "index": 27328,
      "lambda": "1",
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      "source": "supplied candidate38-first-pass.json",
      "method": "supplied prior formula",
      "sharp_outward_centroidal_ray": false,
      "status": "Proved attractive",
      "certificate": "proofs/entry_82.json",
      "group": "previous-current-base",
      "label": "F(1,X27328)",
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      "current_base_position": 8,
      "necessity_status": "proved necessary in B41",
      "family_role": "retained B36 rational map",
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    {
      "position": 15,
      "index": 39141,
      "lambda": "1",
      "list": 2,
      "formula": "2*a**6 - a**4*b**2 - a**4*c**2 + a**2*b**4 - a**2*b**2*c**2 + a**2*c**4 + b**4*c**2 + b**2*c**4",
      "rational": true,
      "source": "https://faculty.evansville.edu/ck6/encyclopedia/ETCPart20.html#X39141",
      "method": "supplied prior formula",
      "sharp_outward_centroidal_ray": false,
      "status": "Proved attractive",
      "certificate": "proofs/entry_87.json",
      "group": "previous-current-base",
      "label": "F(1,X39141)",
      "merge_position": 10,
      "current_base_position": 10,
      "necessity_status": "proved necessary in B41",
      "family_role": "retained B36 rational map",
      "b46_position": 7
    },
    {
      "position": 18,
      "index": 59572,
      "lambda": "1",
      "list": 2,
      "formula": "3*a**3 - 3*a**2*(b + c) - a*(b**2 - 6*b*c + c**2) + (b - c)**2*(b + c)",
      "rational": true,
      "source": "https://faculty.evansville.edu/ck6/encyclopedia/ETCPart30.html#X59572",
      "method": "supplied prior formula",
      "sharp_outward_centroidal_ray": true,
      "status": "Proved attractive",
      "certificate": "proofs/entry_90.json",
      "group": "previous-current-base",
      "label": "F(1,X59572)",
      "merge_position": 12,
      "current_base_position": 12,
      "necessity_status": "proved necessary in B41",
      "family_role": "retained B36 rational map",
      "b46_position": 8
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    {
      "position": 19,
      "index": 59639,
      "lambda": "1",
      "list": 2,
      "formula": "2*a**4 + 3*a**3*(b + c) - a**2*(b + c)**2 - a*(b + c)**3 + (b + c)**2*(b**2 + c**2)",
      "rational": true,
      "source": "https://faculty.evansville.edu/ck6/encyclopedia/ETCPart30.html#X59639",
      "method": "supplied prior formula",
      "sharp_outward_centroidal_ray": true,
      "status": "Proved attractive",
      "certificate": "proofs/entry_91.json",
      "group": "previous-current-base",
      "label": "F(1,X59639)",
      "merge_position": 13,
      "current_base_position": 13,
      "necessity_status": "proved necessary in B41",
      "family_role": "retained B36 rational map",
      "b46_position": 9
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    {
      "position": 20,
      "index": 66632,
      "lambda": "1",
      "list": 2,
      "formula": "2*a**3 - a**2*(b + c) + 2*a*b*c + (b - c)**2*(b + c)",
      "rational": true,
      "source": "https://faculty.evansville.edu/ck6/encyclopedia/ETCPart34.html#X66632",
      "method": "supplied prior formula",
      "sharp_outward_centroidal_ray": true,
      "status": "Proved attractive",
      "certificate": "proofs/entry_92.json",
      "group": "previous-current-base",
      "label": "F(1,X66632)",
      "merge_position": 14,
      "current_base_position": 14,
      "necessity_status": "proved necessary in B41",
      "family_role": "retained B36 rational map",
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    {
      "position": 4,
      "index": 2093,
      "endpoint": "Lambda1",
      "lambda": "-2/7",
      "formula": "a*(a**3 + 3*a**2*(b + c) - a*(b + c)**2 - 3*(b - c)**2*(b + c))",
      "source": "Local ETC.mx exported by installed Mathematica; S=twice area",
      "numerical_lambda": "-0.28571428571",
      "historical_record": {
        "Index": 2093,
        "ETCFunction": "a*(a^3 + 3*a^2*(b + c) - 3*(b - c)^2*(b + c) - a*(b + c)^2)"
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      "rational": true,
      "group": "previous-current-base",
      "merge_position": 18,
      "label": "F(-2/7,X2093)",
      "current_base_position": 18,
      "necessity_status": "proved necessary in B41",
      "family_role": "retained B36 rational map",
      "b46_position": 11
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    {
      "position": 11,
      "index": 2255,
      "endpoint": "Lambda1",
      "lambda": "-1/3",
      "formula": "a**2/(a**3 - a**2*(b + c) - a*(b - c)**2 + (b + c)**3)",
      "source": "Local ETC.mx exported by installed Mathematica; S=twice area",
      "numerical_lambda": "-0.33333333333",
      "historical_record": {
        "Index": 2255,
        "ETCFunction": "a^2/(a^3 - a*(b - c)^2 - a^2*(b + c) + (b + c)^3)"
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      "rational": true,
      "group": "previous-current-base",
      "merge_position": 19,
      "label": "F(-1/3,X2255)",
      "current_base_position": 19,
      "necessity_status": "proved necessary in B41",
      "family_role": "retained B36 rational map",
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    {
      "position": 164,
      "index": 3794,
      "endpoint": "Lambda2",
      "lambda": "1",
      "formula": "a*(a + b)*(a + c)*(a - b - c)*(b**2 - b*c + c**2)",
      "source": "Local ETC.mx exported by installed Mathematica; S=twice area",
      "numerical_lambda": "1.0",
      "historical_record": {
        "Index": 3794,
        "ETCFunction": "a*(a + b)*(a - b - c)*(a + c)*(b^2 - b*c + c^2)"
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      "rational": true,
      "group": "previous-current-base",
      "merge_position": 21,
      "label": "F(1,X3794)",
      "current_base_position": 21,
      "necessity_status": "proved necessary in B41",
      "family_role": "retained B36 rational map",
      "b46_position": 13
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    {
      "position": 171,
      "index": 3825,
      "endpoint": "Lambda2",
      "lambda": "8/5",
      "formula": "-a**2*b**2 + 2*a**2*b*c - a**2*c**2 + a*b**2*c + a*b*c**2 + b**4 - 2*b**2*c**2 + c**4",
      "source": "Local ETC.mx exported by installed Mathematica; S=twice area",
      "numerical_lambda": "1.6",
      "historical_record": {
        "Index": 3825,
        "ETCFunction": "-(a^2*b^2) + b^4 + 2*a^2*b*c + a*b^2*c - a^2*c^2 + a*b*c^2 - 2*b^2*c^2 + c^4"
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      "rational": true,
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      "necessity_status": "proved necessary in B41",
      "family_role": "retained B36 rational map",
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    {
      "position": 316,
      "index": 4308,
      "endpoint": "Lambda1",
      "lambda": "-1/2",
      "formula": "(a - b + c)*(a + b - c)*(5*a**2 - 2*a*b - 2*a*c + b**2 + 2*b*c + c**2)",
      "source": "Local ETC.mx exported by installed Mathematica; S=twice area",
      "numerical_lambda": "-0.5",
      "historical_record": {
        "Index": 4308,
        "ETCFunction": "(a + b - c)*(a - b + c)*(5*a^2 - 2*a*b + b^2 - 2*a*c + 2*b*c + c^2)"
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      "rational": true,
      "group": "previous-current-base",
      "merge_position": 25,
      "label": "F(-1/2,X4308)",
      "current_base_position": 25,
      "necessity_status": "proved necessary in B41",
      "family_role": "retained B36 rational map",
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    {
      "position": 344,
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      "endpoint": "Lambda2",
      "lambda": "1",
      "formula": "(a - b - c)*(3*a**2*b + 3*a**2*c + 4*a*b**2 - 8*a*b*c + 4*a*c**2 + b**3 - b**2*c - b*c**2 + c**3)",
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      "numerical_lambda": "1.0",
      "historical_record": {
        "Index": 4342,
        "ETCFunction": "(a - b - c)*(3*a^2*b + 4*a*b^2 + b^3 + 3*a^2*c - 8*a*b*c - b^2*c + 4*a*c^2 - b*c^2 + c^3)"
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      "rational": true,
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      "merge_position": 27,
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      "necessity_status": "proved necessary in B41",
      "family_role": "retained B36 rational map",
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    {
      "position": 378,
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      "endpoint": "Lambda1",
      "lambda": "-2",
      "formula": "a**3 - a*b**2 - a*c**2 + b**3 + c**3",
      "source": "Local ETC.mx exported by installed Mathematica; S=twice area",
      "numerical_lambda": "-2.0",
      "historical_record": {
        "Index": 4438,
        "ETCFunction": "a^3 - a*b^2 + b^3 - a*c^2 + c^3"
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      "rational": true,
      "group": "previous-current-base",
      "merge_position": 28,
      "label": "F(-2,X4438)",
      "current_base_position": 28,
      "necessity_status": "proved necessary in B41",
      "family_role": "retained B36 rational map",
      "b46_position": 17
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    {
      "position": 479,
      "index": 4911,
      "endpoint": "Lambda2",
      "lambda": "2/5",
      "formula": "a**4 + a**2*b*c - b**4 + b**3*c + b*c**3 - c**4",
      "source": "Local ETC.mx exported by installed Mathematica; S=twice area",
      "numerical_lambda": "0.40000000831",
      "historical_record": {
        "Index": 4911,
        "ETCFunction": "a^4 - b^4 + a^2*b*c + b^3*c + b*c^3 - c^4"
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      "rational": true,
      "group": "previous-current-base",
      "merge_position": 30,
      "label": "F(2/5,X4911)",
      "current_base_position": 30,
      "necessity_status": "proved necessary in B41",
      "family_role": "retained B36 rational map",
      "b46_position": 18
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    {
      "position": 98,
      "index": 5310,
      "endpoint": "Lambda1",
      "lambda": "-1/4",
      "formula": "a**2*(a**4 - a**2*b*c - b**4 - b**3*c - b*c**3 - c**4)",
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      "historical_record": {
        "Index": 5310,
        "ETCFunction": "a^2*(a^4 - b^4 - a^2*b*c - b^3*c - b*c^3 - c^4)"
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      "rational": true,
      "group": "previous-current-base",
      "merge_position": 32,
      "label": "F(-1/4,X5310)",
      "current_base_position": 32,
      "necessity_status": "proved necessary in B41",
      "family_role": "retained B36 rational map",
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    {
      "position": 185,
      "index": 5741,
      "endpoint": "Lambda1",
      "lambda": "-1/2",
      "formula": "-a**2*b - a**2*c + 2*a*b*c + b**3 + c**3",
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      "numerical_lambda": "-0.5",
      "historical_record": {
        "Index": 5741,
        "ETCFunction": "-(a^2*b) + b^3 - a^2*c + 2*a*b*c + c^3"
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      "rational": true,
      "group": "previous-current-base",
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      "label": "F(-1/2,X5741)",
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      "necessity_status": "proved necessary in B41",
      "family_role": "retained B36 rational map",
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    {
      "position": 244,
      "index": 6205,
      "endpoint": "Lambda1",
      "lambda": "-1/2",
      "formula": "a*(a**3 + 2*a**2*b + 2*a**2*c - 2*a*b**2 - 2*a*c**2 - b**3 + 2*b**2*c + 2*b*c**2 - c**3)",
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      "historical_record": {
        "Index": 6205,
        "ETCFunction": "a*(a^3 + 2*a^2*b - 2*a*b^2 - b^3 + 2*a^2*c + 2*b^2*c - 2*a*c^2 + 2*b*c^2 - c^3)"
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      "necessity_status": "proved necessary in B41",
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    {
      "position": 457,
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      "endpoint": "Lambda1",
      "lambda": "-4/3",
      "formula": "-a**4 + 2*a**2*b**2 + 2*a**2*c**2 + 2*b**4 - 2*b**2*c**2 + 2*c**4",
      "source": "ETC_X1_X72807.wxf; SHA256 ACE501D40DD83785F89B4DE8E4DDCC0C5081D82DE82E1BAF37816D10E547CBFA; S=twice area",
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      "historical_record": {
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        "ETCFunction": "-a^4 + 2*a^2*b^2 + 2*b^4 + 2*a^2*c^2 - 2*b^2*c^2 + 2*c^4"
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      "group": "previous-current-base",
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      "label": "F(-4/3,X7872)",
      "current_base_position": 36,
      "necessity_status": "proved necessary in B41",
      "family_role": "retained B36 rational map",
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    {
      "position": 618,
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      "endpoint": "Lambda2",
      "lambda": "5/11",
      "formula": "-a**4 + 2*a**2*b**2 - 2*a**2*b*c + 2*a**2*c**2 + b**4 - 2*b**2*c**2 + c**4",
      "source": "ETC_X1_X72807.wxf; SHA256 ACE501D40DD83785F89B4DE8E4DDCC0C5081D82DE82E1BAF37816D10E547CBFA; S=twice area",
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        "ETCFunction": "-a^4 + 2*a^2*b^2 + b^4 - 2*a^2*b*c + 2*a^2*c^2 - 2*b^2*c^2 + c^4"
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      "rational": true,
      "group": "previous-current-base",
      "merge_position": 37,
      "label": "F(5/11,X9597)",
      "current_base_position": 37,
      "necessity_status": "proved necessary in B41",
      "family_role": "retained B36 rational map",
      "b46_position": 23
    },
    {
      "position": 672,
      "index": 10000,
      "endpoint": "Lambda2",
      "lambda": "7/6",
      "formula": "a**8 + a**4*b**4 + a**4*b**2*c**2 + a**4*c**4 + a**2*b**4*c**2 + a**2*b**2*c**4 + b**6*c**2 + b**4*c**4 + b**2*c**6",
      "source": "ETC_X1_X72807.wxf; SHA256 ACE501D40DD83785F89B4DE8E4DDCC0C5081D82DE82E1BAF37816D10E547CBFA; S=twice area",
      "numerical_lambda": "1.1666666667",
      "historical_record": {
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      },
      "rational": true,
      "group": "previous-current-base",
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      "label": "F(7/6,X10000)",
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      "necessity_status": "proved necessary in B41",
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      "b46_position": 24
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    {
      "id": "X11164_L1d2",
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      "parameter": "1/2",
      "formula": "13*a**4 - 7*a**2*b**2 - 7*a**2*c**2 - 2*b**4 + 14*b**2*c**2 - 2*c**4",
      "certificate_file": "X10001-X20000\\exact\\X11164_L1d2.json",
      "label": "F(1/2,X11164)",
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      "family_role": "certified enlargement",
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    {
      "id": "X11373_Lm1d2",
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      "parameter": "-1/2",
      "formula": "a**4 - a**3*b - a**3*c - 2*a**2*b**2 + 6*a**2*b*c - 2*a**2*c**2 + a*b**3 - a*b**2*c - a*b*c**2 + a*c**3 + b**4 - 2*b**2*c**2 + c**4",
      "certificate_file": "X10001-X20000\\exact\\X11373_Lm1d2.json",
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      "separation_gap_lower": "0.030882634703091474735967109254731776761109246314836736820498969735",
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      "family_role": "certified enlargement",
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    {
      "id": "X10935_L1",
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      "parameter": "1",
      "formula": "-a**10 + 4*a**9*b + 4*a**9*c - 3*a**8*b**2 - 22*a**8*b*c - 3*a**8*c**2 - 8*a**7*b**3 + 40*a**7*b**2*c + 40*a**7*b*c**2 - 8*a**7*c**3 + 14*a**6*b**4 + 4*a**6*b**3*c - 120*a**6*b**2*c**2 + 4*a**6*b*c**3 + 14*a**6*c**4 - 80*a**5*b**4*c + 112*a**5*b**3*c**2 + 112*a**5*b**2*c**3 - 80*a**5*b*c**4 - 14*a**4*b**6 + 56*a**4*b**5*c + 70*a**4*b**4*c**2 - 272*a**4*b**3*c**3 + 70*a**4*b**2*c**4 + 56*a**4*b*c**5 - 14*a**4*c**6 + 8*a**3*b**7 + 24*a**3*b**6*c - 152*a**3*b**5*c**2 + 120*a**3*b**4*c**3 + 120*a**3*b**3*c**4 - 152*a**3*b**2*c**5 + 24*a**3*b*c**6 + 8*a**3*c**7 + 3*a**2*b**8 - 36*a**2*b**7*c + 56*a**2*b**6*c**2 + 36*a**2*b**5*c**3 - 118*a**2*b**4*c**4 + 36*a**2*b**3*c**5 + 56*a**2*b**2*c**6 - 36*a**2*b*c**7 + 3*a**2*c**8 - 4*a*b**9 + 12*a*b**8*c - 32*a*b**6*c**3 + 24*a*b**5*c**4 + 24*a*b**4*c**5 - 32*a*b**3*c**6 + 12*a*b*c**8 - 4*a*c**9 + b**10 - 2*b**9*c - 3*b**8*c**2 + 8*b**7*c**3 + 2*b**6*c**4 - 12*b**5*c**5 + 2*b**4*c**6 + 8*b**3*c**7 - 3*b**2*c**8 - 2*b*c**9 + c**10",
      "certificate_file": "X10001-X20000\\exact\\X10935_L1.json",
      "label": "F(1,X10935)",
      "sides_abc": [
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        11,
        3
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      "separation_gap_lower": "0.0068170791448145663847895231549941760341037297784904181711871550845",
      "sharp_ray_endpoint": true,
      "lambda": "1",
      "family_role": "certified enlargement",
      "b46_position": 27
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    {
      "id": "X18236_L1",
      "index": 18236,
      "parameter": "1",
      "formula": "a**5*b + a**5*c - 2*a**4*b**2 - 4*a**4*b*c - 2*a**4*c**2 + 6*a**3*b**2*c + 6*a**3*b*c**2 + 2*a**2*b**4 - 12*a**2*b**2*c**2 + 2*a**2*c**4 - a*b**5 - 3*a*b**4*c + 4*a*b**3*c**2 + 4*a*b**2*c**3 - 3*a*b*c**4 - a*c**5",
      "certificate_file": "X10001-X20000\\exact\\X18236_L1.json",
      "label": "F(1,X18236)",
      "sides_abc": [
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        11,
        3
      ],
      "separation_gap_lower": "0.0022730339613386971712157334327182139735865362201540354054953370293",
      "sharp_ray_endpoint": true,
      "lambda": "1",
      "family_role": "certified enlargement",
      "b46_position": 28
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    {
      "id": "X13725_Lm27d2",
      "index": 13725,
      "parameter": "-27/2",
      "formula": "a**4 - 2*a**3*b - 2*a**3*c - 4*a**2*b**2 - 6*a**2*b*c - 4*a**2*c**2 - 2*a*b**3 - 6*a*b**2*c - 6*a*b*c**2 - 2*a*c**3 - b**4 - 2*b**3*c - 2*b**2*c**2 - 2*b*c**3 - c**4",
      "certificate_file": "X10001-X20000\\exact\\X13725_Lm27d2.json",
      "label": "F(-27/2,X13725)",
      "sides_abc": [
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        11,
        5
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      "separation_gap_lower": "0.13186326781579735909147957798742249712332848866911934580480224517",
      "sharp_ray_endpoint": true,
      "lambda": "-27/2",
      "family_role": "certified enlargement",
      "b46_position": 29
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    {
      "id": "X10324_Lm2d7",
      "index": 10324,
      "parameter": "-2/7",
      "formula": "3*a**4*b + 3*a**4*c - 8*a**3*b**2 - 4*a**3*b*c - 8*a**3*c**2 + 6*a**2*b**3 + 14*a**2*b**2*c + 14*a**2*b*c**2 + 6*a**2*c**3 - 12*a*b**3*c - 8*a*b**2*c**2 - 12*a*b*c**3 - b**5 - b**4*c + 2*b**3*c**2 + 2*b**2*c**3 - b*c**4 - c**5",
      "certificate_file": "X10001-X20000\\exact\\X10324_Lm2d7.json",
      "label": "F(-2/7,X10324)",
      "sides_abc": [
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        23,
        31
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      "separation_gap_lower": "0.0018964517578417781953846897903326196922890219690504416689099607561",
      "sharp_ray_endpoint": true,
      "lambda": "-2/7",
      "family_role": "certified enlargement",
      "b46_position": 30
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    {
      "id": "X10978_L1d10",
      "index": 10978,
      "parameter": "1/10",
      "formula": "3*a**5 - 3*a**4*b - 3*a**4*c - 6*a**3*b**2 - 2*a**3*b*c - 6*a**3*c**2 + 6*a**2*b**3 + 8*a**2*b**2*c + 8*a**2*b*c**2 + 6*a**2*c**3 + 3*a*b**4 + 2*a*b**3*c + 6*a*b**2*c**2 + 2*a*b*c**3 + 3*a*c**4 - 3*b**5 - 5*b**4*c - 8*b**3*c**2 - 8*b**2*c**3 - 5*b*c**4 - 3*c**5",
      "certificate_file": "X10001-X20000\\exact\\X10978_L1d10.json",
      "label": "F(1/10,X10978)",
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        23,
        31
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      "separation_gap_lower": "0.0097889190886634878161724967652874461214109926471909135671091479104",
      "sharp_ray_endpoint": true,
      "lambda": "1/10",
      "family_role": "certified enlargement",
      "b46_position": 31
    },
    {
      "id": "X14997_L5d12",
      "index": 14997,
      "parameter": "5/12",
      "formula": "2*a**3 + 2*a**2*b + 2*a**2*c - 3*a*b*c",
      "certificate_file": "X10001-X20000\\exact\\X14997_L5d12.json",
      "label": "F(5/12,X14997)",
      "sides_abc": [
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        31
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      "separation_gap_lower": "0.0050410936201912325273607895955222034321845913064876704740295726894",
      "sharp_ray_endpoint": true,
      "lambda": "5/12",
      "family_role": "certified enlargement",
      "b46_position": 32
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    {
      "id": "X10321_L1",
      "index": 10321,
      "parameter": "1",
      "formula": "a**7 - a**6*b - a**6*c - 3*a**5*b**2 + 2*a**5*b*c - 3*a**5*c**2 + 3*a**4*b**3 + a**4*b**2*c + a**4*b*c**2 + 3*a**4*c**3 + 3*a**3*b**4 - 4*a**3*b**3*c - 6*a**3*b**2*c**2 - 4*a**3*b*c**3 + 3*a**3*c**4 - 3*a**2*b**5 + a**2*b**4*c + 2*a**2*b**3*c**2 + 2*a**2*b**2*c**3 + a**2*b*c**4 - 3*a**2*c**5 - a*b**6 + 2*a*b**5*c + a*b**4*c**2 - 4*a*b**3*c**3 + a*b**2*c**4 + 2*a*b*c**5 - a*c**6 + b**7 - b**6*c - 3*b**5*c**2 + 3*b**4*c**3 + 3*b**3*c**4 - 3*b**2*c**5 - b*c**6 + c**7",
      "certificate_file": "X10001-X20000\\exact\\X10321_L1.json",
      "label": "F(1,X10321)",
      "sides_abc": [
        24,
        23,
        31
      ],
      "separation_gap_lower": "0.0010366992214284720659750175419005466997942593277303279805058272906",
      "sharp_ray_endpoint": true,
      "lambda": "1",
      "family_role": "certified enlargement",
      "b46_position": 33
    },
    {
      "label": "M_-",
      "kind": "power minimizer",
      "p": "4-2*sqrt(2)",
      "family_role": "retained B36 power map",
      "b46_position": 34
    },
    {
      "label": "M_+",
      "kind": "power minimizer",
      "p": "4+2*sqrt(2)",
      "family_role": "retained B36 power map",
      "b46_position": 35
    },
    {
      "index": 24211,
      "lambda": "1",
      "kind": "source",
      "formula": "a**3*b + a**3*c + a*b**2*c + a*b*c**2 + b**4 - b**3*c - b*c**3 + c**4",
      "id": "X24211_L1",
      "label": "F(1,X24211)",
      "certificate_file": "MINIMAL_BASE_NATIVE_CERTS\\exact\\X24211_L1.json",
      "status": "exact PSD plus distinct-flat regularity; independently replayed",
      "b46_position": 36
    },
    {
      "index": 24212,
      "lambda": "1",
      "kind": "source",
      "formula": "a**3*b**2 + a**3*c**2 + a*b**4 - a*b**3*c + 2*a*b**2*c**2 - a*b*c**3 + a*c**4 + b**4*c - b**3*c**2 - b**2*c**3 + b*c**4",
      "id": "X24212_L1",
      "label": "F(1,X24212)",
      "certificate_file": "MINIMAL_BASE_NATIVE_CERTS\\exact\\X24212_L1.json",
      "status": "exact PSD plus distinct-flat regularity; independently replayed",
      "b46_position": 37
    },
    {
      "index": 24217,
      "lambda": "1",
      "kind": "source",
      "formula": "a**2*b + a**2*c - a*b**2 + 3*a*b*c - a*c**2 + b**3 - b**2*c - b*c**2 + c**3",
      "id": "X24217_L1",
      "label": "F(1,X24217)",
      "certificate_file": "MINIMAL_BASE_NATIVE_CERTS\\exact\\X24217_L1.json",
      "status": "exact PSD plus distinct-flat regularity; independently replayed",
      "b46_position": 38
    },
    {
      "index": 35999,
      "lambda": "1",
      "kind": "source",
      "formula": "a**6*b + a**6*c + a**5*b**2 + 2*a**5*b*c + a**5*c**2 - a**4*b**3 + a**4*b**2*c + a**4*b*c**2 - a**4*c**3 - a**3*b**4 - a**3*c**4 + a**2*b**3*c**2 + a**2*b**2*c**3 + a*b**4*c**2 + 2*a*b**3*c**3 + a*b**2*c**4",
      "id": "X35999_L1",
      "label": "F(1,X35999)",
      "certificate_file": "MINIMAL_BASE_NATIVE_CERTS\\exact\\X35999_L1.json",
      "status": "exact PSD plus distinct-flat regularity; independently replayed",
      "b46_position": 39
    },
    {
      "index": 37280,
      "lambda": "1",
      "kind": "source",
      "formula": "a**5 + 3*a**4*b + 3*a**4*c - 2*a**3*b**2 + 2*a**3*b*c - 2*a**3*c**2 - 2*a**2*b**3 - 2*a**2*c**3 + a*b**4 + 2*a*b**3*c + 2*a*b**2*c**2 + 2*a*b*c**3 + a*c**4 - b**5 + b**4*c + b*c**4 - c**5",
      "id": "X37280_L1",
      "label": "F(1,X37280)",
      "certificate_file": "MINIMAL_BASE_NATIVE_CERTS\\exact\\X37280_L1.json",
      "status": "exact PSD plus distinct-flat regularity; independently replayed",
      "b46_position": 40
    },
    {
      "index": 43180,
      "lambda": "1",
      "kind": "source",
      "formula": "2*a**3 + 5*a**2*b + 5*a**2*c - 4*a*b**2 + 8*a*b*c - 4*a*c**2 - 3*b**3 + 3*b**2*c + 3*b*c**2 - 3*c**3",
      "id": "X43180_L1",
      "label": "F(1,X43180)",
      "certificate_file": "MINIMAL_BASE_NATIVE_CERTS\\exact\\X43180_L1.json",
      "status": "exact PSD plus distinct-flat regularity; independently replayed",
      "b46_position": 41
    },
    {
      "index": 59689,
      "lambda": "1",
      "kind": "source",
      "formula": "3*a**4*b + 3*a**4*c - a**3*b**2 - a**3*c**2 - 3*a**2*b**3 - a**2*b**2*c - a**2*b*c**2 - 3*a**2*c**3 + a*b**4 + 2*a*b**3*c + 2*a*b**2*c**2 + 2*a*b*c**3 + a*c**4",
      "id": "X59689_L1",
      "label": "F(1,X59689)",
      "certificate_file": "MINIMAL_BASE_NATIVE_CERTS\\exact\\X59689_L1.json",
      "status": "exact PSD plus distinct-flat regularity; independently replayed",
      "b46_position": 42
    },
    {
      "index": 68177,
      "lambda": "1",
      "kind": "source",
      "formula": "-6*a**4 + a**2*b**2 + a**2*c**2 + b**4 - 6*b**2*c**2 + c**4",
      "id": "X68177_L1",
      "label": "F(1,X68177)",
      "certificate_file": "MINIMAL_BASE_NATIVE_CERTS\\exact\\X68177_L1.json",
      "status": "exact PSD plus distinct-flat regularity; independently replayed",
      "b46_position": 43
    },
    {
      "index": 32979,
      "lambda_value": "1",
      "lambda": "1",
      "formula": "5*a**4 + 2*a**2*b**2 + 2*a**2*c**2 - 3*b**4 + 10*b**2*c**2 - 3*c**4",
      "label": "F(1,X32979)",
      "status": "Proved attractive; independent exact derivative/PSD replay passed",
      "certificate": "REMAINING_ENLARGEMENTS/boundary_square/X32979.json",
      "b46_position": 44
    },
    {
      "index": 37608,
      "lambda_value": "1",
      "lambda": "1",
      "formula": "2*a**4 + a**3*b + a**3*c - a**2*b**2 + 3*a**2*b*c - a**2*c**2 + a*b**2*c + a*b*c**2",
      "label": "F(1,X37608)",
      "status": "Proved attractive; independent exact derivative/PSD replay passed",
      "certificate": "REMAINING_ENLARGEMENTS/exact/X37608.json",
      "b46_position": 45
    },
    {
      "index": 69251,
      "lambda_value": "1",
      "lambda": "1",
      "formula": "a*b**2 - 2*a*b*c + a*c**2 + b**3 + c**3",
      "label": "F(1,X69251)",
      "status": "Proved attractive; independent exact derivative/PSD replay passed",
      "certificate": "REMAINING_ENLARGEMENTS/midline_square/X69251.json",
      "b46_position": 46
    }
  ]
}