claim2_rows.json

[
 {
  "n_stationary_isolated": 81,
  "n_integral": 10,
  "n_nonintegral": 71,
  "integral_localmax_thm36": 10,
  "integral_localmax_D4": 10,
  "integral_NOT_localmax": 0,
  "certs_disagree": 0,
  "ascent_found_inside_radius": 0,
  "ascent_found_at_4x_radius": 0,
  "localmax_probed": 10,
  "nonintegral_strict_saddle": 71,
  "nonintegral_no_saddle_cert": 0,
  "min_saddle_curvature": "1",
  "min_localmax_sigma": "1/2",
  "min_localmax_radius": 0.09090909090909091,
  "n_families": 0,
  "n_unhandled": 0,
  "families_all_nonintegral_with_cert": true,
  "counterexamples": [],
  "curvature_ge_2lam_minus_2": true,
  "sigma_ge_lam_minus_1": true,
  "graph": "K5 clique",
  "n": 5,
  "k": 2,
  "lam": "3/2",
  "arm": "main"
 },
 {
  "n_stationary_isolated": 81,
  "n_integral": 10,
  "n_nonintegral": 71,
  "integral_localmax_thm36": 10,
  "integral_localmax_D4": 10,
  "integral_NOT_localmax": 0,
  "certs_disagree": 0,
  "ascent_found_inside_radius": 0,
  "ascent_found_at_4x_radius": 0,
  "localmax_probed": 10,
  "nonintegral_strict_saddle": 71,
  "nonintegral_no_saddle_cert": 0,
  "min_saddle_curvature": "2",
  "min_localmax_sigma": "1",
  "min_localmax_radius": 0.16666666666666666,
  "n_families": 0,
  "n_unhandled": 0,
  "families_all_nonintegral_with_cert": true,
  "counterexamples": [],
  "curvature_ge_2lam_minus_2": true,
  "sigma_ge_lam_minus_1": true,
  "graph": "K5 clique",
  "n": 5,
  "k": 2,
  "lam": "2",
  "arm": "M1_lam_integral"
 },
 {
  "n_stationary_isolated": 1,
  "n_integral": 0,
  "n_nonintegral": 1,
  "integral_localmax_thm36": 0,
  "integral_localmax_D4": 0,
  "integral_NOT_localmax": 0,
  "certs_disagree": 0,
  "ascent_found_inside_radius": 0,
  "ascent_found_at_4x_radius": 0,
  "localmax_probed": 0,
  "nonintegral_strict_saddle": 0,
  "nonintegral_no_saddle_cert": 1,
  "min_saddle_curvature": null,
  "min_localmax_sigma": null,
  "min_localmax_radius": null,
  "n_families": 0,
  "n_unhandled": 0,
  "families_all_nonintegral_with_cert": true,
  "counterexamples": [
   {
    "type": "non-integral stationary with no strict-saddle certificate",
    "Sf": [
     0,
     1,
     2,
     3,
     4
    ],
    "x": [
     "2/5",
     "2/5",
     "2/5",
     "2/5",
     "2/5"
    ]
   }
  ],
  "curvature_ge_2lam_minus_2": true,
  "sigma_ge_lam_minus_1": true,
  "graph": "K5 clique",
  "n": 5,
  "k": 2,
  "lam": "1/2",
  "arm": "M2_lam_lt_1"
 },
 {
  "n_stationary_isolated": 81,
  "n_integral": 10,
  "n_nonintegral": 71,
  "integral_localmax_thm36": 10,
  "integral_localmax_D4": 10,
  "integral_NOT_localmax": 0,
  "certs_disagree": 0,
  "ascent_found_inside_radius": 0,
  "ascent_found_at_4x_radius": 0,
  "localmax_probed": 10,
  "nonintegral_strict_saddle": 71,
  "nonintegral_no_saddle_cert": 0,
  "min_saddle_curvature": "1",
  "min_localmax_sigma": "1/2",
  "min_localmax_radius": 0.09090909090909091,
  "n_families": 0,
  "n_unhandled": 0,
  "families_all_nonintegral_with_cert": true,
  "counterexamples": [],
  "curvature_ge_2lam_minus_2": true,
  "sigma_ge_lam_minus_1": true,
  "graph": "K5 clique",
  "n": 5,
  "k": 3,
  "lam": "3/2",
  "arm": "main"
 },
 {
  "n_stationary_isolated": 81,
  "n_integral": 10,
  "n_nonintegral": 71,
  "integral_localmax_thm36": 10,
  "integral_localmax_D4": 10,
  "integral_NOT_localmax": 0,
  "certs_disagree": 0,
  "ascent_found_inside_radius": 0,
  "ascent_found_at_4x_radius": 0,
  "localmax_probed": 10,
  "nonintegral_strict_saddle": 71,
  "nonintegral_no_saddle_cert": 0,
  "min_saddle_curvature": "2",
  "min_localmax_sigma": "1",
  "min_localmax_radius": 0.16666666666666666,
  "n_families": 0,
  "n_unhandled": 0,
  "families_all_nonintegral_with_cert": true,
  "counterexamples": [],
  "curvature_ge_2lam_minus_2": true,
  "sigma_ge_lam_minus_1": true,
  "graph": "K5 clique",
  "n": 5,
  "k": 3,
  "lam": "2",
  "arm": "M1_lam_integral"
 },
 {
  "n_stationary_isolated": 1,
  "n_integral": 0,
  "n_nonintegral": 1,
  "integral_localmax_thm36": 0,
  "integral_localmax_D4": 0,
  "integral_NOT_localmax": 0,
  "certs_disagree": 0,
  "ascent_found_inside_radius": 0,
  "ascent_found_at_4x_radius": 0,
  "localmax_probed": 0,
  "nonintegral_strict_saddle": 0,
  "nonintegral_no_saddle_cert": 1,
  "min_saddle_curvature": null,
  "min_localmax_sigma": null,
  "min_localmax_radius": null,
  "n_families": 0,
  "n_unhandled": 0,
  "families_all_nonintegral_with_cert": true,
  "counterexamples": [
   {
    "type": "non-integral stationary with no strict-saddle certificate",
    "Sf": [
     0,
     1,
     2,
     3,
     4
    ],
    "x": [
     "3/5",
     "3/5",
     "3/5",
     "3/5",
     "3/5"
    ]
   }
  ],
  "curvature_ge_2lam_minus_2": true,
  "sigma_ge_lam_minus_1": true,
  "graph": "K5 clique",
  "n": 5,
  "k": 3,
  "lam": "1/2",
  "arm": "M2_lam_lt_1"
 },
 {
  "n_stationary_isolated": 31,
  "n_integral": 5,
  "n_nonintegral": 26,
  "integral_localmax_thm36": 5,
  "integral_localmax_D4": 5,
  "integral_NOT_localmax": 0,
  "certs_disagree": 0,
  "ascent_found_inside_radius": 0,
  "ascent_found_at_4x_radius": 0,
  "localmax_probed": 5,
  "nonintegral_strict_saddle": 26,
  "nonintegral_no_saddle_cert": 0,
  "min_saddle_curvature": "1",
  "min_localmax_sigma": "1/2",
  "min_localmax_radius": 0.09090909090909091,
  "n_families": 0,
  "n_unhandled": 0,
  "families_all_nonintegral_with_cert": true,
  "counterexamples": [],
  "curvature_ge_2lam_minus_2": true,
  "sigma_ge_lam_minus_1": true,
  "graph": "K5 clique",
  "n": 5,
  "k": 4,
  "lam": "3/2",
  "arm": "main"
 },
 {
  "n_stationary_isolated": 31,
  "n_integral": 5,
  "n_nonintegral": 26,
  "integral_localmax_thm36": 5,
  "integral_localmax_D4": 5,
  "integral_NOT_localmax": 0,
  "certs_disagree": 0,
  "ascent_found_inside_radius": 0,
  "ascent_found_at_4x_radius": 0,
  "localmax_probed": 5,
  "nonintegral_strict_saddle": 26,
  "nonintegral_no_saddle_cert": 0,
  "min_saddle_curvature": "2",
  "min_localmax_sigma": "1",
  "min_localmax_radius": 0.16666666666666666,
  "n_families": 0,
  "n_unhandled": 0,
  "families_all_nonintegral_with_cert": true,
  "counterexamples": [],
  "curvature_ge_2lam_minus_2": true,
  "sigma_ge_lam_minus_1": true,
  "graph": "K5 clique",
  "n": 5,
  "k": 4,
  "lam": "2",
  "arm": "M1_lam_integral"
 },
 {
  "n_stationary_isolated": 1,
  "n_integral": 0,
  "n_nonintegral": 1,
  "integral_localmax_thm36": 0,
  "integral_localmax_D4": 0,
  "integral_NOT_localmax": 0,
  "certs_disagree": 0,
  "ascent_found_inside_radius": 0,
  "ascent_found_at_4x_radius": 0,
  "localmax_probed": 0,
  "nonintegral_strict_saddle": 0,
  "nonintegral_no_saddle_cert": 1,
  "min_saddle_curvature": null,
  "min_localmax_sigma": null,
  "min_localmax_radius": null,
  "n_families": 0,
  "n_unhandled": 0,
  "families_all_nonintegral_with_cert": true,
  "counterexamples": [
   {
    "type": "non-integral stationary with no strict-saddle certificate",
    "Sf": [
     0,
     1,
     2,
     3,
     4
    ],
    "x": [
     "4/5",
     "4/5",
     "4/5",
     "4/5",
     "4/5"
    ]
   }
  ],
  "curvature_ge_2lam_minus_2": true,
  "sigma_ge_lam_minus_1": true,
  "graph": "K5 clique",
  "n": 5,
  "k": 4,
  "lam": "1/2",
  "arm": "M2_lam_lt_1"
 },
 {
  "n_stationary_isolated": 43,
  "n_integral": 9,
  "n_nonintegral": 34,
  "integral_localmax_thm36": 9,
  "integral_localmax_D4": 9,
  "integral_NOT_localmax": 0,
  "certs_disagree": 0,
  "ascent_found_inside_radius": 0,
  "ascent_found_at_4x_radius": 0,
  "localmax_probed": 9,
  "nonintegral_strict_saddle": 34,
  "nonintegral_no_saddle_cert": 0,
  "min_saddle_curvature": "3",
  "min_localmax_sigma": "1/2",
  "min_localmax_radius": 0.14285714285714285,
  "n_families": 0,
  "n_unhandled": 0,
  "families_all_nonintegral_with_cert": true,
  "counterexamples": [],
  "curvature_ge_2lam_minus_2": true,
  "sigma_ge_lam_minus_1": true,
  "graph": "C6 cycle",
  "n": 6,
  "k": 2,
  "lam": "3/2",
  "arm": "main"
 },
 {
  "n_stationary_isolated": 74,
  "n_integral": 15,
  "n_nonintegral": 59,
  "integral_localmax_thm36": 9,
  "integral_localmax_D4": 9,
  "integral_NOT_localmax": 6,
  "certs_disagree": 0,
  "ascent_found_inside_radius": 0,
  "ascent_found_at_4x_radius": 0,
  "localmax_probed": 9,
  "nonintegral_strict_saddle": 59,
  "nonintegral_no_saddle_cert": 0,
  "min_saddle_curvature": "2",
  "min_localmax_sigma": "0",
  "min_localmax_radius": 0.25,
  "n_families": 1,
  "n_unhandled": 0,
  "families_all_nonintegral_with_cert": true,
  "counterexamples": [
   {
    "type": "integral stationary but not local max",
    "S1": [
     0,
     2
    ],
    "sigma": "0"
   },
   {
    "type": "integral stationary but not local max",
    "S1": [
     0,
     4
    ],
    "sigma": "0"
   },
   {
    "type": "integral stationary but not local max",
    "S1": [
     1,
     3
    ],
    "sigma": "0"
   },
   {
    "type": "integral stationary but not local max",
    "S1": [
     1,
     5
    ],
    "sigma": "0"
   },
   {
    "type": "integral stationary but not local max",
    "S1": [
     2,
     4
    ],
    "sigma": "0"
   },
   {
    "type": "integral stationary but not local max",
    "S1": [
     3,
     5
    ],
    "sigma": "0"
   }
  ],
  "curvature_ge_2lam_minus_2": true,
  "sigma_ge_lam_minus_1": false,
  "graph": "C6 cycle",
  "n": 6,
  "k": 2,
  "lam": "2",
  "arm": "M1_lam_integral"
 },
 {
  "n_stationary_isolated": 13,
  "n_integral": 6,
  "n_nonintegral": 7,
  "integral_localmax_thm36": 6,
  "integral_localmax_D4": 6,
  "integral_NOT_localmax": 0,
  "certs_disagree": 0,
  "ascent_found_inside_radius": 0,
  "ascent_found_at_4x_radius": 0,
  "localmax_probed": 6,
  "nonintegral_strict_saddle": 7,
  "nonintegral_no_saddle_cert": 0,
  "min_saddle_curvature": "1",
  "min_localmax_sigma": "1/2",
  "min_localmax_radius": 0.2,
  "n_families": 0,
  "n_unhandled": 0,
  "families_all_nonintegral_with_cert": true,
  "counterexamples": [],
  "curvature_ge_2lam_minus_2": true,
  "sigma_ge_lam_minus_1": true,
  "graph": "C6 cycle",
  "n": 6,
  "k": 2,
  "lam": "1/2",
  "arm": "M2_lam_lt_1"
 },
 {
  "n_stationary_isolated": 61,
  "n_integral": 6,
  "n_nonintegral": 55,
  "integral_localmax_thm36": 6,
  "integral_localmax_D4": 6,
  "integral_NOT_localmax": 0,
  "certs_disagree": 0,
  "ascent_found_inside_radius": 0,
  "ascent_found_at_4x_radius": 0,
  "localmax_probed": 6,
  "nonintegral_strict_saddle": 55,
  "nonintegral_no_saddle_cert": 0,
  "min_saddle_curvature": "3",
  "min_localmax_sigma": "3/2",
  "min_localmax_radius": 0.42857142857142855,
  "n_families": 0,
  "n_unhandled": 0,
  "families_all_nonintegral_with_cert": true,
  "counterexamples": [],
  "curvature_ge_2lam_minus_2": true,
  "sigma_ge_lam_minus_1": true,
  "graph": "C6 cycle",
  "n": 6,
  "k": 3,
  "lam": "3/2",
  "arm": "main"
 },
 {
  "n_stationary_isolated": 98,
  "n_integral": 20,
  "n_nonintegral": 78,
  "integral_localmax_thm36": 6,
  "integral_localmax_D4": 6,
  "integral_NOT_localmax": 14,
  "certs_disagree": 0,
  "ascent_found_inside_radius": 0,
  "ascent_found_at_4x_radius": 0,
  "localmax_probed": 6,
  "nonintegral_strict_saddle": 78,
  "nonintegral_no_saddle_cert": 0,
  "min_saddle_curvature": "2",
  "min_localmax_sigma": "0",
  "min_localmax_radius": 0.5,
  "n_families": 1,
  "n_unhandled": 0,
  "families_all_nonintegral_with_cert": true,
  "counterexamples": [
   {
    "type": "integral stationary but not local max",
    "S1": [
     0,
     1,
     3
    ],
    "sigma": "0"
   },
   {
    "type": "integral stationary but not local max",
    "S1": [
     0,
     1,
     4
    ],
    "sigma": "0"
   },
   {
    "type": "integral stationary but not local max",
    "S1": [
     0,
     2,
     3
    ],
    "sigma": "0"
   },
   {
    "type": "integral stationary but not local max",
    "S1": [
     0,
     2,
     4
    ],
    "sigma": "0"
   },
   {
    "type": "integral stationary but not local max",
    "S1": [
     0,
     2,
     5
    ],
    "sigma": "0"
   },
   {
    "type": "integral stationary but not local max",
    "S1": [
     0,
     3,
     4
    ],
    "sigma": "0"
   },
   {
    "type": "integral stationary but not local max",
    "S1": [
     0,
     3,
     5
    ],
    "sigma": "0"
   },
   {
    "type": "integral stationary but not local max",
    "S1": [
     1,
     2,
     4
    ],
    "sigma": "0"
   },
   {
    "type": "integral stationary but not local max",
    "S1": [
     1,
     2,
     5
    ],
    "sigma": "0"
   },
   {
    "type": "integral stationary but not local max",
    "S1": [
     1,
     3,
     4
    ],
    "sigma": "0"
   },
   {
    "type": "integral stationary but not local max",
    "S1": [
     1,
     3,
     5
    ],
    "sigma": "0"
   },
   {
    "type": "integral stationary but not local max",
    "S1": [
     1,
     4,
     5
    ],
    "sigma": "0"
   },
   {
    "type": "integral stationary but not local max",
    "S1": [
     2,
     3,
     5
    ],
    "sigma": "0"
   },
   {
    "type": "integral stationary but not local max",
    "S1": [
     2,
     4,
     5
    ],
    "sigma": "0"
   }
  ],
  "curvature_ge_2lam_minus_2": true,
  "sigma_ge_lam_minus_1": false,
  "graph": "C6 cycle",
  "n": 6,
  "k": 3,
  "lam": "2",
  "arm": "M1_lam_integral"
 },
 {
  "n_stationary_isolated": 13,
  "n_integral": 6,
  "n_nonintegral": 7,
  "integral_localmax_thm36": 6,
  "integral_localmax_D4": 6,
  "integral_NOT_localmax": 0,
  "certs_disagree": 0,
  "ascent_found_inside_radius": 0,
  "ascent_found_at_4x_radius": 0,
  "localmax_probed": 6,
  "nonintegral_strict_saddle": 7,
  "nonintegral_no_saddle_cert": 0,
  "min_saddle_curvature": "1",
  "min_localmax_sigma": "1/2",
  "min_localmax_radius": 0.2,
  "n_families": 12,
  "n_unhandled": 0,
  "families_all_nonintegral_with_cert": true,
  "counterexamples": [],
  "curvature_ge_2lam_minus_2": true,
  "sigma_ge_lam_minus_1": true,
  "graph": "C6 cycle",
  "n": 6,
  "k": 3,
  "lam": "1/2",
  "arm": "M2_lam_lt_1"
 },
 {
  "n_stationary_isolated": 43,
  "n_integral": 9,
  "n_nonintegral": 34,
  "integral_localmax_thm36": 9,
  "integral_localmax_D4": 9,
  "integral_NOT_localmax": 0,
  "certs_disagree": 0,
  "ascent_found_inside_radius": 0,
  "ascent_found_at_4x_radius": 0,
  "localmax_probed": 9,
  "nonintegral_strict_saddle": 34,
  "nonintegral_no_saddle_cert": 0,
  "min_saddle_curvature": "3",
  "min_localmax_sigma": "1/2",
  "min_localmax_radius": 0.14285714285714285,
  "n_families": 0,
  "n_unhandled": 0,
  "families_all_nonintegral_with_cert": true,
  "counterexamples": [],
  "curvature_ge_2lam_minus_2": true,
  "sigma_ge_lam_minus_1": true,
  "graph": "C6 cycle",
  "n": 6,
  "k": 4,
  "lam": "3/2",
  "arm": "main"
 },
 {
  "n_stationary_isolated": 74,
  "n_integral": 15,
  "n_nonintegral": 59,
  "integral_localmax_thm36": 9,
  "integral_localmax_D4": 9,
  "integral_NOT_localmax": 6,
  "certs_disagree": 0,
  "ascent_found_inside_radius": 0,
  "ascent_found_at_4x_radius": 0,
  "localmax_probed": 9,
  "nonintegral_strict_saddle": 59,
  "nonintegral_no_saddle_cert": 0,
  "min_saddle_curvature": "2",
  "min_localmax_sigma": "0",
  "min_localmax_radius": 0.25,
  "n_families": 1,
  "n_unhandled": 0,
  "families_all_nonintegral_with_cert": true,
  "counterexamples": [
   {
    "type": "integral stationary but not local max",
    "S1": [
     0,
     1,
     2,
     4
    ],
    "sigma": "0"
   },
   {
    "type": "integral stationary but not local max",
    "S1": [
     0,
     1,
     3,
     5
    ],
    "sigma": "0"
   },
   {
    "type": "integral stationary but not local max",
    "S1": [
     0,
     2,
     3,
     4
    ],
    "sigma": "0"
   },
   {
    "type": "integral stationary but not local max",
    "S1": [
     0,
     2,
     4,
     5
    ],
    "sigma": "0"
   },
   {
    "type": "integral stationary but not local max",
    "S1": [
     1,
     2,
     3,
     5
    ],
    "sigma": "0"
   },
   {
    "type": "integral stationary but not local max",
    "S1": [
     1,
     3,
     4,
     5
    ],
    "sigma": "0"
   }
  ],
  "curvature_ge_2lam_minus_2": true,
  "sigma_ge_lam_minus_1": false,
  "graph": "C6 cycle",
  "n": 6,
  "k": 4,
  "lam": "2",
  "arm": "M1_lam_integral"
 },
 {
  "n_stationary_isolated": 13,
  "n_integral": 6,
  "n_nonintegral": 7,
  "integral_localmax_thm36": 6,
  "integral_localmax_D4": 6,
  "integral_NOT_localmax": 0,
  "certs_disagree": 0,
  "ascent_found_inside_radius": 0,
  "ascent_found_at_4x_radius": 0,
  "localmax_probed": 6,
  "nonintegral_strict_saddle": 7,
  "nonintegral_no_saddle_cert": 0,
  "min_saddle_curvature": "1",
  "min_localmax_sigma": "1/2",
  "min_localmax_radius": 0.2,
  "n_families": 0,
  "n_unhandled": 0,
  "families_all_nonintegral_with_cert": true,
  "counterexamples": [],
  "curvature_ge_2lam_minus_2": true,
  "sigma_ge_lam_minus_1": true,
  "graph": "C6 cycle",
  "n": 6,
  "k": 4,
  "lam": "1/2",
  "arm": "M2_lam_lt_1"
 },
 {
  "n_stationary_isolated": 49,
  "n_integral": 9,
  "n_nonintegral": 40,
  "integral_localmax_thm36": 9,
  "integral_localmax_D4": 9,
  "integral_NOT_localmax": 0,
  "certs_disagree": 0,
  "ascent_found_inside_radius": 0,
  "ascent_found_at_4x_radius": 0,
  "localmax_probed": 9,
  "nonintegral_strict_saddle": 40,
  "nonintegral_no_saddle_cert": 0,
  "min_saddle_curvature": "3",
  "min_localmax_sigma": "3/2",
  "min_localmax_radius": 0.3333333333333333,
  "n_families": 0,
  "n_unhandled": 0,
  "families_all_nonintegral_with_cert": true,
  "counterexamples": [],
  "curvature_ge_2lam_minus_2": true,
  "sigma_ge_lam_minus_1": true,
  "graph": "K33",
  "n": 6,
  "k": 2,
  "lam": "3/2",
  "arm": "main"
 },
 {
  "n_stationary_isolated": 40,
  "n_integral": 15,
  "n_nonintegral": 25,
  "integral_localmax_thm36": 9,
  "integral_localmax_D4": 9,
  "integral_NOT_localmax": 6,
  "certs_disagree": 0,
  "ascent_found_inside_radius": 0,
  "ascent_found_at_4x_radius": 0,
  "localmax_probed": 9,
  "nonintegral_strict_saddle": 25,
  "nonintegral_no_saddle_cert": 0,
  "min_saddle_curvature": "4",
  "min_localmax_sigma": "0",
  "min_localmax_radius": 0.4,
  "n_families": 9,
  "n_unhandled": 0,
  "families_all_nonintegral_with_cert": true,
  "counterexamples": [
   {
    "type": "integral stationary but not local max",
    "S1": [
     0,
     1
    ],
    "sigma": "0"
   },
   {
    "type": "integral stationary but not local max",
    "S1": [
     0,
     2
    ],
    "sigma": "0"
   },
   {
    "type": "integral stationary but not local max",
    "S1": [
     1,
     2
    ],
    "sigma": "0"
   },
   {
    "type": "integral stationary but not local max",
    "S1": [
     3,
     4
    ],
    "sigma": "0"
   },
   {
    "type": "integral stationary but not local max",
    "S1": [
     3,
     5
    ],
    "sigma": "0"
   },
   {
    "type": "integral stationary but not local max",
    "S1": [
     4,
     5
    ],
    "sigma": "0"
   }
  ],
  "curvature_ge_2lam_minus_2": true,
  "sigma_ge_lam_minus_1": false,
  "graph": "K33",
  "n": 6,
  "k": 2,
  "lam": "2",
  "arm": "M1_lam_integral"
 },
 {
  "n_stationary_isolated": 49,
  "n_integral": 9,
  "n_nonintegral": 40,
  "integral_localmax_thm36": 9,
  "integral_localmax_D4": 9,
  "integral_NOT_localmax": 0,
  "certs_disagree": 0,
  "ascent_found_inside_radius": 0,
  "ascent_found_at_4x_radius": 0,
  "localmax_probed": 9,
  "nonintegral_strict_saddle": 40,
  "nonintegral_no_saddle_cert": 0,
  "min_saddle_curvature": "1",
  "min_localmax_sigma": "1/2",
  "min_localmax_radius": 0.14285714285714285,
  "n_families": 0,
  "n_unhandled": 0,
  "families_all_nonintegral_with_cert": true,
  "counterexamples": [],
  "curvature_ge_2lam_minus_2": true,
  "sigma_ge_lam_minus_1": true,
  "graph": "K33",
  "n": 6,
  "k": 2,
  "lam": "1/2",
  "arm": "M2_lam_lt_1"
 },
 {
  "n_stationary_isolated": 85,
  "n_integral": 18,
  "n_nonintegral": 67,
  "integral_localmax_thm36": 18,
  "integral_localmax_D4": 18,
  "integral_NOT_localmax": 0,
  "certs_disagree": 0,
  "ascent_found_inside_radius": 0,
  "ascent_found_at_4x_radius": 0,
  "localmax_probed": 18,
  "nonintegral_strict_saddle": 67,
  "nonintegral_no_saddle_cert": 0,
  "min_saddle_curvature": "1",
  "min_localmax_sigma": "1/2",
  "min_localmax_radius": 0.1111111111111111,
  "n_families": 12,
  "n_unhandled": 0,
  "families_all_nonintegral_with_cert": true,
  "counterexamples": [],
  "curvature_ge_2lam_minus_2": true,
  "sigma_ge_lam_minus_1": true,
  "graph": "K33",
  "n": 6,
  "k": 3,
  "lam": "3/2",
  "arm": "main"
 },
 {
  "n_stationary_isolated": 115,
  "n_integral": 18,
  "n_nonintegral": 97,
  "integral_localmax_thm36": 18,
  "integral_localmax_D4": 18,
  "integral_NOT_localmax": 0,
  "certs_disagree": 0,
  "ascent_found_inside_radius": 0,
  "ascent_found_at_4x_radius": 0,
  "localmax_probed": 18,
  "nonintegral_strict_saddle": 97,
  "nonintegral_no_saddle_cert": 0,
  "min_saddle_curvature": "2",
  "min_localmax_sigma": "1",
  "min_localmax_radius": 0.2,
  "n_families": 18,
  "n_unhandled": 0,
  "families_all_nonintegral_with_cert": true,
  "counterexamples": [],
  "curvature_ge_2lam_minus_2": true,
  "sigma_ge_lam_minus_1": true,
  "graph": "K33",
  "n": 6,
  "k": 3,
  "lam": "2",
  "arm": "M1_lam_integral"
 },
 {
  "n_stationary_isolated": 169,
  "n_integral": 0,
  "n_nonintegral": 169,
  "integral_localmax_thm36": 0,
  "integral_localmax_D4": 0,
  "integral_NOT_localmax": 0,
  "certs_disagree": 0,
  "ascent_found_inside_radius": 0,
  "ascent_found_at_4x_radius": 0,
  "localmax_probed": 0,
  "nonintegral_strict_saddle": 133,
  "nonintegral_no_saddle_cert": 36,
  "min_saddle_curvature": "1",
  "min_localmax_sigma": null,
  "min_localmax_radius": null,
  "n_families": 0,
  "n_unhandled": 0,
  "families_all_nonintegral_with_cert": true,
  "counterexamples": [
   {
    "type": "non-integral stationary with no strict-saddle certificate",
    "Sf": [
     0,
     3
    ],
    "x": [
     "1/2",
     "1",
     "0",
     "1/2",
     "1",
     "0"
    ]
   },
   {
    "type": "non-integral stationary with no strict-saddle certificate",
    "Sf": [
     0,
     3
    ],
    "x": [
     "1/2",
     "1",
     "0",
     "1/2",
     "0",
     "1"
    ]
   },
   {
    "type": "non-integral stationary with no strict-saddle certificate",
    "Sf": [
     0,
     3
    ],
    "x": [
     "1/2",
     "0",
     "1",
     "1/2",
     "1",
     "0"
    ]
   },
   {
    "type": "non-integral stationary with no strict-saddle certificate",
    "Sf": [
     0,
     3
    ],
    "x": [
     "1/2",
     "0",
     "1",
     "1/2",
     "0",
     "1"
    ]
   },
   {
    "type": "non-integral stationary with no strict-saddle certificate",
    "Sf": [
     0,
     4
    ],
    "x": [
     "1/2",
     "1",
     "0",
     "1",
     "1/2",
     "0"
    ]
   },
   {
    "type": "non-integral stationary with no strict-saddle certificate",
    "Sf": [
     0,
     4
    ],
    "x": [
     "1/2",
     "1",
     "0",
     "0",
     "1/2",
     "1"
    ]
   },
   {
    "type": "non-integral stationary with no strict-saddle certificate",
    "Sf": [
     0,
     4
    ],
    "x": [
     "1/2",
     "0",
     "1",
     "1",
     "1/2",
     "0"
    ]
   },
   {
    "type": "non-integral stationary with no strict-saddle certificate",
    "Sf": [
     0,
     4
    ],
    "x": [
     "1/2",
     "0",
     "1",
     "0",
     "1/2",
     "1"
    ]
   },
   {
    "type": "non-integral stationary with no strict-saddle certificate",
    "Sf": [
     0,
     5
    ],
    "x": [
     "1/2",
     "1",
     "0",
     "1",
     "0",
     "1/2"
    ]
   },
   {
    "type": "non-integral stationary with no strict-saddle certificate",
    "Sf": [
     0,
     5
    ],
    "x": [
     "1/2",
     "1",
     "0",
     "0",
     "1",
     "1/2"
    ]
   },
   {
    "type": "non-integral stationary with no strict-saddle certificate",
    "Sf": [
     0,
     5
    ],
    "x": [
     "1/2",
     "0",
     "1",
     "1",
     "0",
     "1/2"
    ]
   },
   {
    "type": "non-integral stationary with no strict-saddle certificate",
    "Sf": [
     0,
     5
    ],
    "x": [
     "1/2",
     "0",
     "1",
     "0",
     "1",
     "1/2"
    ]
   },
   {
    "type": "non-integral stationary with no strict-saddle certificate",
    "Sf": [
     1,
     3
    ],
    "x": [
     "1",
     "1/2",
     "0",
     "1/2",
     "1",
     "0"
    ]
   },
   {
    "type": "non-integral stationary with no strict-saddle certificate",
    "Sf": [
     1,
     3
    ],
    "x": [
     "1",
     "1/2",
     "0",
     "1/2",
     "0",
     "1"
    ]
   },
   {
    "type": "non-integral stationary with no strict-saddle certificate",
    "Sf": [
     1,
     3
    ],
    "x": [
     "0",
     "1/2",
     "1",
     "1/2",
     "1",
     "0"
    ]
   },
   {
    "type": "non-integral stationary with no strict-saddle certificate",
    "Sf": [
     1,
     3
    ],
    "x": [
     "0",
     "1/2",
     "1",
     "1/2",
     "0",
     "1"
    ]
   },
   {
    "type": "non-integral stationary with no strict-saddle certificate",
    "Sf": [
     1,
     4
    ],
    "x": [
     "1",
     "1/2",
     "0",
     "1",
     "1/2",
     "0"
    ]
   },
   {
    "type": "non-integral stationary with no strict-saddle certificate",
    "Sf": [
     1,
     4
    ],
    "x": [
     "1",
     "1/2",
     "0",
     "0",
     "1/2",
     "1"
    ]
   },
   {
    "type": "non-integral stationary with no strict-saddle certificate",
    "Sf": [
     1,
     4
    ],
    "x": [
     "0",
     "1/2",
     "1",
     "1",
     "1/2",
     "0"
    ]
   },
   {
    "type": "non-integral stationary with no strict-saddle certificate",
    "Sf": [
     1,
     4
    ],
    "x": [
     "0",
     "1/2",
     "1",
     "0",
     "1/2",
     "1"
    ]
   },
   {
    "type": "non-integral stationary with no strict-saddle certificate",
    "Sf": [
     1,
     5
    ],
    "x": [
     "1",
     "1/2",
     "0",
     "1",
     "0",
     "1/2"
    ]
   },
   {
    "type": "non-integral stationary with no strict-saddle certificate",
    "Sf": [
     1,
     5
    ],
    "x": [
     "1",
     "1/2",
     "0",
     "0",
     "1",
     "1/2"
    ]
   },
   {
    "type": "non-integral stationary with no strict-saddle certificate",
    "Sf": [
     1,
     5
    ],
    "x": [
     "0",
     "1/2",
     "1",
     "1",
     "0",
     "1/2"
    ]
   },
   {
    "type": "non-integral stationary with no strict-saddle certificate",
    "Sf": [
     1,
     5
    ],
    "x": [
     "0",
     "1/2",
     "1",
     "0",
     "1",
     "1/2"
    ]
   },
   {
    "type": "non-integral stationary with no strict-saddle certificate",
    "Sf": [
     2,
     3
    ],
    "x": [
     "1",
     "0",
     "1/2",
     "1/2",
     "1",
     "0"
    ]
   },
   {
    "type": "non-integral stationary with no strict-saddle certificate",
    "Sf": [
     2,
     3
    ],
    "x": [
     "1",
     "0",
     "1/2",
     "1/2",
     "0",
     "1"
    ]
   },
   {
    "type": "non-integral stationary with no strict-saddle certificate",
    "Sf": [
     2,
     3
    ],
    "x": [
     "0",
     "1",
     "1/2",
     "1/2",
     "1",
     "0"
    ]
   },
   {
    "type": "non-integral stationary with no strict-saddle certificate",
    "Sf": [
     2,
     3
    ],
    "x": [
     "0",
     "1",
     "1/2",
     "1/2",
     "0",
     "1"
    ]
   },
   {
    "type": "non-integral stationary with no strict-saddle certificate",
    "Sf": [
     2,
     4
    ],
    "x": [
     "1",
     "0",
     "1/2",
     "1",
     "1/2",
     "0"
    ]
   },
   {
    "type": "non-integral stationary with no strict-saddle certificate",
    "Sf": [
     2,
     4
    ],
    "x": [
     "1",
     "0",
     "1/2",
     "0",
     "1/2",
     "1"
    ]
   },
   {
    "type": "non-integral stationary with no strict-saddle certificate",
    "Sf": [
     2,
     4
    ],
    "x": [
     "0",
     "1",
     "1/2",
     "1",
     "1/2",
     "0"
    ]
   },
   {
    "type": "non-integral stationary with no strict-saddle certificate",
    "Sf": [
     2,
     4
    ],
    "x": [
     "0",
     "1",
     "1/2",
     "0",
     "1/2",
     "1"
    ]
   },
   {
    "type": "non-integral stationary with no strict-saddle certificate",
    "Sf": [
     2,
     5
    ],
    "x": [
     "1",
     "0",
     "1/2",
     "1",
     "0",
     "1/2"
    ]
   },
   {
    "type": "non-integral stationary with no strict-saddle certificate",
    "Sf": [
     2,
     5
    ],
    "x": [
     "1",
     "0",
     "1/2",
     "0",
     "1",
     "1/2"
    ]
   },
   {
    "type": "non-integral stationary with no strict-saddle certificate",
    "Sf": [
     2,
     5
    ],
    "x": [
     "0",
     "1",
     "1/2",
     "1",
     "0",
     "1/2"
    ]
   },
   {
    "type": "non-integral stationary with no strict-saddle certificate",
    "Sf": [
     2,
     5
    ],
    "x": [
     "0",
     "1",
     "1/2",
     "0",
     "1",
     "1/2"
    ]
   }
  ],
  "curvature_ge_2lam_minus_2": true,
  "sigma_ge_lam_minus_1": true,
  "graph": "K33",
  "n": 6,
  "k": 3,
  "lam": "1/2",
  "arm": "M2_lam_lt_1"
 },
 {
  "n_stationary_isolated": 49,
  "n_integral": 9,
  "n_nonintegral": 40,
  "integral_localmax_thm36": 9,
  "integral_localmax_D4": 9,
  "integral_NOT_localmax": 0,
  "certs_disagree": 0,
  "ascent_found_inside_radius": 0,
  "ascent_found_at_4x_radius": 0,
  "localmax_probed": 9,
  "nonintegral_strict_saddle": 40,
  "nonintegral_no_saddle_cert": 0,
  "min_saddle_curvature": "3",
  "min_localmax_sigma": "3/2",
  "min_localmax_radius": 0.3333333333333333,
  "n_families": 0,
  "n_unhandled": 0,
  "families_all_nonintegral_with_cert": true,
  "counterexamples": [],
  "curvature_ge_2lam_minus_2": true,
  "sigma_ge_lam_minus_1": true,
  "graph": "K33",
  "n": 6,
  "k": 4,
  "lam": "3/2",
  "arm": "main"
 },
 {
  "n_stationary_isolated": 40,
  "n_integral": 15,
  "n_nonintegral": 25,
  "integral_localmax_thm36": 9,
  "integral_localmax_D4": 9,
  "integral_NOT_localmax": 6,
  "certs_disagree": 0,
  "ascent_found_inside_radius": 0,
  "ascent_found_at_4x_radius": 0,
  "localmax_probed": 9,
  "nonintegral_strict_saddle": 25,
  "nonintegral_no_saddle_cert": 0,
  "min_saddle_curvature": "4",
  "min_localmax_sigma": "0",
  "min_localmax_radius": 0.4,
  "n_families": 9,
  "n_unhandled": 0,
  "families_all_nonintegral_with_cert": true,
  "counterexamples": [
   {
    "type": "integral stationary but not local max",
    "S1": [
     0,
     1,
     2,
     3
    ],
    "sigma": "0"
   },
   {
    "type": "integral stationary but not local max",
    "S1": [
     0,
     1,
     2,
     4
    ],
    "sigma": "0"
   },
   {
    "type": "integral stationary but not local max",
    "S1": [
     0,
     1,
     2,
     5
    ],
    "sigma": "0"
   },
   {
    "type": "integral stationary but not local max",
    "S1": [
     0,
     3,
     4,
     5
    ],
    "sigma": "0"
   },
   {
    "type": "integral stationary but not local max",
    "S1": [
     1,
     3,
     4,
     5
    ],
    "sigma": "0"
   },
   {
    "type": "integral stationary but not local max",
    "S1": [
     2,
     3,
     4,
     5
    ],
    "sigma": "0"
   }
  ],
  "curvature_ge_2lam_minus_2": true,
  "sigma_ge_lam_minus_1": false,
  "graph": "K33",
  "n": 6,
  "k": 4,
  "lam": "2",
  "arm": "M1_lam_integral"
 },
 {
  "n_stationary_isolated": 49,
  "n_integral": 9,
  "n_nonintegral": 40,
  "integral_localmax_thm36": 9,
  "integral_localmax_D4": 9,
  "integral_NOT_localmax": 0,
  "certs_disagree": 0,
  "ascent_found_inside_radius": 0,
  "ascent_found_at_4x_radius": 0,
  "localmax_probed": 9,
  "nonintegral_strict_saddle": 40,
  "nonintegral_no_saddle_cert": 0,
  "min_saddle_curvature": "1",
  "min_localmax_sigma": "1/2",
  "min_localmax_radius": 0.14285714285714285,
  "n_families": 0,
  "n_unhandled": 0,
  "families_all_nonintegral_with_cert": true,
  "counterexamples": [],
  "curvature_ge_2lam_minus_2": true,
  "sigma_ge_lam_minus_1": true,
  "graph": "K33",
  "n": 6,
  "k": 4,
  "lam": "1/2",
  "arm": "M2_lam_lt_1"
 },
 {
  "n_stationary_isolated": 213,
  "n_integral": 15,
  "n_nonintegral": 198,
  "integral_localmax_thm36": 15,
  "integral_localmax_D4": 15,
  "integral_NOT_localmax": 0,
  "certs_disagree": 0,
  "ascent_found_inside_radius": 0,
  "ascent_found_at_4x_radius": 0,
  "localmax_probed": 15,
  "nonintegral_strict_saddle": 198,
  "nonintegral_no_saddle_cert": 0,
  "min_saddle_curvature": "1",
  "min_localmax_sigma": "1/2",
  "min_localmax_radius": 0.14285714285714285,
  "n_families": 0,
  "n_unhandled": 0,
  "families_all_nonintegral_with_cert": true,
  "counterexamples": [],
  "curvature_ge_2lam_minus_2": true,
  "sigma_ge_lam_minus_1": true,
  "graph": "two triangles",
  "n": 6,
  "k": 2,
  "lam": "3/2",
  "arm": "main"
 },
 {
  "n_stationary_isolated": 213,
  "n_integral": 15,
  "n_nonintegral": 198,
  "integral_localmax_thm36": 15,
  "integral_localmax_D4": 15,
  "integral_NOT_localmax": 0,
  "certs_disagree": 0,
  "ascent_found_inside_radius": 0,
  "ascent_found_at_4x_radius": 0,
  "localmax_probed": 15,
  "nonintegral_strict_saddle": 198,
  "nonintegral_no_saddle_cert": 0,
  "min_saddle_curvature": "2",
  "min_localmax_sigma": "1",
  "min_localmax_radius": 0.25,
  "n_families": 0,
  "n_unhandled": 0,
  "families_all_nonintegral_with_cert": true,
  "counterexamples": [],
  "curvature_ge_2lam_minus_2": true,
  "sigma_ge_lam_minus_1": true,
  "graph": "two triangles",
  "n": 6,
  "k": 2,
  "lam": "2",
  "arm": "M1_lam_integral"
 },
 {
  "n_stationary_isolated": 3,
  "n_integral": 0,
  "n_nonintegral": 3,
  "integral_localmax_thm36": 0,
  "integral_localmax_D4": 0,
  "integral_NOT_localmax": 0,
  "certs_disagree": 0,
  "ascent_found_inside_radius": 0,
  "ascent_found_at_4x_radius": 0,
  "localmax_probed": 0,
  "nonintegral_strict_saddle": 1,
  "nonintegral_no_saddle_cert": 2,
  "min_saddle_curvature": "1",
  "min_localmax_sigma": null,
  "min_localmax_radius": null,
  "n_families": 0,
  "n_unhandled": 0,
  "families_all_nonintegral_with_cert": true,
  "counterexamples": [
   {
    "type": "non-integral stationary with no strict-saddle certificate",
    "Sf": [
     0,
     1,
     2
    ],
    "x": [
     "2/3",
     "2/3",
     "2/3",
     "0",
     "0",
     "0"
    ]
   },
   {
    "type": "non-integral stationary with no strict-saddle certificate",
    "Sf": [
     3,
     4,
     5
    ],
    "x": [
     "0",
     "0",
     "0",
     "2/3",
     "2/3",
     "2/3"
    ]
   }
  ],
  "curvature_ge_2lam_minus_2": true,
  "sigma_ge_lam_minus_1": true,
  "graph": "two triangles",
  "n": 6,
  "k": 2,
  "lam": "1/2",
  "arm": "M2_lam_lt_1"
 },
 {
  "n_stationary_isolated": 171,
  "n_integral": 2,
  "n_nonintegral": 169,
  "integral_localmax_thm36": 2,
  "integral_localmax_D4": 2,
  "integral_NOT_localmax": 0,
  "certs_disagree": 0,
  "ascent_found_inside_radius": 0,
  "ascent_found_at_4x_radius": 0,
  "localmax_probed": 2,
  "nonintegral_strict_saddle": 169,
  "nonintegral_no_saddle_cert": 0,
  "min_saddle_curvature": "3",
  "min_localmax_sigma": "7/2",
  "min_localmax_radius": 1.0,
  "n_families": 0,
  "n_unhandled": 0,
  "families_all_nonintegral_with_cert": true,
  "counterexamples": [],
  "curvature_ge_2lam_minus_2": true,
  "sigma_ge_lam_minus_1": true,
  "graph": "two triangles",
  "n": 6,
  "k": 3,
  "lam": "3/2",
  "arm": "main"
 },
 {
  "n_stationary_isolated": 189,
  "n_integral": 20,
  "n_nonintegral": 169,
  "integral_localmax_thm36": 2,
  "integral_localmax_D4": 2,
  "integral_NOT_localmax": 18,
  "certs_disagree": 0,
  "ascent_found_inside_radius": 0,
  "ascent_found_at_4x_radius": 0,
  "localmax_probed": 2,
  "nonintegral_strict_saddle": 169,
  "nonintegral_no_saddle_cert": 0,
  "min_saddle_curvature": "4",
  "min_localmax_sigma": "0",
  "min_localmax_radius": 1.0,
  "n_families": 0,
  "n_unhandled": 0,
  "families_all_nonintegral_with_cert": true,
  "counterexamples": [
   {
    "type": "integral stationary but not local max",
    "S1": [
     0,
     1,
     3
    ],
    "sigma": "0"
   },
   {
    "type": "integral stationary but not local max",
    "S1": [
     0,
     1,
     4
    ],
    "sigma": "0"
   },
   {
    "type": "integral stationary but not local max",
    "S1": [
     0,
     1,
     5
    ],
    "sigma": "0"
   },
   {
    "type": "integral stationary but not local max",
    "S1": [
     0,
     2,
     3
    ],
    "sigma": "0"
   },
   {
    "type": "integral stationary but not local max",
    "S1": [
     0,
     2,
     4
    ],
    "sigma": "0"
   },
   {
    "type": "integral stationary but not local max",
    "S1": [
     0,
     2,
     5
    ],
    "sigma": "0"
   },
   {
    "type": "integral stationary but not local max",
    "S1": [
     0,
     3,
     4
    ],
    "sigma": "0"
   },
   {
    "type": "integral stationary but not local max",
    "S1": [
     0,
     3,
     5
    ],
    "sigma": "0"
   },
   {
    "type": "integral stationary but not local max",
    "S1": [
     0,
     4,
     5
    ],
    "sigma": "0"
   },
   {
    "type": "integral stationary but not local max",
    "S1": [
     1,
     2,
     3
    ],
    "sigma": "0"
   },
   {
    "type": "integral stationary but not local max",
    "S1": [
     1,
     2,
     4
    ],
    "sigma": "0"
   },
   {
    "type": "integral stationary but not local max",
    "S1": [
     1,
     2,
     5
    ],
    "sigma": "0"
   },
   {
    "type": "integral stationary but not local max",
    "S1": [
     1,
     3,
     4
    ],
    "sigma": "0"
   },
   {
    "type": "integral stationary but not local max",
    "S1": [
     1,
     3,
     5
    ],
    "sigma": "0"
   },
   {
    "type": "integral stationary but not local max",
    "S1": [
     1,
     4,
     5
    ],
    "sigma": "0"
   },
   {
    "type": "integral stationary but not local max",
    "S1": [
     2,
     3,
     4
    ],
    "sigma": "0"
   },
   {
    "type": "integral stationary but not local max",
    "S1": [
     2,
     3,
     5
    ],
    "sigma": "0"
   },
   {
    "type": "integral stationary but not local max",
    "S1": [
     2,
     4,
     5
    ],
    "sigma": "0"
   }
  ],
  "curvature_ge_2lam_minus_2": true,
  "sigma_ge_lam_minus_1": false,
  "graph": "two triangles",
  "n": 6,
  "k": 3,
  "lam": "2",
  "arm": "M1_lam_integral"
 },
 {
  "n_stationary_isolated": 3,
  "n_integral": 2,
  "n_nonintegral": 1,
  "integral_localmax_thm36": 2,
  "integral_localmax_D4": 2,
  "integral_NOT_localmax": 0,
  "certs_disagree": 0,
  "ascent_found_inside_radius": 0,
  "ascent_found_at_4x_radius": 0,
  "localmax_probed": 2,
  "nonintegral_strict_saddle": 1,
  "nonintegral_no_saddle_cert": 0,
  "min_saddle_curvature": "1",
  "min_localmax_sigma": "5/2",
  "min_localmax_radius": 1.0,
  "n_families": 0,
  "n_unhandled": 0,
  "families_all_nonintegral_with_cert": true,
  "counterexamples": [],
  "curvature_ge_2lam_minus_2": true,
  "sigma_ge_lam_minus_1": true,
  "graph": "two triangles",
  "n": 6,
  "k": 3,
  "lam": "1/2",
  "arm": "M2_lam_lt_1"
 },
 {
  "n_stationary_isolated": 213,
  "n_integral": 15,
  "n_nonintegral": 198,
  "integral_localmax_thm36": 15,
  "integral_localmax_D4": 15,
  "integral_NOT_localmax": 0,
  "certs_disagree": 0,
  "ascent_found_inside_radius": 0,
  "ascent_found_at_4x_radius": 0,
  "localmax_probed": 15,
  "nonintegral_strict_saddle": 198,
  "nonintegral_no_saddle_cert": 0,
  "min_saddle_curvature": "1",
  "min_localmax_sigma": "1/2",
  "min_localmax_radius": 0.14285714285714285,
  "n_families": 0,
  "n_unhandled": 0,
  "families_all_nonintegral_with_cert": true,
  "counterexamples": [],
  "curvature_ge_2lam_minus_2": true,
  "sigma_ge_lam_minus_1": true,
  "graph": "two triangles",
  "n": 6,
  "k": 4,
  "lam": "3/2",
  "arm": "main"
 },
 {
  "n_stationary_isolated": 213,
  "n_integral": 15,
  "n_nonintegral": 198,
  "integral_localmax_thm36": 15,
  "integral_localmax_D4": 15,
  "integral_NOT_localmax": 0,
  "certs_disagree": 0,
  "ascent_found_inside_radius": 0,
  "ascent_found_at_4x_radius": 0,
  "localmax_probed": 15,
  "nonintegral_strict_saddle": 198,
  "nonintegral_no_saddle_cert": 0,
  "min_saddle_curvature": "2",
  "min_localmax_sigma": "1",
  "min_localmax_radius": 0.25,
  "n_families": 0,
  "n_unhandled": 0,
  "families_all_nonintegral_with_cert": true,
  "counterexamples": [],
  "curvature_ge_2lam_minus_2": true,
  "sigma_ge_lam_minus_1": true,
  "graph": "two triangles",
  "n": 6,
  "k": 4,
  "lam": "2",
  "arm": "M1_lam_integral"
 },
 {
  "n_stationary_isolated": 3,
  "n_integral": 0,
  "n_nonintegral": 3,
  "integral_localmax_thm36": 0,
  "integral_localmax_D4": 0,
  "integral_NOT_localmax": 0,
  "certs_disagree": 0,
  "ascent_found_inside_radius": 0,
  "ascent_found_at_4x_radius": 0,
  "localmax_probed": 0,
  "nonintegral_strict_saddle": 1,
  "nonintegral_no_saddle_cert": 2,
  "min_saddle_curvature": "1",
  "min_localmax_sigma": null,
  "min_localmax_radius": null,
  "n_families": 0,
  "n_unhandled": 0,
  "families_all_nonintegral_with_cert": true,
  "counterexamples": [
   {
    "type": "non-integral stationary with no strict-saddle certificate",
    "Sf": [
     0,
     1,
     2
    ],
    "x": [
     "1/3",
     "1/3",
     "1/3",
     "1",
     "1",
     "1"
    ]
   },
   {
    "type": "non-integral stationary with no strict-saddle certificate",
    "Sf": [
     3,
     4,
     5
    ],
    "x": [
     "1",
     "1",
     "1",
     "1/3",
     "1/3",
     "1/3"
    ]
   }
  ],
  "curvature_ge_2lam_minus_2": true,
  "sigma_ge_lam_minus_1": true,
  "graph": "two triangles",
  "n": 6,
  "k": 4,
  "lam": "1/2",
  "arm": "M2_lam_lt_1"
 },
 {
  "n_stationary_isolated": 119,
  "n_integral": 21,
  "n_nonintegral": 98,
  "integral_localmax_thm36": 21,
  "integral_localmax_D4": 21,
  "integral_NOT_localmax": 0,
  "certs_disagree": 0,
  "ascent_found_inside_radius": 0,
  "ascent_found_at_4x_radius": 0,
  "localmax_probed": 21,
  "nonintegral_strict_saddle": 98,
  "nonintegral_no_saddle_cert": 0,
  "min_saddle_curvature": "1",
  "min_localmax_sigma": "1/2",
  "min_localmax_radius": 0.07692307692307693,
  "n_families": 5,
  "n_unhandled": 0,
  "families_all_nonintegral_with_cert": true,
  "counterexamples": [],
  "curvature_ge_2lam_minus_2": true,
  "sigma_ge_lam_minus_1": true,
  "graph": "G(8,0.45) seed=11",
  "n": 8,
  "k": 3,
  "lam": "3/2",
  "arm": "main"
 },
 {
  "n_stationary_isolated": 246,
  "n_integral": 43,
  "n_nonintegral": 203,
  "integral_localmax_thm36": 21,
  "integral_localmax_D4": 21,
  "integral_NOT_localmax": 22,
  "certs_disagree": 0,
  "ascent_found_inside_radius": 0,
  "ascent_found_at_4x_radius": 0,
  "localmax_probed": 21,
  "nonintegral_strict_saddle": 203,
  "nonintegral_no_saddle_cert": 0,
  "min_saddle_curvature": "2",
  "min_localmax_sigma": "0",
  "min_localmax_radius": 0.14285714285714285,
  "n_families": 15,
  "n_unhandled": 0,
  "families_all_nonintegral_with_cert": true,
  "counterexamples": [
   {
    "type": "integral stationary but not local max",
    "S1": [
     0,
     1,
     2
    ],
    "sigma": "0"
   },
   {
    "type": "integral stationary but not local max",
    "S1": [
     0,
     1,
     6
    ],
    "sigma": "0"
   },
   {
    "type": "integral stationary but not local max",
    "S1": [
     0,
     2,
     3
    ],
    "sigma": "0"
   },
   {
    "type": "integral stationary but not local max",
    "S1": [
     0,
     2,
     4
    ],
    "sigma": "0"
   },
   {
    "type": "integral stationary but not local max",
    "S1": [
     0,
     2,
     5
    ],
    "sigma": "0"
   },
   {
    "type": "integral stationary but not local max",
    "S1": [
     0,
     2,
     6
    ],
    "sigma": "0"
   },
   {
    "type": "integral stationary but not local max",
    "S1": [
     0,
     2,
     7
    ],
    "sigma": "0"
   },
   {
    "type": "integral stationary but not local max",
    "S1": [
     0,
     3,
     6
    ],
    "sigma": "0"
   },
   {
    "type": "integral stationary but not local max",
    "S1": [
     0,
     4,
     6
    ],
    "sigma": "0"
   },
   {
    "type": "integral stationary but not local max",
    "S1": [
     0,
     5,
     6
    ],
    "sigma": "0"
   },
   {
    "type": "integral stationary but not local max",
    "S1": [
     0,
     6,
     7
    ],
    "sigma": "0"
   },
   {
    "type": "integral stationary but not local max",
    "S1": [
     1,
     2,
     3
    ],
    "sigma": "0"
   },
   {
    "type": "integral stationary but not local max",
    "S1": [
     1,
     2,
     4
    ],
    "sigma": "0"
   },
   {
    "type": "integral stationary but not local max",
    "S1": [
     1,
     6,
     7
    ],
    "sigma": "0"
   },
   {
    "type": "integral stationary but not local max",
    "S1": [
     2,
     3,
     4
    ],
    "sigma": "0"
   },
   {
    "type": "integral stationary but not local max",
    "S1": [
     2,
     3,
     5
    ],
    "sigma": "0"
   },
   {
    "type": "integral stationary but not local max",
    "S1": [
     2,
     3,
     6
    ],
    "sigma": "0"
   },
   {
    "type": "integral stationary but not local max",
    "S1": [
     2,
     3,
     7
    ],
    "sigma": "0"
   },
   {
    "type": "integral stationary but not local max",
    "S1": [
     2,
     4,
     5
    ],
    "sigma": "0"
   },
   {
    "type": "integral stationary but not local max",
    "S1": [
     2,
     4,
     6
    ],
    "sigma": "0"
   },
   {
    "type": "integral stationary but not local max",
    "S1": [
     2,
     4,
     7
    ],
    "sigma": "0"
   },
   {
    "type": "integral stationary but not local max",
    "S1": [
     5,
     6,
     7
    ],
    "sigma": "0"
   }
  ],
  "curvature_ge_2lam_minus_2": true,
  "sigma_ge_lam_minus_1": false,
  "graph": "G(8,0.45) seed=11",
  "n": 8,
  "k": 3,
  "lam": "2",
  "arm": "M1_lam_integral"
 },
 {
  "n_stationary_isolated": 45,
  "n_integral": 4,
  "n_nonintegral": 41,
  "integral_localmax_thm36": 4,
  "integral_localmax_D4": 4,
  "integral_NOT_localmax": 0,
  "certs_disagree": 0,
  "ascent_found_inside_radius": 0,
  "ascent_found_at_4x_radius": 0,
  "localmax_probed": 4,
  "nonintegral_strict_saddle": 33,
  "nonintegral_no_saddle_cert": 8,
  "min_saddle_curvature": "1",
  "min_localmax_sigma": "1/2",
  "min_localmax_radius": 0.09090909090909091,
  "n_families": 0,
  "n_unhandled": 0,
  "families_all_nonintegral_with_cert": true,
  "counterexamples": [
   {
    "type": "non-integral stationary with no strict-saddle certificate",
    "Sf": [
     3,
     6
    ],
    "x": [
     "0",
     "0",
     "0",
     "1/2",
     "1",
     "0",
     "1/2",
     "1"
    ]
   },
   {
    "type": "non-integral stationary with no strict-saddle certificate",
    "Sf": [
     3,
     7
    ],
    "x": [
     "0",
     "0",
     "0",
     "1/2",
     "1",
     "0",
     "1",
     "1/2"
    ]
   },
   {
    "type": "non-integral stationary with no strict-saddle certificate",
    "Sf": [
     4,
     6
    ],
    "x": [
     "0",
     "0",
     "0",
     "1",
     "1/2",
     "0",
     "1/2",
     "1"
    ]
   },
   {
    "type": "non-integral stationary with no strict-saddle certificate",
    "Sf": [
     4,
     7
    ],
    "x": [
     "0",
     "0",
     "0",
     "1",
     "1/2",
     "0",
     "1",
     "1/2"
    ]
   },
   {
    "type": "non-integral stationary with no strict-saddle certificate",
    "Sf": [
     1,
     5,
     6
    ],
    "x": [
     "0",
     "1/3",
     "0",
     "1",
     "0",
     "1/3",
     "1/3",
     "1"
    ]
   },
   {
    "type": "non-integral stationary with no strict-saddle certificate",
    "Sf": [
     1,
     5,
     6
    ],
    "x": [
     "0",
     "1/3",
     "0",
     "0",
     "1",
     "1/3",
     "1/3",
     "1"
    ]
   },
   {
    "type": "non-integral stationary with no strict-saddle certificate",
    "Sf": [
     1,
     5,
     7
    ],
    "x": [
     "0",
     "1/3",
     "0",
     "1",
     "0",
     "1/3",
     "1",
     "1/3"
    ]
   },
   {
    "type": "non-integral stationary with no strict-saddle certificate",
    "Sf": [
     1,
     5,
     7
    ],
    "x": [
     "0",
     "1/3",
     "0",
     "0",
     "1",
     "1/3",
     "1",
     "1/3"
    ]
   }
  ],
  "curvature_ge_2lam_minus_2": true,
  "sigma_ge_lam_minus_1": true,
  "graph": "G(8,0.45) seed=11",
  "n": 8,
  "k": 3,
  "lam": "1/2",
  "arm": "M2_lam_lt_1"
 },
 {
  "n_stationary_isolated": 131,
  "n_integral": 21,
  "n_nonintegral": 110,
  "integral_localmax_thm36": 21,
  "integral_localmax_D4": 21,
  "integral_NOT_localmax": 0,
  "certs_disagree": 0,
  "ascent_found_inside_radius": 0,
  "ascent_found_at_4x_radius": 0,
  "localmax_probed": 21,
  "nonintegral_strict_saddle": 110,
  "nonintegral_no_saddle_cert": 0,
  "min_saddle_curvature": "1",
  "min_localmax_sigma": "1/2",
  "min_localmax_radius": 0.07692307692307693,
  "n_families": 10,
  "n_unhandled": 0,
  "families_all_nonintegral_with_cert": true,
  "counterexamples": [],
  "curvature_ge_2lam_minus_2": true,
  "sigma_ge_lam_minus_1": true,
  "graph": "G(8,0.45) seed=11",
  "n": 8,
  "k": 4,
  "lam": "3/2",
  "arm": "main"
 },
 {
  "n_stationary_isolated": 245,
  "n_integral": 39,
  "n_nonintegral": 206,
  "integral_localmax_thm36": 21,
  "integral_localmax_D4": 21,
  "integral_NOT_localmax": 18,
  "certs_disagree": 0,
  "ascent_found_inside_radius": 0,
  "ascent_found_at_4x_radius": 0,
  "localmax_probed": 21,
  "nonintegral_strict_saddle": 206,
  "nonintegral_no_saddle_cert": 0,
  "min_saddle_curvature": "2",
  "min_localmax_sigma": "0",
  "min_localmax_radius": 0.14285714285714285,
  "n_families": 10,
  "n_unhandled": 0,
  "families_all_nonintegral_with_cert": true,
  "counterexamples": [
   {
    "type": "integral stationary but not local max",
    "S1": [
     0,
     1,
     6,
     7
    ],
    "sigma": "0"
   },
   {
    "type": "integral stationary but not local max",
    "S1": [
     0,
     2,
     3,
     6
    ],
    "sigma": "0"
   },
   {
    "type": "integral stationary but not local max",
    "S1": [
     0,
     2,
     3,
     7
    ],
    "sigma": "0"
   },
   {
    "type": "integral stationary but not local max",
    "S1": [
     0,
     2,
     4,
     6
    ],
    "sigma": "0"
   },
   {
    "type": "integral stationary but not local max",
    "S1": [
     0,
     2,
     4,
     7
    ],
    "sigma": "0"
   },
   {
    "type": "integral stationary but not local max",
    "S1": [
     0,
     2,
     5,
     6
    ],
    "sigma": "0"
   },
   {
    "type": "integral stationary but not local max",
    "S1": [
     0,
     5,
     6,
     7
    ],
    "sigma": "0"
   },
   {
    "type": "integral stationary but not local max",
    "S1": [
     1,
     3,
     4,
     6
    ],
    "sigma": "0"
   },
   {
    "type": "integral stationary but not local max",
    "S1": [
     1,
     3,
     4,
     7
    ],
    "sigma": "0"
   },
   {
    "type": "integral stationary but not local max",
    "S1": [
     1,
     3,
     5,
     6
    ],
    "sigma": "0"
   },
   {
    "type": "integral stationary but not local max",
    "S1": [
     1,
     3,
     5,
     7
    ],
    "sigma": "0"
   },
   {
    "type": "integral stationary but not local max",
    "S1": [
     1,
     4,
     5,
     6
    ],
    "sigma": "0"
   },
   {
    "type": "integral stationary but not local max",
    "S1": [
     1,
     4,
     5,
     7
    ],
    "sigma": "0"
   },
   {
    "type": "integral stationary but not local max",
    "S1": [
     2,
     3,
     4,
     6
    ],
    "sigma": "0"
   },
   {
    "type": "integral stationary but not local max",
    "S1": [
     2,
     3,
     4,
     7
    ],
    "sigma": "0"
   },
   {
    "type": "integral stationary but not local max",
    "S1": [
     2,
     5,
     6,
     7
    ],
    "sigma": "0"
   },
   {
    "type": "integral stationary but not local max",
    "S1": [
     3,
     4,
     5,
     6
    ],
    "sigma": "0"
   },
   {
    "type": "integral stationary but not local max",
    "S1": [
     3,
     4,
     5,
     7
    ],
    "sigma": "0"
   }
  ],
  "curvature_ge_2lam_minus_2": true,
  "sigma_ge_lam_minus_1": false,
  "graph": "G(8,0.45) seed=11",
  "n": 8,
  "k": 4,
  "lam": "2",
  "arm": "M1_lam_integral"
 },
 {
  "n_stationary_isolated": 5,
  "n_integral": 2,
  "n_nonintegral": 3,
  "integral_localmax_thm36": 2,
  "integral_localmax_D4": 2,
  "integral_NOT_localmax": 0,
  "certs_disagree": 0,
  "ascent_found_inside_radius": 0,
  "ascent_found_at_4x_radius": 0,
  "localmax_probed": 2,
  "nonintegral_strict_saddle": 3,
  "nonintegral_no_saddle_cert": 0,
  "min_saddle_curvature": "1",
  "min_localmax_sigma": "1/2",
  "min_localmax_radius": 0.09090909090909091,
  "n_families": 0,
  "n_unhandled": 0,
  "families_all_nonintegral_with_cert": true,
  "counterexamples": [],
  "curvature_ge_2lam_minus_2": true,
  "sigma_ge_lam_minus_1": true,
  "graph": "G(8,0.45) seed=11",
  "n": 8,
  "k": 4,
  "lam": "1/2",
  "arm": "M2_lam_lt_1"
 },
 {
  "n_stationary_isolated": 59,
  "n_integral": 10,
  "n_nonintegral": 49,
  "integral_localmax_thm36": 10,
  "integral_localmax_D4": 10,
  "integral_NOT_localmax": 0,
  "certs_disagree": 0,
  "ascent_found_inside_radius": 0,
  "ascent_found_at_4x_radius": 0,
  "localmax_probed": 10,
  "nonintegral_strict_saddle": 49,
  "nonintegral_no_saddle_cert": 0,
  "min_saddle_curvature": "1",
  "min_localmax_sigma": "1/2",
  "min_localmax_radius": 0.07692307692307693,
  "n_families": 2,
  "n_unhandled": 0,
  "families_all_nonintegral_with_cert": true,
  "counterexamples": [],
  "curvature_ge_2lam_minus_2": true,
  "sigma_ge_lam_minus_1": true,
  "graph": "G(8,0.45) seed=11",
  "n": 8,
  "k": 5,
  "lam": "3/2",
  "arm": "main"
 },
 {
  "n_stationary_isolated": 107,
  "n_integral": 28,
  "n_nonintegral": 79,
  "integral_localmax_thm36": 10,
  "integral_localmax_D4": 10,
  "integral_NOT_localmax": 18,
  "certs_disagree": 0,
  "ascent_found_inside_radius": 0,
  "ascent_found_at_4x_radius": 0,
  "localmax_probed": 10,
  "nonintegral_strict_saddle": 79,
  "nonintegral_no_saddle_cert": 0,
  "min_saddle_curvature": "2",
  "min_localmax_sigma": "0",
  "min_localmax_radius": 0.14285714285714285,
  "n_families": 4,
  "n_unhandled": 0,
  "families_all_nonintegral_with_cert": true,
  "counterexamples": [
   {
    "type": "integral stationary but not local max",
    "S1": [
     0,
     1,
     3,
     4,
     7
    ],
    "sigma": "0"
   },
   {
    "type": "integral stationary but not local max",
    "S1": [
     0,
     1,
     3,
     5,
     7
    ],
    "sigma": "0"
   },
   {
    "type": "integral stationary but not local max",
    "S1": [
     0,
     1,
     3,
     6,
     7
    ],
    "sigma": "0"
   },
   {
    "type": "integral stationary but not local max",
    "S1": [
     0,
     1,
     4,
     5,
     7
    ],
    "sigma": "0"
   },
   {
    "type": "integral stationary but not local max",
    "S1": [
     0,
     1,
     4,
     6,
     7
    ],
    "sigma": "0"
   },
   {
    "type": "integral stationary but not local max",
    "S1": [
     0,
     2,
     3,
     4,
     7
    ],
    "sigma": "0"
   },
   {
    "type": "integral stationary but not local max",
    "S1": [
     0,
     2,
     5,
     6,
     7
    ],
    "sigma": "0"
   },
   {
    "type": "integral stationary but not local max",
    "S1": [
     0,
     3,
     4,
     5,
     7
    ],
    "sigma": "0"
   },
   {
    "type": "integral stationary but not local max",
    "S1": [
     0,
     3,
     5,
     6,
     7
    ],
    "sigma": "0"
   },
   {
    "type": "integral stationary but not local max",
    "S1": [
     0,
     4,
     5,
     6,
     7
    ],
    "sigma": "0"
   },
   {
    "type": "integral stationary but not local max",
    "S1": [
     1,
     2,
     3,
     5,
     6
    ],
    "sigma": "0"
   },
   {
    "type": "integral stationary but not local max",
    "S1": [
     1,
     2,
     3,
     5,
     7
    ],
    "sigma": "0"
   },
   {
    "type": "integral stationary but not local max",
    "S1": [
     1,
     2,
     4,
     5,
     6
    ],
    "sigma": "0"
   },
   {
    "type": "integral stationary but not local max",
    "S1": [
     1,
     2,
     4,
     5,
     7
    ],
    "sigma": "0"
   },
   {
    "type": "integral stationary but not local max",
    "S1": [
     2,
     3,
     4,
     5,
     6
    ],
    "sigma": "0"
   },
   {
    "type": "integral stationary but not local max",
    "S1": [
     2,
     3,
     4,
     5,
     7
    ],
    "sigma": "0"
   },
   {
    "type": "integral stationary but not local max",
    "S1": [
     2,
     3,
     5,
     6,
     7
    ],
    "sigma": "0"
   },
   {
    "type": "integral stationary but not local max",
    "S1": [
     2,
     4,
     5,
     6,
     7
    ],
    "sigma": "0"
   }
  ],
  "curvature_ge_2lam_minus_2": true,
  "sigma_ge_lam_minus_1": false,
  "graph": "G(8,0.45) seed=11",
  "n": 8,
  "k": 5,
  "lam": "2",
  "arm": "M1_lam_integral"
 },
 {
  "n_stationary_isolated": 3,
  "n_integral": 2,
  "n_nonintegral": 1,
  "integral_localmax_thm36": 2,
  "integral_localmax_D4": 2,
  "integral_NOT_localmax": 0,
  "certs_disagree": 0,
  "ascent_found_inside_radius": 0,
  "ascent_found_at_4x_radius": 0,
  "localmax_probed": 2,
  "nonintegral_strict_saddle": 1,
  "nonintegral_no_saddle_cert": 0,
  "min_saddle_curvature": "1",
  "min_localmax_sigma": "1/2",
  "min_localmax_radius": 0.09090909090909091,
  "n_families": 0,
  "n_unhandled": 0,
  "families_all_nonintegral_with_cert": true,
  "counterexamples": [],
  "curvature_ge_2lam_minus_2": true,
  "sigma_ge_lam_minus_1": true,
  "graph": "G(8,0.45) seed=11",
  "n": 8,
  "k": 5,
  "lam": "1/2",
  "arm": "M2_lam_lt_1"
 },
 {
  "n_stationary_isolated": 202,
  "n_integral": 25,
  "n_nonintegral": 177,
  "integral_localmax_thm36": 25,
  "integral_localmax_D4": 25,
  "integral_NOT_localmax": 0,
  "certs_disagree": 0,
  "ascent_found_inside_radius": 0,
  "ascent_found_at_4x_radius": 0,
  "localmax_probed": 25,
  "nonintegral_strict_saddle": 177,
  "nonintegral_no_saddle_cert": 0,
  "min_saddle_curvature": "1",
  "min_localmax_sigma": "1/2",
  "min_localmax_radius": 0.07692307692307693,
  "n_families": 3,
  "n_unhandled": 0,
  "families_all_nonintegral_with_cert": true,
  "counterexamples": [],
  "curvature_ge_2lam_minus_2": true,
  "sigma_ge_lam_minus_1": true,
  "graph": "G(9,0.35) seed=5",
  "n": 9,
  "k": 3,
  "lam": "3/2",
  "arm": "main"
 },
 {
  "n_stationary_isolated": 520,
  "n_integral": 70,
  "n_nonintegral": 450,
  "integral_localmax_thm36": 25,
  "integral_localmax_D4": 25,
  "integral_NOT_localmax": 45,
  "certs_disagree": 0,
  "ascent_found_inside_radius": 0,
  "ascent_found_at_4x_radius": 0,
  "localmax_probed": 25,
  "nonintegral_strict_saddle": 450,
  "nonintegral_no_saddle_cert": 0,
  "min_saddle_curvature": "2",
  "min_localmax_sigma": "0",
  "min_localmax_radius": 0.14285714285714285,
  "n_families": 111,
  "n_unhandled": 0,
  "families_all_nonintegral_with_cert": true,
  "counterexamples": [
   {
    "type": "integral stationary but not local max",
    "S1": [
     0,
     1,
     2
    ],
    "sigma": "0"
   },
   {
    "type": "integral stationary but not local max",
    "S1": [
     0,
     1,
     3
    ],
    "sigma": "0"
   },
   {
    "type": "integral stationary but not local max",
    "S1": [
     0,
     1,
     5
    ],
    "sigma": "0"
   },
   {
    "type": "integral stationary but not local max",
    "S1": [
     0,
     1,
     6
    ],
    "sigma": "0"
   },
   {
    "type": "integral stationary but not local max",
    "S1": [
     0,
     1,
     8
    ],
    "sigma": "0"
   },
   {
    "type": "integral stationary but not local max",
    "S1": [
     0,
     2,
     3
    ],
    "sigma": "0"
   },
   {
    "type": "integral stationary but not local max",
    "S1": [
     0,
     2,
     4
    ],
    "sigma": "0"
   },
   {
    "type": "integral stationary but not local max",
    "S1": [
     0,
     2,
     5
    ],
    "sigma": "0"
   },
   {
    "type": "integral stationary but not local max",
    "S1": [
     0,
     2,
     7
    ],
    "sigma": "0"
   },
   {
    "type": "integral stationary but not local max",
    "S1": [
     0,
     2,
     8
    ],
    "sigma": "0"
   },
   {
    "type": "integral stationary but not local max",
    "S1": [
     0,
     3,
     4
    ],
    "sigma": "0"
   },
   {
    "type": "integral stationary but not local max",
    "S1": [
     0,
     3,
     5
    ],
    "sigma": "0"
   },
   {
    "type": "integral stationary but not local max",
    "S1": [
     0,
     3,
     7
    ],
    "sigma": "0"
   },
   {
    "type": "integral stationary but not local max",
    "S1": [
     0,
     3,
     8
    ],
    "sigma": "0"
   },
   {
    "type": "integral stationary but not local max",
    "S1": [
     0,
     4,
     5
    ],
    "sigma": "0"
   },
   {
    "type": "integral stationary but not local max",
    "S1": [
     0,
     4,
     6
    ],
    "sigma": "0"
   },
   {
    "type": "integral stationary but not local max",
    "S1": [
     0,
     4,
     8
    ],
    "sigma": "0"
   },
   {
    "type": "integral stationary but not local max",
    "S1": [
     0,
     5,
     6
    ],
    "sigma": "0"
   },
   {
    "type": "integral stationary but not local max",
    "S1": [
     0,
     5,
     7
    ],
    "sigma": "0"
   },
   {
    "type": "integral stationary but not local max",
    "S1": [
     0,
     5,
     8
    ],
    "sigma": "0"
   },
   {
    "type": "integral stationary but not local max",
    "S1": [
     0,
     6,
     8
    ],
    "sigma": "0"
   },
   {
    "type": "integral stationary but not local max",
    "S1": [
     0,
     7,
     8
    ],
    "sigma": "0"
   },
   {
    "type": "integral stationary but not local max",
    "S1": [
     1,
     2,
     3
    ],
    "sigma": "0"
   },
   {
    "type": "integral stationary but not local max",
    "S1": [
     1,
     2,
     6
    ],
    "sigma": "0"
   },
   {
    "type": "integral stationary but not local max",
    "S1": [
     1,
     2,
     7
    ],
    "sigma": "0"
   },
   {
    "type": "integral stationary but not local max",
    "S1": [
     1,
     3,
     4
    ],
    "sigma": "0"
   },
   {
    "type": "integral stationary but not local max",
    "S1": [
     1,
     3,
     5
    ],
    "sigma": "0"
   },
   {
    "type": "integral stationary but not local max",
    "S1": [
     1,
     3,
     7
    ],
    "sigma": "0"
   },
   {
    "type": "integral stationary but not local max",
    "S1": [
     1,
     3,
     8
    ],
    "sigma": "0"
   },
   {
    "type": "integral stationary but not local max",
    "S1": [
     1,
     4,
     6
    ],
    "sigma": "0"
   },
   {
    "type": "integral stationary but not local max",
    "S1": [
     1,
     5,
     6
    ],
    "sigma": "0"
   },
   {
    "type": "integral stationary but not local max",
    "S1": [
     1,
     6,
     8
    ],
    "sigma": "0"
   },
   {
    "type": "integral stationary but not local max",
    "S1": [
     1,
     7,
     8
    ],
    "sigma": "0"
   },
   {
    "type": "integral stationary but not local max",
    "S1": [
     2,
     4,
     8
    ],
    "sigma": "0"
   },
   {
    "type": "integral stationary but not local max",
    "S1": [
     2,
     5,
     8
    ],
    "sigma": "0"
   },
   {
    "type": "integral stationary but not local max",
    "S1": [
     2,
     6,
     7
    ],
    "sigma": "0"
   },
   {
    "type": "integral stationary but not local max",
    "S1": [
     2,
     6,
     8
    ],
    "sigma": "0"
   },
   {
    "type": "integral stationary but not local max",
    "S1": [
     3,
     4,
     5
    ],
    "sigma": "0"
   },
   {
    "type": "integral stationary but not local max",
    "S1": [
     3,
     5,
     6
    ],
    "sigma": "0"
   },
   {
    "type": "integral stationary but not local max",
    "S1": [
     3,
     5,
     8
    ],
    "sigma": "0"
   },
   {
    "type": "integral stationary but not local max",
    "S1": [
     3,
     6,
     7
    ],
    "sigma": "0"
   },
   {
    "type": "integral stationary but not local max",
    "S1": [
     4,
     6,
     7
    ],
    "sigma": "0"
   },
   {
    "type": "integral stationary but not local max",
    "S1": [
     5,
     6,
     7
    ],
    "sigma": "0"
   },
   {
    "type": "integral stationary but not local max",
    "S1": [
     5,
     6,
     8
    ],
    "sigma": "0"
   },
   {
    "type": "integral stationary but not local max",
    "S1": [
     6,
     7,
     8
    ],
    "sigma": "0"
   }
  ],
  "curvature_ge_2lam_minus_2": true,
  "sigma_ge_lam_minus_1": false,
  "graph": "G(9,0.35) seed=5",
  "n": 9,
  "k": 3,
  "lam": "2",
  "arm": "M1_lam_integral"
 },
 {
  "n_stationary_isolated": 40,
  "n_integral": 5,
  "n_nonintegral": 35,
  "integral_localmax_thm36": 5,
  "integral_localmax_D4": 5,
  "integral_NOT_localmax": 0,
  "certs_disagree": 0,
  "ascent_found_inside_radius": 0,
  "ascent_found_at_4x_radius": 0,
  "localmax_probed": 5,
  "nonintegral_strict_saddle": 30,
  "nonintegral_no_saddle_cert": 5,
  "min_saddle_curvature": "1",
  "min_localmax_sigma": "1/2",
  "min_localmax_radius": 0.09090909090909091,
  "n_families": 30,
  "n_unhandled": 0,
  "families_all_nonintegral_with_cert": true,
  "counterexamples": [
   {
    "type": "non-integral stationary with no strict-saddle certificate",
    "Sf": [
     1,
     5
    ],
    "x": [
     "0",
     "1/2",
     "0",
     "0",
     "1",
     "1/2",
     "0",
     "1",
     "0"
    ]
   },
   {
    "type": "non-integral stationary with no strict-saddle certificate",
    "Sf": [
     2,
     4
    ],
    "x": [
     "0",
     "0",
     "1/2",
     "1",
     "1/2",
     "0",
     "1",
     "0",
     "0"
    ]
   },
   {
    "type": "non-integral stationary with no strict-saddle certificate",
    "Sf": [
     3,
     4
    ],
    "x": [
     "0",
     "0",
     "1",
     "1/2",
     "1/2",
     "0",
     "1",
     "0",
     "0"
    ]
   },
   {
    "type": "non-integral stationary with no strict-saddle certificate",
    "Sf": [
     4,
     5
    ],
    "x": [
     "0",
     "1",
     "0",
     "0",
     "1/2",
     "1/2",
     "0",
     "1",
     "0"
    ]
   },
   {
    "type": "non-integral stationary with no strict-saddle certificate",
    "Sf": [
     4,
     7
    ],
    "x": [
     "0",
     "1",
     "0",
     "0",
     "1/2",
     "1",
     "0",
     "1/2",
     "0"
    ]
   }
  ],
  "curvature_ge_2lam_minus_2": true,
  "sigma_ge_lam_minus_1": true,
  "graph": "G(9,0.35) seed=5",
  "n": 9,
  "k": 3,
  "lam": "1/2",
  "arm": "M2_lam_lt_1"
 },
 {
  "n_stationary_isolated": 196,
  "n_integral": 28,
  "n_nonintegral": 168,
  "integral_localmax_thm36": 28,
  "integral_localmax_D4": 28,
  "integral_NOT_localmax": 0,
  "certs_disagree": 0,
  "ascent_found_inside_radius": 0,
  "ascent_found_at_4x_radius": 0,
  "localmax_probed": 28,
  "nonintegral_strict_saddle": 168,
  "nonintegral_no_saddle_cert": 0,
  "min_saddle_curvature": "1",
  "min_localmax_sigma": "1/2",
  "min_localmax_radius": 0.07692307692307693,
  "n_families": 13,
  "n_unhandled": 0,
  "families_all_nonintegral_with_cert": true,
  "counterexamples": [],
  "curvature_ge_2lam_minus_2": true,
  "sigma_ge_lam_minus_1": true,
  "graph": "G(9,0.35) seed=5",
  "n": 9,
  "k": 4,
  "lam": "3/2",
  "arm": "main"
 },
 {
  "n_stationary_isolated": 456,
  "n_integral": 83,
  "n_nonintegral": 373,
  "integral_localmax_thm36": 28,
  "integral_localmax_D4": 28,
  "integral_NOT_localmax": 55,
  "certs_disagree": 0,
  "ascent_found_inside_radius": 0,
  "ascent_found_at_4x_radius": 0,
  "localmax_probed": 28,
  "nonintegral_strict_saddle": 373,
  "nonintegral_no_saddle_cert": 0,
  "min_saddle_curvature": "2",
  "min_localmax_sigma": "0",
  "min_localmax_radius": 0.14285714285714285,
  "n_families": 130,
  "n_unhandled": 0,
  "families_all_nonintegral_with_cert": true,
  "counterexamples": [
   {
    "type": "integral stationary but not local max",
    "S1": [
     0,
     1,
     2,
     3
    ],
    "sigma": "0"
   },
   {
    "type": "integral stationary but not local max",
    "S1": [
     0,
     1,
     2,
     5
    ],
    "sigma": "0"
   },
   {
    "type": "integral stationary but not local max",
    "S1": [
     0,
     1,
     2,
     6
    ],
    "sigma": "0"
   },
   {
    "type": "integral stationary but not local max",
    "S1": [
     0,
     1,
     2,
     7
    ],
    "sigma": "0"
   },
   {
    "type": "integral stationary but not local max",
    "S1": [
     0,
     1,
     3,
     5
    ],
    "sigma": "0"
   },
   {
    "type": "integral stationary but not local max",
    "S1": [
     0,
     1,
     3,
     6
    ],
    "sigma": "0"
   },
   {
    "type": "integral stationary but not local max",
    "S1": [
     0,
     1,
     3,
     7
    ],
    "sigma": "0"
   },
   {
    "type": "integral stationary but not local max",
    "S1": [
     0,
     1,
     3,
     8
    ],
    "sigma": "0"
   },
   {
    "type": "integral stationary but not local max",
    "S1": [
     0,
     1,
     5,
     6
    ],
    "sigma": "0"
   },
   {
    "type": "integral stationary but not local max",
    "S1": [
     0,
     1,
     5,
     8
    ],
    "sigma": "0"
   },
   {
    "type": "integral stationary but not local max",
    "S1": [
     0,
     1,
     6,
     8
    ],
    "sigma": "0"
   },
   {
    "type": "integral stationary but not local max",
    "S1": [
     0,
     1,
     7,
     8
    ],
    "sigma": "0"
   },
   {
    "type": "integral stationary but not local max",
    "S1": [
     0,
     2,
     3,
     4
    ],
    "sigma": "0"
   },
   {
    "type": "integral stationary but not local max",
    "S1": [
     0,
     2,
     3,
     6
    ],
    "sigma": "0"
   },
   {
    "type": "integral stationary but not local max",
    "S1": [
     0,
     2,
     4,
     5
    ],
    "sigma": "0"
   },
   {
    "type": "integral stationary but not local max",
    "S1": [
     0,
     2,
     4,
     6
    ],
    "sigma": "0"
   },
   {
    "type": "integral stationary but not local max",
    "S1": [
     0,
     2,
     5,
     6
    ],
    "sigma": "0"
   },
   {
    "type": "integral stationary but not local max",
    "S1": [
     0,
     2,
     5,
     7
    ],
    "sigma": "0"
   },
   {
    "type": "integral stationary but not local max",
    "S1": [
     0,
     2,
     6,
     8
    ],
    "sigma": "0"
   },
   {
    "type": "integral stationary but not local max",
    "S1": [
     0,
     3,
     4,
     6
    ],
    "sigma": "0"
   },
   {
    "type": "integral stationary but not local max",
    "S1": [
     0,
     3,
     4,
     8
    ],
    "sigma": "0"
   },
   {
    "type": "integral stationary but not local max",
    "S1": [
     0,
     3,
     5,
     6
    ],
    "sigma": "0"
   },
   {
    "type": "integral stationary but not local max",
    "S1": [
     0,
     3,
     6,
     8
    ],
    "sigma": "0"
   },
   {
    "type": "integral stationary but not local max",
    "S1": [
     0,
     3,
     7,
     8
    ],
    "sigma": "0"
   },
   {
    "type": "integral stationary but not local max",
    "S1": [
     0,
     4,
     5,
     8
    ],
    "sigma": "0"
   },
   {
    "type": "integral stationary but not local max",
    "S1": [
     0,
     4,
     6,
     7
    ],
    "sigma": "0"
   },
   {
    "type": "integral stationary but not local max",
    "S1": [
     0,
     5,
     6,
     7
    ],
    "sigma": "0"
   },
   {
    "type": "integral stationary but not local max",
    "S1": [
     0,
     5,
     6,
     8
    ],
    "sigma": "0"
   },
   {
    "type": "integral stationary but not local max",
    "S1": [
     0,
     5,
     7,
     8
    ],
    "sigma": "0"
   },
   {
    "type": "integral stationary but not local max",
    "S1": [
     0,
     6,
     7,
     8
    ],
    "sigma": "0"
   },
   {
    "type": "integral stationary but not local max",
    "S1": [
     1,
     2,
     3,
     6
    ],
    "sigma": "0"
   },
   {
    "type": "integral stationary but not local max",
    "S1": [
     1,
     2,
     4,
     7
    ],
    "sigma": "0"
   },
   {
    "type": "integral stationary but not local max",
    "S1": [
     1,
     2,
     5,
     7
    ],
    "sigma": "0"
   },
   {
    "type": "integral stationary but not local max",
    "S1": [
     1,
     2,
     5,
     8
    ],
    "sigma": "0"
   },
   {
    "type": "integral stationary but not local max",
    "S1": [
     1,
     3,
     4,
     5
    ],
    "sigma": "0"
   },
   {
    "type": "integral stationary but not local max",
    "S1": [
     1,
     3,
     4,
     6
    ],
    "sigma": "0"
   },
   {
    "type": "integral stationary but not local max",
    "S1": [
     1,
     3,
     5,
     8
    ],
    "sigma": "0"
   },
   {
    "type": "integral stationary but not local max",
    "S1": [
     1,
     3,
     6,
     8
    ],
    "sigma": "0"
   },
   {
    "type": "integral stationary but not local max",
    "S1": [
     1,
     3,
     7,
     8
    ],
    "sigma": "0"
   },
   {
    "type": "integral stationary but not local max",
    "S1": [
     1,
     4,
     6,
     7
    ],
    "sigma": "0"
   },
   {
    "type": "integral stationary but not local max",
    "S1": [
     1,
     4,
     7,
     8
    ],
    "sigma": "0"
   },
   {
    "type": "integral stationary but not local max",
    "S1": [
     1,
     5,
     6,
     7
    ],
    "sigma": "0"
   },
   {
    "type": "integral stationary but not local max",
    "S1": [
     1,
     5,
     6,
     8
    ],
    "sigma": "0"
   },
   {
    "type": "integral stationary but not local max",
    "S1": [
     1,
     5,
     7,
     8
    ],
    "sigma": "0"
   },
   {
    "type": "integral stationary but not local max",
    "S1": [
     1,
     6,
     7,
     8
    ],
    "sigma": "0"
   },
   {
    "type": "integral stationary but not local max",
    "S1": [
     2,
     3,
     4,
     5
    ],
    "sigma": "0"
   },
   {
    "type": "integral stationary but not local max",
    "S1": [
     2,
     3,
     4,
     8
    ],
    "sigma": "0"
   },
   {
    "type": "integral stationary but not local max",
    "S1": [
     2,
     3,
     5,
     6
    ],
    "sigma": "0"
   },
   {
    "type": "integral stationary but not local max",
    "S1": [
     2,
     3,
     6,
     8
    ],
    "sigma": "0"
   },
   {
    "type": "integral stationary but not local max",
    "S1": [
     2,
     4,
     6,
     8
    ],
    "sigma": "0"
   },
   {
    "type": "integral stationary but not local max",
    "S1": [
     2,
     4,
     7,
     8
    ],
    "sigma": "0"
   },
   {
    "type": "integral stationary but not local max",
    "S1": [
     2,
     5,
     6,
     8
    ],
    "sigma": "0"
   },
   {
    "type": "integral stationary but not local max",
    "S1": [
     3,
     4,
     5,
     6
    ],
    "sigma": "0"
   },
   {
    "type": "integral stationary but not local max",
    "S1": [
     3,
     4,
     5,
     7
    ],
    "sigma": "0"
   },
   {
    "type": "integral stationary but not local max",
    "S1": [
     3,
     5,
     6,
     8
    ],
    "sigma": "0"
   }
  ],
  "curvature_ge_2lam_minus_2": true,
  "sigma_ge_lam_minus_1": false,
  "graph": "G(9,0.35) seed=5",
  "n": 9,
  "k": 4,
  "lam": "2",
  "arm": "M1_lam_integral"
 },
 {
  "n_stationary_isolated": 11,
  "n_integral": 4,
  "n_nonintegral": 7,
  "integral_localmax_thm36": 4,
  "integral_localmax_D4": 4,
  "integral_NOT_localmax": 0,
  "certs_disagree": 0,
  "ascent_found_inside_radius": 0,
  "ascent_found_at_4x_radius": 0,
  "localmax_probed": 4,
  "nonintegral_strict_saddle": 7,
  "nonintegral_no_saddle_cert": 0,
  "min_saddle_curvature": "1",
  "min_localmax_sigma": "1/2",
  "min_localmax_radius": 0.09090909090909091,
  "n_families": 45,
  "n_unhandled": 0,
  "families_all_nonintegral_with_cert": true,
  "counterexamples": [],
  "curvature_ge_2lam_minus_2": true,
  "sigma_ge_lam_minus_1": true,
  "graph": "G(9,0.35) seed=5",
  "n": 9,
  "k": 4,
  "lam": "1/2",
  "arm": "M2_lam_lt_1"
 },
 {
  "n_stationary_isolated": 257,
  "n_integral": 29,
  "n_nonintegral": 228,
  "integral_localmax_thm36": 29,
  "integral_localmax_D4": 29,
  "integral_NOT_localmax": 0,
  "certs_disagree": 0,
  "ascent_found_inside_radius": 0,
  "ascent_found_at_4x_radius": 0,
  "localmax_probed": 29,
  "nonintegral_strict_saddle": 228,
  "nonintegral_no_saddle_cert": 0,
  "min_saddle_curvature": "1",
  "min_localmax_sigma": "1/2",
  "min_localmax_radius": 0.06666666666666667,
  "n_families": 39,
  "n_unhandled": 0,
  "families_all_nonintegral_with_cert": true,
  "counterexamples": [],
  "curvature_ge_2lam_minus_2": true,
  "sigma_ge_lam_minus_1": true,
  "graph": "G(9,0.6) seed=8",
  "n": 9,
  "k": 3,
  "lam": "3/2",
  "arm": "main"
 },
 {
  "n_stationary_isolated": 543,
  "n_integral": 66,
  "n_nonintegral": 477,
  "integral_localmax_thm36": 29,
  "integral_localmax_D4": 29,
  "integral_NOT_localmax": 37,
  "certs_disagree": 0,
  "ascent_found_inside_radius": 0,
  "ascent_found_at_4x_radius": 0,
  "localmax_probed": 29,
  "nonintegral_strict_saddle": 477,
  "nonintegral_no_saddle_cert": 0,
  "min_saddle_curvature": "2",
  "min_localmax_sigma": "0",
  "min_localmax_radius": 0.125,
  "n_families": 163,
  "n_unhandled": 0,
  "families_all_nonintegral_with_cert": true,
  "counterexamples": [
   {
    "type": "integral stationary but not local max",
    "S1": [
     0,
     1,
     4
    ],
    "sigma": "0"
   },
   {
    "type": "integral stationary but not local max",
    "S1": [
     0,
     2,
     3
    ],
    "sigma": "0"
   },
   {
    "type": "integral stationary but not local max",
    "S1": [
     0,
     2,
     5
    ],
    "sigma": "0"
   },
   {
    "type": "integral stationary but not local max",
    "S1": [
     0,
     2,
     6
    ],
    "sigma": "0"
   },
   {
    "type": "integral stationary but not local max",
    "S1": [
     0,
     2,
     8
    ],
    "sigma": "0"
   },
   {
    "type": "integral stationary but not local max",
    "S1": [
     0,
     3,
     4
    ],
    "sigma": "0"
   },
   {
    "type": "integral stationary but not local max",
    "S1": [
     0,
     3,
     6
    ],
    "sigma": "0"
   },
   {
    "type": "integral stationary but not local max",
    "S1": [
     0,
     3,
     8
    ],
    "sigma": "0"
   },
   {
    "type": "integral stationary but not local max",
    "S1": [
     0,
     4,
     5
    ],
    "sigma": "0"
   },
   {
    "type": "integral stationary but not local max",
    "S1": [
     0,
     5,
     8
    ],
    "sigma": "0"
   },
   {
    "type": "integral stationary but not local max",
    "S1": [
     0,
     6,
     7
    ],
    "sigma": "0"
   },
   {
    "type": "integral stationary but not local max",
    "S1": [
     0,
     7,
     8
    ],
    "sigma": "0"
   },
   {
    "type": "integral stationary but not local max",
    "S1": [
     1,
     2,
     3
    ],
    "sigma": "0"
   },
   {
    "type": "integral stationary but not local max",
    "S1": [
     1,
     2,
     4
    ],
    "sigma": "0"
   },
   {
    "type": "integral stationary but not local max",
    "S1": [
     1,
     2,
     5
    ],
    "sigma": "0"
   },
   {
    "type": "integral stationary but not local max",
    "S1": [
     1,
     2,
     6
    ],
    "sigma": "0"
   },
   {
    "type": "integral stationary but not local max",
    "S1": [
     1,
     2,
     8
    ],
    "sigma": "0"
   },
   {
    "type": "integral stationary but not local max",
    "S1": [
     1,
     3,
     6
    ],
    "sigma": "0"
   },
   {
    "type": "integral stationary but not local max",
    "S1": [
     1,
     3,
     7
    ],
    "sigma": "0"
   },
   {
    "type": "integral stationary but not local max",
    "S1": [
     1,
     3,
     8
    ],
    "sigma": "0"
   },
   {
    "type": "integral stationary but not local max",
    "S1": [
     1,
     4,
     6
    ],
    "sigma": "0"
   },
   {
    "type": "integral stationary but not local max",
    "S1": [
     1,
     4,
     7
    ],
    "sigma": "0"
   },
   {
    "type": "integral stationary but not local max",
    "S1": [
     1,
     5,
     8
    ],
    "sigma": "0"
   },
   {
    "type": "integral stationary but not local max",
    "S1": [
     1,
     6,
     7
    ],
    "sigma": "0"
   },
   {
    "type": "integral stationary but not local max",
    "S1": [
     1,
     7,
     8
    ],
    "sigma": "0"
   },
   {
    "type": "integral stationary but not local max",
    "S1": [
     2,
     3,
     6
    ],
    "sigma": "0"
   },
   {
    "type": "integral stationary but not local max",
    "S1": [
     2,
     3,
     7
    ],
    "sigma": "0"
   },
   {
    "type": "integral stationary but not local max",
    "S1": [
     2,
     4,
     6
    ],
    "sigma": "0"
   },
   {
    "type": "integral stationary but not local max",
    "S1": [
     2,
     4,
     7
    ],
    "sigma": "0"
   },
   {
    "type": "integral stationary but not local max",
    "S1": [
     2,
     5,
     8
    ],
    "sigma": "0"
   },
   {
    "type": "integral stationary but not local max",
    "S1": [
     2,
     6,
     7
    ],
    "sigma": "0"
   },
   {
    "type": "integral stationary but not local max",
    "S1": [
     2,
     7,
     8
    ],
    "sigma": "0"
   },
   {
    "type": "integral stationary but not local max",
    "S1": [
     3,
     5,
     6
    ],
    "sigma": "0"
   },
   {
    "type": "integral stationary but not local max",
    "S1": [
     3,
     5,
     7
    ],
    "sigma": "0"
   },
   {
    "type": "integral stationary but not local max",
    "S1": [
     4,
     5,
     6
    ],
    "sigma": "0"
   },
   {
    "type": "integral stationary but not local max",
    "S1": [
     4,
     5,
     7
    ],
    "sigma": "0"
   },
   {
    "type": "integral stationary but not local max",
    "S1": [
     5,
     6,
     8
    ],
    "sigma": "0"
   }
  ],
  "curvature_ge_2lam_minus_2": true,
  "sigma_ge_lam_minus_1": false,
  "graph": "G(9,0.6) seed=8",
  "n": 9,
  "k": 3,
  "lam": "2",
  "arm": "M1_lam_integral"
 },
 {
  "n_stationary_isolated": 31,
  "n_integral": 4,
  "n_nonintegral": 27,
  "integral_localmax_thm36": 4,
  "integral_localmax_D4": 4,
  "integral_NOT_localmax": 0,
  "certs_disagree": 0,
  "ascent_found_inside_radius": 0,
  "ascent_found_at_4x_radius": 0,
  "localmax_probed": 4,
  "nonintegral_strict_saddle": 22,
  "nonintegral_no_saddle_cert": 5,
  "min_saddle_curvature": "1",
  "min_localmax_sigma": "1/2",
  "min_localmax_radius": 0.07692307692307693,
  "n_families": 34,
  "n_unhandled": 0,
  "families_all_nonintegral_with_cert": true,
  "counterexamples": [
   {
    "type": "non-integral stationary with no strict-saddle certificate",
    "Sf": [
     0,
     1,
     3,
     5
    ],
    "x": [
     "3/4",
     "3/4",
     "0",
     "3/4",
     "0",
     "3/4",
     "0",
     "0",
     "0"
    ]
   },
   {
    "type": "non-integral stationary with no strict-saddle certificate",
    "Sf": [
     0,
     1,
     5,
     6
    ],
    "x": [
     "3/4",
     "3/4",
     "0",
     "0",
     "0",
     "3/4",
     "3/4",
     "0",
     "0"
    ]
   },
   {
    "type": "non-integral stationary with no strict-saddle certificate",
    "Sf": [
     0,
     1,
     6,
     8
    ],
    "x": [
     "3/4",
     "3/4",
     "0",
     "0",
     "0",
     "0",
     "3/4",
     "0",
     "3/4"
    ]
   },
   {
    "type": "non-integral stationary with no strict-saddle certificate",
    "Sf": [
     1,
     3,
     4,
     5
    ],
    "x": [
     "0",
     "3/4",
     "0",
     "3/4",
     "3/4",
     "3/4",
     "0",
     "0",
     "0"
    ]
   },
   {
    "type": "non-integral stationary with no strict-saddle certificate",
    "Sf": [
     2,
     3,
     4,
     5
    ],
    "x": [
     "0",
     "0",
     "3/4",
     "3/4",
     "3/4",
     "3/4",
     "0",
     "0",
     "0"
    ]
   }
  ],
  "curvature_ge_2lam_minus_2": true,
  "sigma_ge_lam_minus_1": true,
  "graph": "G(9,0.6) seed=8",
  "n": 9,
  "k": 3,
  "lam": "1/2",
  "arm": "M2_lam_lt_1"
 },
 {
  "n_stationary_isolated": 335,
  "n_integral": 36,
  "n_nonintegral": 299,
  "integral_localmax_thm36": 36,
  "integral_localmax_D4": 36,
  "integral_NOT_localmax": 0,
  "certs_disagree": 0,
  "ascent_found_inside_radius": 0,
  "ascent_found_at_4x_radius": 0,
  "localmax_probed": 36,
  "nonintegral_strict_saddle": 299,
  "nonintegral_no_saddle_cert": 0,
  "min_saddle_curvature": "1",
  "min_localmax_sigma": "1/2",
  "min_localmax_radius": 0.06666666666666667,
  "n_families": 83,
  "n_unhandled": 0,
  "families_all_nonintegral_with_cert": true,
  "counterexamples": [],
  "curvature_ge_2lam_minus_2": true,
  "sigma_ge_lam_minus_1": true,
  "graph": "G(9,0.6) seed=8",
  "n": 9,
  "k": 4,
  "lam": "3/2",
  "arm": "main"
 },
 {
  "n_stationary_isolated": 732,
  "n_integral": 79,
  "n_nonintegral": 653,
  "integral_localmax_thm36": 36,
  "integral_localmax_D4": 36,
  "integral_NOT_localmax": 43,
  "certs_disagree": 0,
  "ascent_found_inside_radius": 0,
  "ascent_found_at_4x_radius": 0,
  "localmax_probed": 36,
  "nonintegral_strict_saddle": 653,
  "nonintegral_no_saddle_cert": 0,
  "min_saddle_curvature": "2",
  "min_localmax_sigma": "0",
  "min_localmax_radius": 0.125,
  "n_families": 221,
  "n_unhandled": 0,
  "families_all_nonintegral_with_cert": true,
  "counterexamples": [
   {
    "type": "integral stationary but not local max",
    "S1": [
     0,
     1,
     3,
     4
    ],
    "sigma": "0"
   },
   {
    "type": "integral stationary but not local max",
    "S1": [
     0,
     1,
     3,
     6
    ],
    "sigma": "0"
   },
   {
    "type": "integral stationary but not local max",
    "S1": [
     0,
     1,
     3,
     7
    ],
    "sigma": "0"
   },
   {
    "type": "integral stationary but not local max",
    "S1": [
     0,
     1,
     4,
     5
    ],
    "sigma": "0"
   },
   {
    "type": "integral stationary but not local max",
    "S1": [
     0,
     1,
     4,
     8
    ],
    "sigma": "0"
   },
   {
    "type": "integral stationary but not local max",
    "S1": [
     0,
     1,
     5,
     8
    ],
    "sigma": "0"
   },
   {
    "type": "integral stationary but not local max",
    "S1": [
     0,
     2,
     3,
     6
    ],
    "sigma": "0"
   },
   {
    "type": "integral stationary but not local max",
    "S1": [
     0,
     2,
     3,
     7
    ],
    "sigma": "0"
   },
   {
    "type": "integral stationary but not local max",
    "S1": [
     0,
     2,
     4,
     8
    ],
    "sigma": "0"
   },
   {
    "type": "integral stationary but not local max",
    "S1": [
     0,
     2,
     5,
     8
    ],
    "sigma": "0"
   },
   {
    "type": "integral stationary but not local max",
    "S1": [
     0,
     3,
     4,
     5
    ],
    "sigma": "0"
   },
   {
    "type": "integral stationary but not local max",
    "S1": [
     0,
     3,
     4,
     7
    ],
    "sigma": "0"
   },
   {
    "type": "integral stationary but not local max",
    "S1": [
     0,
     3,
     5,
     6
    ],
    "sigma": "0"
   },
   {
    "type": "integral stationary but not local max",
    "S1": [
     0,
     3,
     5,
     7
    ],
    "sigma": "0"
   },
   {
    "type": "integral stationary but not local max",
    "S1": [
     0,
     4,
     6,
     7
    ],
    "sigma": "0"
   },
   {
    "type": "integral stationary but not local max",
    "S1": [
     0,
     4,
     7,
     8
    ],
    "sigma": "0"
   },
   {
    "type": "integral stationary but not local max",
    "S1": [
     0,
     5,
     6,
     7
    ],
    "sigma": "0"
   },
   {
    "type": "integral stationary but not local max",
    "S1": [
     0,
     5,
     6,
     8
    ],
    "sigma": "0"
   },
   {
    "type": "integral stationary but not local max",
    "S1": [
     1,
     2,
     3,
     4
    ],
    "sigma": "0"
   },
   {
    "type": "integral stationary but not local max",
    "S1": [
     1,
     2,
     3,
     5
    ],
    "sigma": "0"
   },
   {
    "type": "integral stationary but not local max",
    "S1": [
     1,
     2,
     3,
     6
    ],
    "sigma": "0"
   },
   {
    "type": "integral stationary but not local max",
    "S1": [
     1,
     2,
     4,
     5
    ],
    "sigma": "0"
   },
   {
    "type": "integral stationary but not local max",
    "S1": [
     1,
     2,
     4,
     6
    ],
    "sigma": "0"
   },
   {
    "type": "integral stationary but not local max",
    "S1": [
     1,
     2,
     5,
     8
    ],
    "sigma": "0"
   },
   {
    "type": "integral stationary but not local max",
    "S1": [
     1,
     3,
     4,
     8
    ],
    "sigma": "0"
   },
   {
    "type": "integral stationary but not local max",
    "S1": [
     1,
     3,
     5,
     6
    ],
    "sigma": "0"
   },
   {
    "type": "integral stationary but not local max",
    "S1": [
     1,
     4,
     5,
     8
    ],
    "sigma": "0"
   },
   {
    "type": "integral stationary but not local max",
    "S1": [
     1,
     4,
     6,
     8
    ],
    "sigma": "0"
   },
   {
    "type": "integral stationary but not local max",
    "S1": [
     1,
     5,
     6,
     7
    ],
    "sigma": "0"
   },
   {
    "type": "integral stationary but not local max",
    "S1": [
     1,
     5,
     6,
     8
    ],
    "sigma": "0"
   },
   {
    "type": "integral stationary but not local max",
    "S1": [
     2,
     3,
     4,
     8
    ],
    "sigma": "0"
   },
   {
    "type": "integral stationary but not local max",
    "S1": [
     2,
     3,
     5,
     8
    ],
    "sigma": "0"
   },
   {
    "type": "integral stationary but not local max",
    "S1": [
     2,
     3,
     6,
     8
    ],
    "sigma": "0"
   },
   {
    "type": "integral stationary but not local max",
    "S1": [
     2,
     4,
     5,
     8
    ],
    "sigma": "0"
   },
   {
    "type": "integral stationary but not local max",
    "S1": [
     2,
     4,
     6,
     8
    ],
    "sigma": "0"
   },
   {
    "type": "integral stationary but not local max",
    "S1": [
     2,
     5,
     6,
     7
    ],
    "sigma": "0"
   },
   {
    "type": "integral stationary but not local max",
    "S1": [
     3,
     4,
     6,
     7
    ],
    "sigma": "0"
   },
   {
    "type": "integral stationary but not local max",
    "S1": [
     3,
     4,
     7,
     8
    ],
    "sigma": "0"
   },
   {
    "type": "integral stationary but not local max",
    "S1": [
     3,
     5,
     7,
     8
    ],
    "sigma": "0"
   },
   {
    "type": "integral stationary but not local max",
    "S1": [
     3,
     6,
     7,
     8
    ],
    "sigma": "0"
   },
   {
    "type": "integral stationary but not local max",
    "S1": [
     4,
     5,
     7,
     8
    ],
    "sigma": "0"
   },
   {
    "type": "integral stationary but not local max",
    "S1": [
     4,
     6,
     7,
     8
    ],
    "sigma": "0"
   },
   {
    "type": "integral stationary but not local max",
    "S1": [
     5,
     6,
     7,
     8
    ],
    "sigma": "0"
   }
  ],
  "curvature_ge_2lam_minus_2": true,
  "sigma_ge_lam_minus_1": false,
  "graph": "G(9,0.6) seed=8",
  "n": 9,
  "k": 4,
  "lam": "2",
  "arm": "M1_lam_integral"
 },
 {
  "n_stationary_isolated": 27,
  "n_integral": 6,
  "n_nonintegral": 21,
  "integral_localmax_thm36": 6,
  "integral_localmax_D4": 6,
  "integral_NOT_localmax": 0,
  "certs_disagree": 0,
  "ascent_found_inside_radius": 0,
  "ascent_found_at_4x_radius": 0,
  "localmax_probed": 6,
  "nonintegral_strict_saddle": 17,
  "nonintegral_no_saddle_cert": 4,
  "min_saddle_curvature": "1",
  "min_localmax_sigma": "1/2",
  "min_localmax_radius": 0.07692307692307693,
  "n_families": 55,
  "n_unhandled": 0,
  "families_all_nonintegral_with_cert": true,
  "counterexamples": [
   {
    "type": "non-integral stationary with no strict-saddle certificate",
    "Sf": [
     0,
     1,
     3
    ],
    "x": [
     "1/3",
     "1/3",
     "1",
     "1/3",
     "0",
     "1",
     "1",
     "0",
     "0"
    ]
   },
   {
    "type": "non-integral stationary with no strict-saddle certificate",
    "Sf": [
     0,
     1,
     5
    ],
    "x": [
     "1/3",
     "1/3",
     "1",
     "0",
     "0",
     "1/3",
     "1",
     "0",
     "1"
    ]
   },
   {
    "type": "non-integral stationary with no strict-saddle certificate",
    "Sf": [
     0,
     1,
     8
    ],
    "x": [
     "1/3",
     "1/3",
     "1",
     "0",
     "0",
     "1",
     "1",
     "0",
     "1/3"
    ]
   },
   {
    "type": "non-integral stationary with no strict-saddle certificate",
    "Sf": [
     1,
     3,
     4
    ],
    "x": [
     "0",
     "1/3",
     "1",
     "1/3",
     "1/3",
     "1",
     "1",
     "0",
     "0"
    ]
   }
  ],
  "curvature_ge_2lam_minus_2": true,
  "sigma_ge_lam_minus_1": true,
  "graph": "G(9,0.6) seed=8",
  "n": 9,
  "k": 4,
  "lam": "1/2",
  "arm": "M2_lam_lt_1"
 },
 {
  "n_stationary_isolated": 612,
  "n_integral": 58,
  "n_nonintegral": 554,
  "integral_localmax_thm36": 58,
  "integral_localmax_D4": 58,
  "integral_NOT_localmax": 0,
  "certs_disagree": 0,
  "ascent_found_inside_radius": 0,
  "ascent_found_at_4x_radius": 0,
  "localmax_probed": 58,
  "nonintegral_strict_saddle": 554,
  "nonintegral_no_saddle_cert": 0,
  "min_saddle_curvature": "1",
  "min_localmax_sigma": "1/2",
  "min_localmax_radius": 0.09090909090909091,
  "n_families": 67,
  "n_unhandled": 0,
  "families_all_nonintegral_with_cert": true,
  "counterexamples": [],
  "curvature_ge_2lam_minus_2": true,
  "sigma_ge_lam_minus_1": true,
  "graph": "4-regular n=10",
  "n": 10,
  "k": 4,
  "lam": "3/2",
  "arm": "main"
 },
 {
  "n_stationary_isolated": 1517,
  "n_integral": 133,
  "n_nonintegral": 1384,
  "integral_localmax_thm36": 58,
  "integral_localmax_D4": 58,
  "integral_NOT_localmax": 75,
  "certs_disagree": 0,
  "ascent_found_inside_radius": 0,
  "ascent_found_at_4x_radius": 0,
  "localmax_probed": 58,
  "nonintegral_strict_saddle": 1384,
  "nonintegral_no_saddle_cert": 0,
  "min_saddle_curvature": "2",
  "min_localmax_sigma": "0",
  "min_localmax_radius": 0.16666666666666666,
  "n_families": 481,
  "n_unhandled": 0,
  "families_all_nonintegral_with_cert": true,
  "counterexamples": [
   {
    "type": "integral stationary but not local max",
    "S1": [
     0,
     1,
     2,
     4
    ],
    "sigma": "0"
   },
   {
    "type": "integral stationary but not local max",
    "S1": [
     0,
     1,
     2,
     8
    ],
    "sigma": "0"
   },
   {
    "type": "integral stationary but not local max",
    "S1": [
     0,
     1,
     2,
     9
    ],
    "sigma": "0"
   },
   {
    "type": "integral stationary but not local max",
    "S1": [
     0,
     1,
     3,
     6
    ],
    "sigma": "0"
   },
   {
    "type": "integral stationary but not local max",
    "S1": [
     0,
     1,
     3,
     7
    ],
    "sigma": "0"
   },
   {
    "type": "integral stationary but not local max",
    "S1": [
     0,
     1,
     3,
     9
    ],
    "sigma": "0"
   },
   {
    "type": "integral stationary but not local max",
    "S1": [
     0,
     1,
     4,
     6
    ],
    "sigma": "0"
   },
   {
    "type": "integral stationary but not local max",
    "S1": [
     0,
     1,
     4,
     7
    ],
    "sigma": "0"
   },
   {
    "type": "integral stationary but not local max",
    "S1": [
     0,
     1,
     4,
     9
    ],
    "sigma": "0"
   },
   {
    "type": "integral stationary but not local max",
    "S1": [
     0,
     1,
     6,
     9
    ],
    "sigma": "0"
   },
   {
    "type": "integral stationary but not local max",
    "S1": [
     0,
     1,
     7,
     9
    ],
    "sigma": "0"
   },
   {
    "type": "integral stationary but not local max",
    "S1": [
     0,
     1,
     8,
     9
    ],
    "sigma": "0"
   },
   {
    "type": "integral stationary but not local max",
    "S1": [
     0,
     2,
     3,
     5
    ],
    "sigma": "0"
   },
   {
    "type": "integral stationary but not local max",
    "S1": [
     0,
     2,
     3,
     6
    ],
    "sigma": "0"
   },
   {
    "type": "integral stationary but not local max",
    "S1": [
     0,
     2,
     4,
     5
    ],
    "sigma": "0"
   },
   {
    "type": "integral stationary but not local max",
    "S1": [
     0,
     2,
     5,
     7
    ],
    "sigma": "0"
   },
   {
    "type": "integral stationary but not local max",
    "S1": [
     0,
     2,
     5,
     9
    ],
    "sigma": "0"
   },
   {
    "type": "integral stationary but not local max",
    "S1": [
     0,
     2,
     6,
     7
    ],
    "sigma": "0"
   },
   {
    "type": "integral stationary but not local max",
    "S1": [
     0,
     2,
     6,
     8
    ],
    "sigma": "0"
   },
   {
    "type": "integral stationary but not local max",
    "S1": [
     0,
     3,
     4,
     7
    ],
    "sigma": "0"
   },
   {
    "type": "integral stationary but not local max",
    "S1": [
     0,
     3,
     4,
     9
    ],
    "sigma": "0"
   },
   {
    "type": "integral stationary but not local max",
    "S1": [
     0,
     3,
     5,
     7
    ],
    "sigma": "0"
   },
   {
    "type": "integral stationary but not local max",
    "S1": [
     0,
     3,
     5,
     8
    ],
    "sigma": "0"
   },
   {
    "type": "integral stationary but not local max",
    "S1": [
     0,
     3,
     6,
     8
    ],
    "sigma": "0"
   },
   {
    "type": "integral stationary but not local max",
    "S1": [
     0,
     4,
     5,
     8
    ],
    "sigma": "0"
   },
   {
    "type": "integral stationary but not local max",
    "S1": [
     0,
     4,
     7,
     9
    ],
    "sigma": "0"
   },
   {
    "type": "integral stationary but not local max",
    "S1": [
     0,
     4,
     8,
     9
    ],
    "sigma": "0"
   },
   {
    "type": "integral stationary but not local max",
    "S1": [
     0,
     5,
     6,
     9
    ],
    "sigma": "0"
   },
   {
    "type": "integral stationary but not local max",
    "S1": [
     0,
     5,
     7,
     9
    ],
    "sigma": "0"
   },
   {
    "type": "integral stationary but not local max",
    "S1": [
     0,
     6,
     8,
     9
    ],
    "sigma": "0"
   },
   {
    "type": "integral stationary but not local max",
    "S1": [
     1,
     2,
     3,
     5
    ],
    "sigma": "0"
   },
   {
    "type": "integral stationary but not local max",
    "S1": [
     1,
     2,
     3,
     7
    ],
    "sigma": "0"
   },
   {
    "type": "integral stationary but not local max",
    "S1": [
     1,
     2,
     3,
     8
    ],
    "sigma": "0"
   },
   {
    "type": "integral stationary but not local max",
    "S1": [
     1,
     2,
     3,
     9
    ],
    "sigma": "0"
   },
   {
    "type": "integral stationary but not local max",
    "S1": [
     1,
     2,
     4,
     8
    ],
    "sigma": "0"
   },
   {
    "type": "integral stationary but not local max",
    "S1": [
     1,
     2,
     5,
     9
    ],
    "sigma": "0"
   },
   {
    "type": "integral stationary but not local max",
    "S1": [
     1,
     2,
     7,
     8
    ],
    "sigma": "0"
   },
   {
    "type": "integral stationary but not local max",
    "S1": [
     1,
     3,
     5,
     6
    ],
    "sigma": "0"
   },
   {
    "type": "integral stationary but not local max",
    "S1": [
     1,
     3,
     5,
     9
    ],
    "sigma": "0"
   },
   {
    "type": "integral stationary but not local max",
    "S1": [
     1,
     3,
     6,
     9
    ],
    "sigma": "0"
   },
   {
    "type": "integral stationary but not local max",
    "S1": [
     1,
     3,
     7,
     9
    ],
    "sigma": "0"
   },
   {
    "type": "integral stationary but not local max",
    "S1": [
     1,
     3,
     8,
     9
    ],
    "sigma": "0"
   },
   {
    "type": "integral stationary but not local max",
    "S1": [
     1,
     4,
     5,
     6
    ],
    "sigma": "0"
   },
   {
    "type": "integral stationary but not local max",
    "S1": [
     1,
     4,
     5,
     8
    ],
    "sigma": "0"
   },
   {
    "type": "integral stationary but not local max",
    "S1": [
     1,
     4,
     6,
     7
    ],
    "sigma": "0"
   },
   {
    "type": "integral stationary but not local max",
    "S1": [
     1,
     5,
     6,
     7
    ],
    "sigma": "0"
   },
   {
    "type": "integral stationary but not local max",
    "S1": [
     1,
     5,
     6,
     8
    ],
    "sigma": "0"
   },
   {
    "type": "integral stationary but not local max",
    "S1": [
     1,
     5,
     7,
     8
    ],
    "sigma": "0"
   },
   {
    "type": "integral stationary but not local max",
    "S1": [
     1,
     5,
     8,
     9
    ],
    "sigma": "0"
   },
   {
    "type": "integral stationary but not local max",
    "S1": [
     1,
     6,
     7,
     8
    ],
    "sigma": "0"
   },
   {
    "type": "integral stationary but not local max",
    "S1": [
     1,
     6,
     7,
     9
    ],
    "sigma": "0"
   },
   {
    "type": "integral stationary but not local max",
    "S1": [
     2,
     3,
     5,
     6
    ],
    "sigma": "0"
   },
   {
    "type": "integral stationary but not local max",
    "S1": [
     2,
     3,
     5,
     8
    ],
    "sigma": "0"
   },
   {
    "type": "integral stationary but not local max",
    "S1": [
     2,
     3,
     6,
     8
    ],
    "sigma": "0"
   },
   {
    "type": "integral stationary but not local max",
    "S1": [
     2,
     3,
     6,
     9
    ],
    "sigma": "0"
   },
   {
    "type": "integral stationary but not local max",
    "S1": [
     2,
     3,
     7,
     8
    ],
    "sigma": "0"
   },
   {
    "type": "integral stationary but not local max",
    "S1": [
     2,
     3,
     7,
     9
    ],
    "sigma": "0"
   },
   {
    "type": "integral stationary but not local max",
    "S1": [
     2,
     4,
     5,
     6
    ],
    "sigma": "0"
   },
   {
    "type": "integral stationary but not local max",
    "S1": [
     2,
     4,
     6,
     7
    ],
    "sigma": "0"
   },
   {
    "type": "integral stationary but not local max",
    "S1": [
     2,
     4,
     6,
     8
    ],
    "sigma": "0"
   },
   {
    "type": "integral stationary but not local max",
    "S1": [
     2,
     4,
     7,
     8
    ],
    "sigma": "0"
   },
   {
    "type": "integral stationary but not local max",
    "S1": [
     2,
     5,
     6,
     7
    ],
    "sigma": "0"
   },
   {
    "type": "integral stationary but not local max",
    "S1": [
     2,
     6,
     7,
     9
    ],
    "sigma": "0"
   },
   {
    "type": "integral stationary but not local max",
    "S1": [
     2,
     6,
     8,
     9
    ],
    "sigma": "0"
   },
   {
    "type": "integral stationary but not local max",
    "S1": [
     3,
     4,
     5,
     9
    ],
    "sigma": "0"
   },
   {
    "type": "integral stationary but not local max",
    "S1": [
     3,
     4,
     7,
     8
    ],
    "sigma": "0"
   },
   {
    "type": "integral stationary but not local max",
    "S1": [
     3,
     4,
     8,
     9
    ],
    "sigma": "0"
   },
   {
    "type": "integral stationary but not local max",
    "S1": [
     3,
     5,
     6,
     8
    ],
    "sigma": "0"
   },
   {
    "type": "integral stationary but not local max",
    "S1": [
     3,
     5,
     7,
     8
    ],
    "sigma": "0"
   },
   {
    "type": "integral stationary but not local max",
    "S1": [
     4,
     5,
     6,
     7
    ],
    "sigma": "0"
   },
   {
    "type": "integral stationary but not local max",
    "S1": [
     4,
     5,
     8,
     9
    ],
    "sigma": "0"
   },
   {
    "type": "integral stationary but not local max",
    "S1": [
     4,
     6,
     7,
     8
    ],
    "sigma": "0"
   },
   {
    "type": "integral stationary but not local max",
    "S1": [
     4,
     6,
     7,
     9
    ],
    "sigma": "0"
   },
   {
    "type": "integral stationary but not local max",
    "S1": [
     5,
     6,
     7,
     8
    ],
    "sigma": "0"
   },
   {
    "type": "integral stationary but not local max",
    "S1": [
     5,
     6,
     8,
     9
    ],
    "sigma": "0"
   }
  ],
  "curvature_ge_2lam_minus_2": true,
  "sigma_ge_lam_minus_1": false,
  "graph": "4-regular n=10",
  "n": 10,
  "k": 4,
  "lam": "2",
  "arm": "M1_lam_integral"
 },
 {
  "n_stationary_isolated": 74,
  "n_integral": 9,
  "n_nonintegral": 65,
  "integral_localmax_thm36": 9,
  "integral_localmax_D4": 9,
  "integral_NOT_localmax": 0,
  "certs_disagree": 0,
  "ascent_found_inside_radius": 0,
  "ascent_found_at_4x_radius": 0,
  "localmax_probed": 9,
  "nonintegral_strict_saddle": 60,
  "nonintegral_no_saddle_cert": 5,
  "min_saddle_curvature": "1",
  "min_localmax_sigma": "1/2",
  "min_localmax_radius": 0.1111111111111111,
  "n_families": 271,
  "n_unhandled": 0,
  "families_all_nonintegral_with_cert": true,
  "counterexamples": [
   {
    "type": "non-integral stationary with no strict-saddle certificate",
    "Sf": [
     0,
     2
    ],
    "x": [
     "1/2",
     "0",
     "1/2",
     "0",
     "1",
     "1",
     "0",
     "1",
     "0",
     "0"
    ]
   },
   {
    "type": "non-integral stationary with no strict-saddle certificate",
    "Sf": [
     1,
     2
    ],
    "x": [
     "0",
     "1/2",
     "1/2",
     "0",
     "1",
     "1",
     "0",
     "1",
     "0",
     "0"
    ]
   },
   {
    "type": "non-integral stationary with no strict-saddle certificate",
    "Sf": [
     1,
     8
    ],
    "x": [
     "0",
     "1/2",
     "0",
     "0",
     "1",
     "1",
     "0",
     "1",
     "1/2",
     "0"
    ]
   },
   {
    "type": "non-integral stationary with no strict-saddle certificate",
    "Sf": [
     3,
     8
    ],
    "x": [
     "0",
     "0",
     "0",
     "1/2",
     "1",
     "1",
     "0",
     "1",
     "1/2",
     "0"
    ]
   },
   {
    "type": "non-integral stationary with no strict-saddle certificate",
    "Sf": [
     0,
     3,
     9
    ],
    "x": [
     "1/3",
     "0",
     "0",
     "1/3",
     "1",
     "1",
     "0",
     "1",
     "0",
     "1/3"
    ]
   }
  ],
  "curvature_ge_2lam_minus_2": true,
  "sigma_ge_lam_minus_1": true,
  "graph": "4-regular n=10",
  "n": 10,
  "k": 4,
  "lam": "1/2",
  "arm": "M2_lam_lt_1"
 },
 {
  "n_stationary_isolated": 1593,
  "n_integral": 85,
  "n_nonintegral": 1508,
  "integral_localmax_thm36": 85,
  "integral_localmax_D4": 85,
  "integral_NOT_localmax": 0,
  "certs_disagree": 0,
  "ascent_found_inside_radius": 0,
  "ascent_found_at_4x_radius": 0,
  "localmax_probed": 85,
  "nonintegral_strict_saddle": 1508,
  "nonintegral_no_saddle_cert": 0,
  "min_saddle_curvature": "1",
  "min_localmax_sigma": "1/2",
  "min_localmax_radius": 0.1111111111111111,
  "n_families": 0,
  "n_unhandled": 0,
  "families_all_nonintegral_with_cert": true,
  "counterexamples": [],
  "curvature_ge_2lam_minus_2": true,
  "sigma_ge_lam_minus_1": true,
  "graph": "Petersen n=10",
  "n": 10,
  "k": 4,
  "lam": "3/2",
  "arm": "main"
 },
 {
  "n_stationary_isolated": 2482,
  "n_integral": 150,
  "n_nonintegral": 2332,
  "integral_localmax_thm36": 85,
  "integral_localmax_D4": 85,
  "integral_NOT_localmax": 65,
  "certs_disagree": 0,
  "ascent_found_inside_radius": 0,
  "ascent_found_at_4x_radius": 0,
  "localmax_probed": 85,
  "nonintegral_strict_saddle": 2332,
  "nonintegral_no_saddle_cert": 0,
  "min_saddle_curvature": "2",
  "min_localmax_sigma": "0",
  "min_localmax_radius": 0.2,
  "n_families": 1536,
  "n_unhandled": 0,
  "families_all_nonintegral_with_cert": true,
  "counterexamples": [
   {
    "type": "integral stationary but not local max",
    "S1": [
     0,
     1,
     2,
     8
    ],
    "sigma": "0"
   },
   {
    "type": "integral stationary but not local max",
    "S1": [
     0,
     1,
     2,
     9
    ],
    "sigma": "0"
   },
   {
    "type": "integral stationary but not local max",
    "S1": [
     0,
     1,
     3,
     5
    ],
    "sigma": "0"
   },
   {
    "type": "integral stationary but not local max",
    "S1": [
     0,
     1,
     3,
     6
    ],
    "sigma": "0"
   },
   {
    "type": "integral stationary but not local max",
    "S1": [
     0,
     1,
     4,
     7
    ],
    "sigma": "0"
   },
   {
    "type": "integral stationary but not local max",
    "S1": [
     0,
     1,
     4,
     8
    ],
    "sigma": "0"
   },
   {
    "type": "integral stationary but not local max",
    "S1": [
     0,
     1,
     5,
     9
    ],
    "sigma": "0"
   },
   {
    "type": "integral stationary but not local max",
    "S1": [
     0,
     1,
     6,
     7
    ],
    "sigma": "0"
   },
   {
    "type": "integral stationary but not local max",
    "S1": [
     0,
     2,
     3,
     7
    ],
    "sigma": "0"
   },
   {
    "type": "integral stationary but not local max",
    "S1": [
     0,
     2,
     3,
     8
    ],
    "sigma": "0"
   },
   {
    "type": "integral stationary but not local max",
    "S1": [
     0,
     2,
     4,
     5
    ],
    "sigma": "0"
   },
   {
    "type": "integral stationary but not local max",
    "S1": [
     0,
     2,
     4,
     9
    ],
    "sigma": "0"
   },
   {
    "type": "integral stationary but not local max",
    "S1": [
     0,
     2,
     5,
     8
    ],
    "sigma": "0"
   },
   {
    "type": "integral stationary but not local max",
    "S1": [
     0,
     2,
     7,
     9
    ],
    "sigma": "0"
   },
   {
    "type": "integral stationary but not local max",
    "S1": [
     0,
     2,
     8,
     9
    ],
    "sigma": "0"
   },
   {
    "type": "integral stationary but not local max",
    "S1": [
     0,
     3,
     4,
     6
    ],
    "sigma": "0"
   },
   {
    "type": "integral stationary but not local max",
    "S1": [
     0,
     3,
     4,
     7
    ],
    "sigma": "0"
   },
   {
    "type": "integral stationary but not local max",
    "S1": [
     0,
     3,
     5,
     7
    ],
    "sigma": "0"
   },
   {
    "type": "integral stationary but not local max",
    "S1": [
     0,
     3,
     6,
     7
    ],
    "sigma": "0"
   },
   {
    "type": "integral stationary but not local max",
    "S1": [
     0,
     3,
     6,
     8
    ],
    "sigma": "0"
   },
   {
    "type": "integral stationary but not local max",
    "S1": [
     0,
     4,
     5,
     6
    ],
    "sigma": "0"
   },
   {
    "type": "integral stationary but not local max",
    "S1": [
     0,
     4,
     8,
     9
    ],
    "sigma": "0"
   },
   {
    "type": "integral stationary but not local max",
    "S1": [
     0,
     5,
     6,
     7
    ],
    "sigma": "0"
   },
   {
    "type": "integral stationary but not local max",
    "S1": [
     0,
     5,
     8,
     9
    ],
    "sigma": "0"
   },
   {
    "type": "integral stationary but not local max",
    "S1": [
     0,
     6,
     7,
     9
    ],
    "sigma": "0"
   },
   {
    "type": "integral stationary but not local max",
    "S1": [
     0,
     6,
     8,
     9
    ],
    "sigma": "0"
   },
   {
    "type": "integral stationary but not local max",
    "S1": [
     1,
     2,
     3,
     5
    ],
    "sigma": "0"
   },
   {
    "type": "integral stationary but not local max",
    "S1": [
     1,
     2,
     3,
     9
    ],
    "sigma": "0"
   },
   {
    "type": "integral stationary but not local max",
    "S1": [
     1,
     2,
     4,
     6
    ],
    "sigma": "0"
   },
   {
    "type": "integral stationary but not local max",
    "S1": [
     1,
     2,
     4,
     7
    ],
    "sigma": "0"
   },
   {
    "type": "integral stationary but not local max",
    "S1": [
     1,
     2,
     5,
     6
    ],
    "sigma": "0"
   },
   {
    "type": "integral stationary but not local max",
    "S1": [
     1,
     2,
     7,
     8
    ],
    "sigma": "0"
   },
   {
    "type": "integral stationary but not local max",
    "S1": [
     1,
     3,
     4,
     8
    ],
    "sigma": "0"
   },
   {
    "type": "integral stationary but not local max",
    "S1": [
     1,
     3,
     4,
     9
    ],
    "sigma": "0"
   },
   {
    "type": "integral stationary but not local max",
    "S1": [
     1,
     3,
     5,
     8
    ],
    "sigma": "0"
   },
   {
    "type": "integral stationary but not local max",
    "S1": [
     1,
     3,
     5,
     9
    ],
    "sigma": "0"
   },
   {
    "type": "integral stationary but not local max",
    "S1": [
     1,
     3,
     6,
     9
    ],
    "sigma": "0"
   },
   {
    "type": "integral stationary but not local max",
    "S1": [
     1,
     4,
     6,
     8
    ],
    "sigma": "0"
   },
   {
    "type": "integral stationary but not local max",
    "S1": [
     1,
     4,
     7,
     8
    ],
    "sigma": "0"
   },
   {
    "type": "integral stationary but not local max",
    "S1": [
     1,
     4,
     7,
     9
    ],
    "sigma": "0"
   },
   {
    "type": "integral stationary but not local max",
    "S1": [
     1,
     5,
     6,
     9
    ],
    "sigma": "0"
   },
   {
    "type": "integral stationary but not local max",
    "S1": [
     1,
     5,
     7,
     8
    ],
    "sigma": "0"
   },
   {
    "type": "integral stationary but not local max",
    "S1": [
     1,
     5,
     7,
     9
    ],
    "sigma": "0"
   },
   {
    "type": "integral stationary but not local max",
    "S1": [
     1,
     6,
     7,
     8
    ],
    "sigma": "0"
   },
   {
    "type": "integral stationary but not local max",
    "S1": [
     2,
     3,
     4,
     5
    ],
    "sigma": "0"
   },
   {
    "type": "integral stationary but not local max",
    "S1": [
     2,
     3,
     4,
     6
    ],
    "sigma": "0"
   },
   {
    "type": "integral stationary but not local max",
    "S1": [
     2,
     3,
     6,
     7
    ],
    "sigma": "0"
   },
   {
    "type": "integral stationary but not local max",
    "S1": [
     2,
     3,
     8,
     9
    ],
    "sigma": "0"
   },
   {
    "type": "integral stationary but not local max",
    "S1": [
     2,
     4,
     5,
     6
    ],
    "sigma": "0"
   },
   {
    "type": "integral stationary but not local max",
    "S1": [
     2,
     4,
     5,
     7
    ],
    "sigma": "0"
   },
   {
    "type": "integral stationary but not local max",
    "S1": [
     2,
     4,
     6,
     9
    ],
    "sigma": "0"
   },
   {
    "type": "integral stationary but not local max",
    "S1": [
     2,
     5,
     6,
     7
    ],
    "sigma": "0"
   },
   {
    "type": "integral stationary but not local max",
    "S1": [
     2,
     5,
     6,
     8
    ],
    "sigma": "0"
   },
   {
    "type": "integral stationary but not local max",
    "S1": [
     2,
     6,
     8,
     9
    ],
    "sigma": "0"
   },
   {
    "type": "integral stationary but not local max",
    "S1": [
     2,
     7,
     8,
     9
    ],
    "sigma": "0"
   },
   {
    "type": "integral stationary but not local max",
    "S1": [
     3,
     4,
     5,
     9
    ],
    "sigma": "0"
   },
   {
    "type": "integral stationary but not local max",
    "S1": [
     3,
     4,
     7,
     8
    ],
    "sigma": "0"
   },
   {
    "type": "integral stationary but not local max",
    "S1": [
     3,
     5,
     7,
     9
    ],
    "sigma": "0"
   },
   {
    "type": "integral stationary but not local max",
    "S1": [
     3,
     5,
     8,
     9
    ],
    "sigma": "0"
   },
   {
    "type": "integral stationary but not local max",
    "S1": [
     3,
     6,
     7,
     8
    ],
    "sigma": "0"
   },
   {
    "type": "integral stationary but not local max",
    "S1": [
     3,
     6,
     7,
     9
    ],
    "sigma": "0"
   },
   {
    "type": "integral stationary but not local max",
    "S1": [
     4,
     5,
     6,
     8
    ],
    "sigma": "0"
   },
   {
    "type": "integral stationary but not local max",
    "S1": [
     4,
     5,
     6,
     9
    ],
    "sigma": "0"
   },
   {
    "type": "integral stationary but not local max",
    "S1": [
     4,
     5,
     7,
     8
    ],
    "sigma": "0"
   },
   {
    "type": "integral stationary but not local max",
    "S1": [
     4,
     7,
     8,
     9
    ],
    "sigma": "0"
   }
  ],
  "curvature_ge_2lam_minus_2": true,
  "sigma_ge_lam_minus_1": false,
  "graph": "Petersen n=10",
  "n": 10,
  "k": 4,
  "lam": "2",
  "arm": "M1_lam_integral"
 },
 {
  "n_stationary_isolated": 393,
  "n_integral": 10,
  "n_nonintegral": 383,
  "integral_localmax_thm36": 10,
  "integral_localmax_D4": 10,
  "integral_NOT_localmax": 0,
  "certs_disagree": 0,
  "ascent_found_inside_radius": 0,
  "ascent_found_at_4x_radius": 0,
  "localmax_probed": 10,
  "nonintegral_strict_saddle": 323,
  "nonintegral_no_saddle_cert": 60,
  "min_saddle_curvature": "1",
  "min_localmax_sigma": "1/2",
  "min_localmax_radius": 0.14285714285714285,
  "n_families": 240,
  "n_unhandled": 0,
  "families_all_nonintegral_with_cert": true,
  "counterexamples": [
   {
    "type": "non-integral stationary with no strict-saddle certificate",
    "Sf": [
     0,
     1
    ],
    "x": [
     "1/2",
     "1/2",
     "1",
     "1",
     "1",
     "0",
     "0",
     "0",
     "0",
     "0"
    ]
   },
   {
    "type": "non-integral stationary with no strict-saddle certificate",
    "Sf": [
     0,
     1
    ],
    "x": [
     "1/2",
     "1/2",
     "1",
     "0",
     "0",
     "1",
     "0",
     "1",
     "0",
     "0"
    ]
   },
   {
    "type": "non-integral stationary with no strict-saddle certificate",
    "Sf": [
     0,
     1
    ],
    "x": [
     "1/2",
     "1/2",
     "0",
     "0",
     "1",
     "0",
     "1",
     "0",
     "0",
     "1"
    ]
   },
   {
    "type": "non-integral stationary with no strict-saddle certificate",
    "Sf": [
     0,
     1
    ],
    "x": [
     "1/2",
     "1/2",
     "0",
     "0",
     "0",
     "1",
     "1",
     "0",
     "1",
     "0"
    ]
   },
   {
    "type": "non-integral stationary with no strict-saddle certificate",
    "Sf": [
     0,
     4
    ],
    "x": [
     "1/2",
     "1",
     "1",
     "1",
     "1/2",
     "0",
     "0",
     "0",
     "0",
     "0"
    ]
   },
   {
    "type": "non-integral stationary with no strict-saddle certificate",
    "Sf": [
     0,
     4
    ],
    "x": [
     "1/2",
     "1",
     "0",
     "0",
     "1/2",
     "0",
     "1",
     "0",
     "0",
     "1"
    ]
   },
   {
    "type": "non-integral stationary with no strict-saddle certificate",
    "Sf": [
     0,
     4
    ],
    "x": [
     "1/2",
     "0",
     "0",
     "1",
     "1/2",
     "1",
     "0",
     "0",
     "1",
     "0"
    ]
   },
   {
    "type": "non-integral stationary with no strict-saddle certificate",
    "Sf": [
     0,
     4
    ],
    "x": [
     "1/2",
     "0",
     "0",
     "0",
     "1/2",
     "1",
     "0",
     "1",
     "0",
     "1"
    ]
   },
   {
    "type": "non-integral stationary with no strict-saddle certificate",
    "Sf": [
     0,
     5
    ],
    "x": [
     "1/2",
     "1",
     "1",
     "0",
     "0",
     "1/2",
     "0",
     "1",
     "0",
     "0"
    ]
   },
   {
    "type": "non-integral stationary with no strict-saddle certificate",
    "Sf": [
     0,
     5
    ],
    "x": [
     "1/2",
     "1",
     "0",
     "0",
     "0",
     "1/2",
     "1",
     "0",
     "1",
     "0"
    ]
   },
   {
    "type": "non-integral stationary with no strict-saddle certificate",
    "Sf": [
     0,
     5
    ],
    "x": [
     "1/2",
     "0",
     "0",
     "1",
     "1",
     "1/2",
     "0",
     "0",
     "1",
     "0"
    ]
   },
   {
    "type": "non-integral stationary with no strict-saddle certificate",
    "Sf": [
     0,
     5
    ],
    "x": [
     "1/2",
     "0",
     "0",
     "0",
     "1",
     "1/2",
     "0",
     "1",
     "0",
     "1"
    ]
   },
   {
    "type": "non-integral stationary with no strict-saddle certificate",
    "Sf": [
     1,
     2
    ],
    "x": [
     "1",
     "1/2",
     "1/2",
     "1",
     "1",
     "0",
     "0",
     "0",
     "0",
     "0"
    ]
   },
   {
    "type": "non-integral stationary with no strict-saddle certificate",
    "Sf": [
     1,
     2
    ],
    "x": [
     "1",
     "1/2",
     "1/2",
     "0",
     "0",
     "1",
     "0",
     "1",
     "0",
     "0"
    ]
   },
   {
    "type": "non-integral stationary with no strict-saddle certificate",
    "Sf": [
     1,
     2
    ],
    "x": [
     "0",
     "1/2",
     "1/2",
     "1",
     "0",
     "0",
     "1",
     "0",
     "1",
     "0"
    ]
   },
   {
    "type": "non-integral stationary with no strict-saddle certificate",
    "Sf": [
     1,
     2
    ],
    "x": [
     "0",
     "1/2",
     "1/2",
     "0",
     "0",
     "0",
     "1",
     "1",
     "0",
     "1"
    ]
   },
   {
    "type": "non-integral stationary with no strict-saddle certificate",
    "Sf": [
     1,
     6
    ],
    "x": [
     "1",
     "1/2",
     "0",
     "0",
     "1",
     "0",
     "1/2",
     "0",
     "0",
     "1"
    ]
   },
   {
    "type": "non-integral stationary with no strict-saddle certificate",
    "Sf": [
     1,
     6
    ],
    "x": [
     "1",
     "1/2",
     "0",
     "0",
     "0",
     "1",
     "1/2",
     "0",
     "1",
     "0"
    ]
   },
   {
    "type": "non-integral stationary with no strict-saddle certificate",
    "Sf": [
     1,
     6
    ],
    "x": [
     "0",
     "1/2",
     "1",
     "1",
     "0",
     "0",
     "1/2",
     "0",
     "1",
     "0"
    ]
   },
   {
    "type": "non-integral stationary with no strict-saddle certificate",
    "Sf": [
     1,
     6
    ],
    "x": [
     "0",
     "1/2",
     "1",
     "0",
     "0",
     "0",
     "1/2",
     "1",
     "0",
     "1"
    ]
   },
   {
    "type": "non-integral stationary with no strict-saddle certificate",
    "Sf": [
     2,
     3
    ],
    "x": [
     "1",
     "1",
     "1/2",
     "1/2",
     "1",
     "0",
     "0",
     "0",
     "0",
     "0"
    ]
   },
   {
    "type": "non-integral stationary with no strict-saddle certificate",
    "Sf": [
     2,
     3
    ],
    "x": [
     "0",
     "1",
     "1/2",
     "1/2",
     "0",
     "0",
     "1",
     "0",
     "1",
     "0"
    ]
   },
   {
    "type": "non-integral stationary with no strict-saddle certificate",
    "Sf": [
     2,
     3
    ],
    "x": [
     "0",
     "0",
     "1/2",
     "1/2",
     "1",
     "0",
     "0",
     "1",
     "0",
     "1"
    ]
   },
   {
    "type": "non-integral stationary with no strict-saddle certificate",
    "Sf": [
     2,
     3
    ],
    "x": [
     "0",
     "0",
     "1/2",
     "1/2",
     "0",
     "1",
     "0",
     "1",
     "1",
     "0"
    ]
   },
   {
    "type": "non-integral stationary with no strict-saddle certificate",
    "Sf": [
     2,
     7
    ],
    "x": [
     "1",
     "1",
     "1/2",
     "0",
     "0",
     "1",
     "0",
     "1/2",
     "0",
     "0"
    ]
   },
   {
    "type": "non-integral stationary with no strict-saddle certificate",
    "Sf": [
     2,
     7
    ],
    "x": [
     "0",
     "1",
     "1/2",
     "0",
     "0",
     "0",
     "1",
     "1/2",
     "0",
     "1"
    ]
   },
   {
    "type": "non-integral stationary with no strict-saddle certificate",
    "Sf": [
     2,
     7
    ],
    "x": [
     "0",
     "0",
     "1/2",
     "1",
     "1",
     "0",
     "0",
     "1/2",
     "0",
     "1"
    ]
   },
   {
    "type": "non-integral stationary with no strict-saddle certificate",
    "Sf": [
     2,
     7
    ],
    "x": [
     "0",
     "0",
     "1/2",
     "1",
     "0",
     "1",
     "0",
     "1/2",
     "1",
     "0"
    ]
   },
   {
    "type": "non-integral stationary with no strict-saddle certificate",
    "Sf": [
     3,
     4
    ],
    "x": [
     "1",
     "1",
     "1",
     "1/2",
     "1/2",
     "0",
     "0",
     "0",
     "0",
     "0"
    ]
   },
   {
    "type": "non-integral stationary with no strict-saddle certificate",
    "Sf": [
     3,
     4
    ],
    "x": [
     "1",
     "0",
     "0",
     "1/2",
     "1/2",
     "1",
     "0",
     "0",
     "1",
     "0"
    ]
   },
   {
    "type": "non-integral stationary with no strict-saddle certificate",
    "Sf": [
     3,
     4
    ],
    "x": [
     "0",
     "0",
     "1",
     "1/2",
     "1/2",
     "0",
     "0",
     "1",
     "0",
     "1"
    ]
   },
   {
    "type": "non-integral stationary with no strict-saddle certificate",
    "Sf": [
     3,
     4
    ],
    "x": [
     "0",
     "0",
     "0",
     "1/2",
     "1/2",
     "0",
     "1",
     "0",
     "1",
     "1"
    ]
   },
   {
    "type": "non-integral stationary with no strict-saddle certificate",
    "Sf": [
     3,
     8
    ],
    "x": [
     "1",
     "0",
     "0",
     "1/2",
     "1",
     "1",
     "0",
     "0",
     "1/2",
     "0"
    ]
   },
   {
    "type": "non-integral stationary with no strict-saddle certificate",
    "Sf": [
     3,
     8
    ],
    "x": [
     "0",
     "1",
     "1",
     "1/2",
     "0",
     "0",
     "1",
     "0",
     "1/2",
     "0"
    ]
   },
   {
    "type": "non-integral stationary with no strict-saddle certificate",
    "Sf": [
     3,
     8
    ],
    "x": [
     "0",
     "0",
     "1",
     "1/2",
     "0",
     "1",
     "0",
     "1",
     "1/2",
     "0"
    ]
   },
   {
    "type": "non-integral stationary with no strict-saddle certificate",
    "Sf": [
     3,
     8
    ],
    "x": [
     "0",
     "0",
     "0",
     "1/2",
     "1",
     "0",
     "1",
     "0",
     "1/2",
     "1"
    ]
   },
   {
    "type": "non-integral stationary with no strict-saddle certificate",
    "Sf": [
     4,
     9
    ],
    "x": [
     "1",
     "1",
     "0",
     "0",
     "1/2",
     "0",
     "1",
     "0",
     "0",
     "1/2"
    ]
   },
   {
    "type": "non-integral stationary with no strict-saddle certificate",
    "Sf": [
     4,
     9
    ],
    "x": [
     "1",
     "0",
     "0",
     "0",
     "1/2",
     "1",
     "0",
     "1",
     "0",
     "1/2"
    ]
   },
   {
    "type": "non-integral stationary with no strict-saddle certificate",
    "Sf": [
     4,
     9
    ],
    "x": [
     "0",
     "0",
     "1",
     "1",
     "1/2",
     "0",
     "0",
     "1",
     "0",
     "1/2"
    ]
   },
   {
    "type": "non-integral stationary with no strict-saddle certificate",
    "Sf": [
     4,
     9
    ],
    "x": [
     "0",
     "0",
     "0",
     "1",
     "1/2",
     "0",
     "1",
     "0",
     "1",
     "1/2"
    ]
   },
   {
    "type": "non-integral stationary with no strict-saddle certificate",
    "Sf": [
     5,
     7
    ],
    "x": [
     "1",
     "1",
     "1",
     "0",
     "0",
     "1/2",
     "0",
     "1/2",
     "0",
     "0"
    ]
   },
   {
    "type": "non-integral stationary with no strict-saddle certificate",
    "Sf": [
     5,
     7
    ],
    "x": [
     "1",
     "0",
     "0",
     "0",
     "1",
     "1/2",
     "0",
     "1/2",
     "0",
     "1"
    ]
   },
   {
    "type": "non-integral stationary with no strict-saddle certificate",
    "Sf": [
     5,
     7
    ],
    "x": [
     "0",
     "0",
     "1",
     "1",
     "0",
     "1/2",
     "0",
     "1/2",
     "1",
     "0"
    ]
   },
   {
    "type": "non-integral stationary with no strict-saddle certificate",
    "Sf": [
     5,
     7
    ],
    "x": [
     "0",
     "0",
     "0",
     "0",
     "0",
     "1/2",
     "1",
     "1/2",
     "1",
     "1"
    ]
   },
   {
    "type": "non-integral stationary with no strict-saddle certificate",
    "Sf": [
     5,
     8
    ],
    "x": [
     "1",
     "1",
     "0",
     "0",
     "0",
     "1/2",
     "1",
     "0",
     "1/2",
     "0"
    ]
   },
   {
    "type": "non-integral stationary with no strict-saddle certificate",
    "Sf": [
     5,
     8
    ],
    "x": [
     "1",
     "0",
     "0",
     "1",
     "1",
     "1/2",
     "0",
     "0",
     "1/2",
     "0"
    ]
   },
   {
    "type": "non-integral stationary with no strict-saddle certificate",
    "Sf": [
     5,
     8
    ],
    "x": [
     "0",
     "0",
     "1",
     "1",
     "0",
     "1/2",
     "0",
     "1",
     "1/2",
     "0"
    ]
   },
   {
    "type": "non-integral stationary with no strict-saddle certificate",
    "Sf": [
     5,
     8
    ],
    "x": [
     "0",
     "0",
     "0",
     "0",
     "0",
     "1/2",
     "1",
     "1",
     "1/2",
     "1"
    ]
   },
   {
    "type": "non-integral stationary with no strict-saddle certificate",
    "Sf": [
     6,
     8
    ],
    "x": [
     "1",
     "1",
     "0",
     "0",
     "0",
     "1",
     "1/2",
     "0",
     "1/2",
     "0"
    ]
   },
   {
    "type": "non-integral stationary with no strict-saddle certificate",
    "Sf": [
     6,
     8
    ],
    "x": [
     "0",
     "1",
     "1",
     "1",
     "0",
     "0",
     "1/2",
     "0",
     "1/2",
     "0"
    ]
   },
   {
    "type": "non-integral stationary with no strict-saddle certificate",
    "Sf": [
     6,
     8
    ],
    "x": [
     "0",
     "0",
     "0",
     "1",
     "1",
     "0",
     "1/2",
     "0",
     "1/2",
     "1"
    ]
   },
   {
    "type": "non-integral stationary with no strict-saddle certificate",
    "Sf": [
     6,
     8
    ],
    "x": [
     "0",
     "0",
     "0",
     "0",
     "0",
     "1",
     "1/2",
     "1",
     "1/2",
     "1"
    ]
   },
   {
    "type": "non-integral stationary with no strict-saddle certificate",
    "Sf": [
     6,
     9
    ],
    "x": [
     "1",
     "1",
     "0",
     "0",
     "1",
     "0",
     "1/2",
     "0",
     "0",
     "1/2"
    ]
   },
   {
    "type": "non-integral stationary with no strict-saddle certificate",
    "Sf": [
     6,
     9
    ],
    "x": [
     "0",
     "1",
     "1",
     "0",
     "0",
     "0",
     "1/2",
     "1",
     "0",
     "1/2"
    ]
   },
   {
    "type": "non-integral stationary with no strict-saddle certificate",
    "Sf": [
     6,
     9
    ],
    "x": [
     "0",
     "0",
     "0",
     "1",
     "1",
     "0",
     "1/2",
     "0",
     "1",
     "1/2"
    ]
   },
   {
    "type": "non-integral stationary with no strict-saddle certificate",
    "Sf": [
     6,
     9
    ],
    "x": [
     "0",
     "0",
     "0",
     "0",
     "0",
     "1",
     "1/2",
     "1",
     "1",
     "1/2"
    ]
   },
   {
    "type": "non-integral stationary with no strict-saddle certificate",
    "Sf": [
     7,
     9
    ],
    "x": [
     "1",
     "0",
     "0",
     "0",
     "1",
     "1",
     "0",
     "1/2",
     "0",
     "1/2"
    ]
   },
   {
    "type": "non-integral stationary with no strict-saddle certificate",
    "Sf": [
     7,
     9
    ],
    "x": [
     "0",
     "1",
     "1",
     "0",
     "0",
     "0",
     "1",
     "1/2",
     "0",
     "1/2"
    ]
   },
   {
    "type": "non-integral stationary with no strict-saddle certificate",
    "Sf": [
     7,
     9
    ],
    "x": [
     "0",
     "0",
     "1",
     "1",
     "1",
     "0",
     "0",
     "1/2",
     "0",
     "1/2"
    ]
   },
   {
    "type": "non-integral stationary with no strict-saddle certificate",
    "Sf": [
     7,
     9
    ],
    "x": [
     "0",
     "0",
     "0",
     "0",
     "0",
     "1",
     "1",
     "1/2",
     "1",
     "1/2"
    ]
   }
  ],
  "curvature_ge_2lam_minus_2": true,
  "sigma_ge_lam_minus_1": true,
  "graph": "Petersen n=10",
  "n": 10,
  "k": 4,
  "lam": "1/2",
  "arm": "M2_lam_lt_1"
 },
 {
  "n_stationary_isolated": 1199,
  "n_integral": 82,
  "n_nonintegral": 1117,
  "integral_localmax_thm36": 82,
  "integral_localmax_D4": 82,
  "integral_NOT_localmax": 0,
  "certs_disagree": 0,
  "ascent_found_inside_radius": 0,
  "ascent_found_at_4x_radius": 0,
  "localmax_probed": 82,
  "nonintegral_strict_saddle": 1117,
  "nonintegral_no_saddle_cert": 0,
  "min_saddle_curvature": "1",
  "min_localmax_sigma": "1/2",
  "min_localmax_radius": 0.1111111111111111,
  "n_families": 40,
  "n_unhandled": 0,
  "families_all_nonintegral_with_cert": true,
  "counterexamples": [],
  "curvature_ge_2lam_minus_2": true,
  "sigma_ge_lam_minus_1": true,
  "graph": "3-regular n=10",
  "n": 10,
  "k": 4,
  "lam": "3/2",
  "arm": "main"
 },
 {
  "n_stationary_isolated": 2427,
  "n_integral": 156,
  "n_nonintegral": 2271,
  "integral_localmax_thm36": 82,
  "integral_localmax_D4": 82,
  "integral_NOT_localmax": 74,
  "certs_disagree": 0,
  "ascent_found_inside_radius": 0,
  "ascent_found_at_4x_radius": 0,
  "localmax_probed": 82,
  "nonintegral_strict_saddle": 2271,
  "nonintegral_no_saddle_cert": 0,
  "min_saddle_curvature": "2",
  "min_localmax_sigma": "0",
  "min_localmax_radius": 0.2,
  "n_families": 166,
  "n_unhandled": 0,
  "families_all_nonintegral_with_cert": true,
  "counterexamples": [
   {
    "type": "integral stationary but not local max",
    "S1": [
     0,
     1,
     2,
     6
    ],
    "sigma": "0"
   },
   {
    "type": "integral stationary but not local max",
    "S1": [
     0,
     1,
     2,
     8
    ],
    "sigma": "0"
   },
   {
    "type": "integral stationary but not local max",
    "S1": [
     0,
     1,
     3,
     5
    ],
    "sigma": "0"
   },
   {
    "type": "integral stationary but not local max",
    "S1": [
     0,
     1,
     3,
     7
    ],
    "sigma": "0"
   },
   {
    "type": "integral stationary but not local max",
    "S1": [
     0,
     1,
     4,
     5
    ],
    "sigma": "0"
   },
   {
    "type": "integral stationary but not local max",
    "S1": [
     0,
     1,
     4,
     7
    ],
    "sigma": "0"
   },
   {
    "type": "integral stationary but not local max",
    "S1": [
     0,
     1,
     6,
     8
    ],
    "sigma": "0"
   },
   {
    "type": "integral stationary but not local max",
    "S1": [
     0,
     1,
     7,
     9
    ],
    "sigma": "0"
   },
   {
    "type": "integral stationary but not local max",
    "S1": [
     0,
     1,
     8,
     9
    ],
    "sigma": "0"
   },
   {
    "type": "integral stationary but not local max",
    "S1": [
     0,
     2,
     4,
     6
    ],
    "sigma": "0"
   },
   {
    "type": "integral stationary but not local max",
    "S1": [
     0,
     2,
     4,
     8
    ],
    "sigma": "0"
   },
   {
    "type": "integral stationary but not local max",
    "S1": [
     0,
     2,
     4,
     9
    ],
    "sigma": "0"
   },
   {
    "type": "integral stationary but not local max",
    "S1": [
     0,
     2,
     5,
     7
    ],
    "sigma": "0"
   },
   {
    "type": "integral stationary but not local max",
    "S1": [
     0,
     2,
     5,
     8
    ],
    "sigma": "0"
   },
   {
    "type": "integral stationary but not local max",
    "S1": [
     0,
     2,
     6,
     7
    ],
    "sigma": "0"
   },
   {
    "type": "integral stationary but not local max",
    "S1": [
     0,
     2,
     6,
     9
    ],
    "sigma": "0"
   },
   {
    "type": "integral stationary but not local max",
    "S1": [
     0,
     2,
     7,
     8
    ],
    "sigma": "0"
   },
   {
    "type": "integral stationary but not local max",
    "S1": [
     0,
     3,
     4,
     5
    ],
    "sigma": "0"
   },
   {
    "type": "integral stationary but not local max",
    "S1": [
     0,
     3,
     4,
     7
    ],
    "sigma": "0"
   },
   {
    "type": "integral stationary but not local max",
    "S1": [
     0,
     3,
     5,
     8
    ],
    "sigma": "0"
   },
   {
    "type": "integral stationary but not local max",
    "S1": [
     0,
     3,
     5,
     9
    ],
    "sigma": "0"
   },
   {
    "type": "integral stationary but not local max",
    "S1": [
     0,
     3,
     7,
     8
    ],
    "sigma": "0"
   },
   {
    "type": "integral stationary but not local max",
    "S1": [
     0,
     3,
     7,
     9
    ],
    "sigma": "0"
   },
   {
    "type": "integral stationary but not local max",
    "S1": [
     0,
     4,
     5,
     7
    ],
    "sigma": "0"
   },
   {
    "type": "integral stationary but not local max",
    "S1": [
     0,
     4,
     6,
     8
    ],
    "sigma": "0"
   },
   {
    "type": "integral stationary but not local max",
    "S1": [
     0,
     4,
     8,
     9
    ],
    "sigma": "0"
   },
   {
    "type": "integral stationary but not local max",
    "S1": [
     0,
     5,
     7,
     8
    ],
    "sigma": "0"
   },
   {
    "type": "integral stationary but not local max",
    "S1": [
     0,
     5,
     7,
     9
    ],
    "sigma": "0"
   },
   {
    "type": "integral stationary but not local max",
    "S1": [
     0,
     6,
     7,
     8
    ],
    "sigma": "0"
   },
   {
    "type": "integral stationary but not local max",
    "S1": [
     0,
     6,
     8,
     9
    ],
    "sigma": "0"
   },
   {
    "type": "integral stationary but not local max",
    "S1": [
     1,
     2,
     3,
     6
    ],
    "sigma": "0"
   },
   {
    "type": "integral stationary but not local max",
    "S1": [
     1,
     2,
     3,
     9
    ],
    "sigma": "0"
   },
   {
    "type": "integral stationary but not local max",
    "S1": [
     1,
     2,
     4,
     5
    ],
    "sigma": "0"
   },
   {
    "type": "integral stationary but not local max",
    "S1": [
     1,
     2,
     4,
     7
    ],
    "sigma": "0"
   },
   {
    "type": "integral stationary but not local max",
    "S1": [
     1,
     2,
     5,
     6
    ],
    "sigma": "0"
   },
   {
    "type": "integral stationary but not local max",
    "S1": [
     1,
     2,
     7,
     9
    ],
    "sigma": "0"
   },
   {
    "type": "integral stationary but not local max",
    "S1": [
     1,
     3,
     4,
     5
    ],
    "sigma": "0"
   },
   {
    "type": "integral stationary but not local max",
    "S1": [
     1,
     3,
     4,
     7
    ],
    "sigma": "0"
   },
   {
    "type": "integral stationary but not local max",
    "S1": [
     1,
     3,
     5,
     6
    ],
    "sigma": "0"
   },
   {
    "type": "integral stationary but not local max",
    "S1": [
     1,
     3,
     6,
     8
    ],
    "sigma": "0"
   },
   {
    "type": "integral stationary but not local max",
    "S1": [
     1,
     3,
     7,
     9
    ],
    "sigma": "0"
   },
   {
    "type": "integral stationary but not local max",
    "S1": [
     1,
     3,
     8,
     9
    ],
    "sigma": "0"
   },
   {
    "type": "integral stationary but not local max",
    "S1": [
     1,
     4,
     5,
     6
    ],
    "sigma": "0"
   },
   {
    "type": "integral stationary but not local max",
    "S1": [
     1,
     4,
     6,
     7
    ],
    "sigma": "0"
   },
   {
    "type": "integral stationary but not local max",
    "S1": [
     1,
     5,
     6,
     8
    ],
    "sigma": "0"
   },
   {
    "type": "integral stationary but not local max",
    "S1": [
     1,
     5,
     6,
     9
    ],
    "sigma": "0"
   },
   {
    "type": "integral stationary but not local max",
    "S1": [
     1,
     5,
     8,
     9
    ],
    "sigma": "0"
   },
   {
    "type": "integral stationary but not local max",
    "S1": [
     1,
     6,
     7,
     8
    ],
    "sigma": "0"
   },
   {
    "type": "integral stationary but not local max",
    "S1": [
     1,
     6,
     7,
     9
    ],
    "sigma": "0"
   },
   {
    "type": "integral stationary but not local max",
    "S1": [
     1,
     6,
     8,
     9
    ],
    "sigma": "0"
   },
   {
    "type": "integral stationary but not local max",
    "S1": [
     1,
     7,
     8,
     9
    ],
    "sigma": "0"
   },
   {
    "type": "integral stationary but not local max",
    "S1": [
     2,
     3,
     4,
     6
    ],
    "sigma": "0"
   },
   {
    "type": "integral stationary but not local max",
    "S1": [
     2,
     3,
     4,
     8
    ],
    "sigma": "0"
   },
   {
    "type": "integral stationary but not local max",
    "S1": [
     2,
     3,
     4,
     9
    ],
    "sigma": "0"
   },
   {
    "type": "integral stationary but not local max",
    "S1": [
     2,
     3,
     5,
     6
    ],
    "sigma": "0"
   },
   {
    "type": "integral stationary but not local max",
    "S1": [
     2,
     3,
     5,
     9
    ],
    "sigma": "0"
   },
   {
    "type": "integral stationary but not local max",
    "S1": [
     2,
     3,
     6,
     7
    ],
    "sigma": "0"
   },
   {
    "type": "integral stationary but not local max",
    "S1": [
     2,
     3,
     6,
     9
    ],
    "sigma": "0"
   },
   {
    "type": "integral stationary but not local max",
    "S1": [
     2,
     3,
     7,
     9
    ],
    "sigma": "0"
   },
   {
    "type": "integral stationary but not local max",
    "S1": [
     2,
     4,
     5,
     7
    ],
    "sigma": "0"
   },
   {
    "type": "integral stationary but not local max",
    "S1": [
     2,
     4,
     5,
     8
    ],
    "sigma": "0"
   },
   {
    "type": "integral stationary but not local max",
    "S1": [
     2,
     4,
     5,
     9
    ],
    "sigma": "0"
   },
   {
    "type": "integral stationary but not local max",
    "S1": [
     2,
     4,
     6,
     9
    ],
    "sigma": "0"
   },
   {
    "type": "integral stationary but not local max",
    "S1": [
     2,
     4,
     7,
     8
    ],
    "sigma": "0"
   },
   {
    "type": "integral stationary but not local max",
    "S1": [
     3,
     4,
     5,
     6
    ],
    "sigma": "0"
   },
   {
    "type": "integral stationary but not local max",
    "S1": [
     3,
     4,
     8,
     9
    ],
    "sigma": "0"
   },
   {
    "type": "integral stationary but not local max",
    "S1": [
     3,
     5,
     6,
     8
    ],
    "sigma": "0"
   },
   {
    "type": "integral stationary but not local max",
    "S1": [
     3,
     5,
     6,
     9
    ],
    "sigma": "0"
   },
   {
    "type": "integral stationary but not local max",
    "S1": [
     3,
     6,
     7,
     9
    ],
    "sigma": "0"
   },
   {
    "type": "integral stationary but not local max",
    "S1": [
     3,
     7,
     8,
     9
    ],
    "sigma": "0"
   },
   {
    "type": "integral stationary but not local max",
    "S1": [
     4,
     5,
     6,
     7
    ],
    "sigma": "0"
   },
   {
    "type": "integral stationary but not local max",
    "S1": [
     4,
     5,
     7,
     8
    ],
    "sigma": "0"
   },
   {
    "type": "integral stationary but not local max",
    "S1": [
     4,
     5,
     8,
     9
    ],
    "sigma": "0"
   },
   {
    "type": "integral stationary but not local max",
    "S1": [
     4,
     6,
     8,
     9
    ],
    "sigma": "0"
   }
  ],
  "curvature_ge_2lam_minus_2": true,
  "sigma_ge_lam_minus_1": false,
  "graph": "3-regular n=10",
  "n": 10,
  "k": 4,
  "lam": "2",
  "arm": "M1_lam_integral"
 },
 {
  "n_stationary_isolated": 231,
  "n_integral": 9,
  "n_nonintegral": 222,
  "integral_localmax_thm36": 9,
  "integral_localmax_D4": 9,
  "integral_NOT_localmax": 0,
  "certs_disagree": 0,
  "ascent_found_inside_radius": 0,
  "ascent_found_at_4x_radius": 0,
  "localmax_probed": 9,
  "nonintegral_strict_saddle": 196,
  "nonintegral_no_saddle_cert": 26,
  "min_saddle_curvature": "1",
  "min_localmax_sigma": "1/2",
  "min_localmax_radius": 0.14285714285714285,
  "n_families": 200,
  "n_unhandled": 0,
  "families_all_nonintegral_with_cert": true,
  "counterexamples": [
   {
    "type": "non-integral stationary with no strict-saddle certificate",
    "Sf": [
     0,
     1
    ],
    "x": [
     "1/2",
     "1/2",
     "1",
     "0",
     "0",
     "1",
     "0",
     "0",
     "0",
     "1"
    ]
   },
   {
    "type": "non-integral stationary with no strict-saddle certificate",
    "Sf": [
     0,
     9
    ],
    "x": [
     "1/2",
     "1",
     "1",
     "0",
     "0",
     "1",
     "0",
     "0",
     "0",
     "1/2"
    ]
   },
   {
    "type": "non-integral stationary with no strict-saddle certificate",
    "Sf": [
     1,
     2
    ],
    "x": [
     "1",
     "1/2",
     "1/2",
     "0",
     "0",
     "1",
     "0",
     "0",
     "0",
     "1"
    ]
   },
   {
    "type": "non-integral stationary with no strict-saddle certificate",
    "Sf": [
     1,
     2
    ],
    "x": [
     "0",
     "1/2",
     "1/2",
     "1",
     "0",
     "1",
     "0",
     "0",
     "1",
     "0"
    ]
   },
   {
    "type": "non-integral stationary with no strict-saddle certificate",
    "Sf": [
     1,
     2
    ],
    "x": [
     "0",
     "1/2",
     "1/2",
     "1",
     "0",
     "0",
     "0",
     "1",
     "1",
     "0"
    ]
   },
   {
    "type": "non-integral stationary with no strict-saddle certificate",
    "Sf": [
     2,
     5
    ],
    "x": [
     "1",
     "1",
     "1/2",
     "0",
     "0",
     "1/2",
     "0",
     "0",
     "0",
     "1"
    ]
   },
   {
    "type": "non-integral stationary with no strict-saddle certificate",
    "Sf": [
     2,
     5
    ],
    "x": [
     "0",
     "1",
     "1/2",
     "1",
     "0",
     "1/2",
     "0",
     "0",
     "1",
     "0"
    ]
   },
   {
    "type": "non-integral stationary with no strict-saddle certificate",
    "Sf": [
     2,
     5
    ],
    "x": [
     "0",
     "0",
     "1/2",
     "0",
     "0",
     "1/2",
     "1",
     "1",
     "0",
     "1"
    ]
   },
   {
    "type": "non-integral stationary with no strict-saddle certificate",
    "Sf": [
     2,
     7
    ],
    "x": [
     "0",
     "1",
     "1/2",
     "1",
     "0",
     "0",
     "0",
     "1/2",
     "1",
     "0"
    ]
   },
   {
    "type": "non-integral stationary with no strict-saddle certificate",
    "Sf": [
     2,
     7
    ],
    "x": [
     "0",
     "0",
     "1/2",
     "0",
     "0",
     "1",
     "1",
     "1/2",
     "0",
     "1"
    ]
   },
   {
    "type": "non-integral stationary with no strict-saddle certificate",
    "Sf": [
     3,
     4
    ],
    "x": [
     "0",
     "0",
     "0",
     "1/2",
     "1/2",
     "0",
     "1",
     "1",
     "1",
     "0"
    ]
   },
   {
    "type": "non-integral stationary with no strict-saddle certificate",
    "Sf": [
     3,
     8
    ],
    "x": [
     "0",
     "1",
     "1",
     "1/2",
     "0",
     "1",
     "0",
     "0",
     "1/2",
     "0"
    ]
   },
   {
    "type": "non-integral stationary with no strict-saddle certificate",
    "Sf": [
     3,
     8
    ],
    "x": [
     "0",
     "1",
     "1",
     "1/2",
     "0",
     "0",
     "0",
     "1",
     "1/2",
     "0"
    ]
   },
   {
    "type": "non-integral stationary with no strict-saddle certificate",
    "Sf": [
     3,
     8
    ],
    "x": [
     "0",
     "0",
     "0",
     "1/2",
     "1",
     "0",
     "1",
     "1",
     "1/2",
     "0"
    ]
   },
   {
    "type": "non-integral stationary with no strict-saddle certificate",
    "Sf": [
     4,
     6
    ],
    "x": [
     "0",
     "0",
     "0",
     "1",
     "1/2",
     "0",
     "1/2",
     "1",
     "1",
     "0"
    ]
   },
   {
    "type": "non-integral stationary with no strict-saddle certificate",
    "Sf": [
     5,
     8
    ],
    "x": [
     "0",
     "1",
     "1",
     "1",
     "0",
     "1/2",
     "0",
     "0",
     "1/2",
     "0"
    ]
   },
   {
    "type": "non-integral stationary with no strict-saddle certificate",
    "Sf": [
     5,
     8
    ],
    "x": [
     "0",
     "0",
     "0",
     "0",
     "0",
     "1/2",
     "1",
     "1",
     "1/2",
     "1"
    ]
   },
   {
    "type": "non-integral stationary with no strict-saddle certificate",
    "Sf": [
     5,
     9
    ],
    "x": [
     "1",
     "1",
     "1",
     "0",
     "0",
     "1/2",
     "0",
     "0",
     "0",
     "1/2"
    ]
   },
   {
    "type": "non-integral stationary with no strict-saddle certificate",
    "Sf": [
     5,
     9
    ],
    "x": [
     "0",
     "0",
     "1",
     "0",
     "0",
     "1/2",
     "1",
     "1",
     "0",
     "1/2"
    ]
   },
   {
    "type": "non-integral stationary with no strict-saddle certificate",
    "Sf": [
     5,
     9
    ],
    "x": [
     "0",
     "0",
     "0",
     "0",
     "0",
     "1/2",
     "1",
     "1",
     "1",
     "1/2"
    ]
   },
   {
    "type": "non-integral stationary with no strict-saddle certificate",
    "Sf": [
     6,
     7
    ],
    "x": [
     "0",
     "0",
     "1",
     "0",
     "0",
     "1",
     "1/2",
     "1/2",
     "0",
     "1"
    ]
   },
   {
    "type": "non-integral stationary with no strict-saddle certificate",
    "Sf": [
     6,
     7
    ],
    "x": [
     "0",
     "0",
     "0",
     "1",
     "1",
     "0",
     "1/2",
     "1/2",
     "1",
     "0"
    ]
   },
   {
    "type": "non-integral stationary with no strict-saddle certificate",
    "Sf": [
     6,
     7
    ],
    "x": [
     "0",
     "0",
     "0",
     "0",
     "0",
     "1",
     "1/2",
     "1/2",
     "1",
     "1"
    ]
   },
   {
    "type": "non-integral stationary with no strict-saddle certificate",
    "Sf": [
     7,
     8
    ],
    "x": [
     "0",
     "1",
     "1",
     "1",
     "0",
     "0",
     "0",
     "1/2",
     "1/2",
     "0"
    ]
   },
   {
    "type": "non-integral stationary with no strict-saddle certificate",
    "Sf": [
     7,
     8
    ],
    "x": [
     "0",
     "0",
     "0",
     "1",
     "1",
     "0",
     "1",
     "1/2",
     "1/2",
     "0"
    ]
   },
   {
    "type": "non-integral stationary with no strict-saddle certificate",
    "Sf": [
     7,
     8
    ],
    "x": [
     "0",
     "0",
     "0",
     "0",
     "0",
     "1",
     "1",
     "1/2",
     "1/2",
     "1"
    ]
   }
  ],
  "curvature_ge_2lam_minus_2": true,
  "sigma_ge_lam_minus_1": true,
  "graph": "3-regular n=10",
  "n": 10,
  "k": 4,
  "lam": "1/2",
  "arm": "M2_lam_lt_1"
 },
 {
  "n_stationary_isolated": 793,
  "n_integral": 45,
  "n_nonintegral": 748,
  "integral_localmax_thm36": 45,
  "integral_localmax_D4": 45,
  "integral_NOT_localmax": 0,
  "certs_disagree": 0,
  "ascent_found_inside_radius": 0,
  "ascent_found_at_4x_radius": 0,
  "localmax_probed": 45,
  "nonintegral_strict_saddle": 748,
  "nonintegral_no_saddle_cert": 0,
  "min_saddle_curvature": "1",
  "min_localmax_sigma": "1/2",
  "min_localmax_radius": 0.07692307692307693,
  "n_families": 4,
  "n_unhandled": 0,
  "families_all_nonintegral_with_cert": true,
  "counterexamples": [],
  "curvature_ge_2lam_minus_2": true,
  "sigma_ge_lam_minus_1": true,
  "graph": "G(10,0.3) seed=17",
  "n": 10,
  "k": 4,
  "lam": "3/2",
  "arm": "main"
 },
 {
  "n_stationary_isolated": 1781,
  "n_integral": 157,
  "n_nonintegral": 1624,
  "integral_localmax_thm36": 45,
  "integral_localmax_D4": 45,
  "integral_NOT_localmax": 112,
  "certs_disagree": 0,
  "ascent_found_inside_radius": 0,
  "ascent_found_at_4x_radius": 0,
  "localmax_probed": 45,
  "nonintegral_strict_saddle": 1624,
  "nonintegral_no_saddle_cert": 0,
  "min_saddle_curvature": "2",
  "min_localmax_sigma": "0",
  "min_localmax_radius": 0.14285714285714285,
  "n_families": 7,
  "n_unhandled": 0,
  "families_all_nonintegral_with_cert": true,
  "counterexamples": [
   {
    "type": "integral stationary but not local max",
    "S1": [
     0,
     1,
     3,
     4
    ],
    "sigma": "0"
   },
   {
    "type": "integral stationary but not local max",
    "S1": [
     0,
     1,
     3,
     6
    ],
    "sigma": "0"
   },
   {
    "type": "integral stationary but not local max",
    "S1": [
     0,
     1,
     3,
     7
    ],
    "sigma": "0"
   },
   {
    "type": "integral stationary but not local max",
    "S1": [
     0,
     1,
     3,
     8
    ],
    "sigma": "0"
   },
   {
    "type": "integral stationary but not local max",
    "S1": [
     0,
     1,
     4,
     5
    ],
    "sigma": "0"
   },
   {
    "type": "integral stationary but not local max",
    "S1": [
     0,
     1,
     4,
     6
    ],
    "sigma": "0"
   },
   {
    "type": "integral stationary but not local max",
    "S1": [
     0,
     1,
     4,
     7
    ],
    "sigma": "0"
   },
   {
    "type": "integral stationary but not local max",
    "S1": [
     0,
     1,
     6,
     7
    ],
    "sigma": "0"
   },
   {
    "type": "integral stationary but not local max",
    "S1": [
     0,
     1,
     6,
     8
    ],
    "sigma": "0"
   },
   {
    "type": "integral stationary but not local max",
    "S1": [
     0,
     1,
     7,
     8
    ],
    "sigma": "0"
   },
   {
    "type": "integral stationary but not local max",
    "S1": [
     0,
     2,
     3,
     4
    ],
    "sigma": "0"
   },
   {
    "type": "integral stationary but not local max",
    "S1": [
     0,
     2,
     3,
     6
    ],
    "sigma": "0"
   },
   {
    "type": "integral stationary but not local max",
    "S1": [
     0,
     2,
     3,
     7
    ],
    "sigma": "0"
   },
   {
    "type": "integral stationary but not local max",
    "S1": [
     0,
     2,
     3,
     8
    ],
    "sigma": "0"
   },
   {
    "type": "integral stationary but not local max",
    "S1": [
     0,
     2,
     4,
     5
    ],
    "sigma": "0"
   },
   {
    "type": "integral stationary but not local max",
    "S1": [
     0,
     2,
     4,
     6
    ],
    "sigma": "0"
   },
   {
    "type": "integral stationary but not local max",
    "S1": [
     0,
     2,
     6,
     7
    ],
    "sigma": "0"
   },
   {
    "type": "integral stationary but not local max",
    "S1": [
     0,
     2,
     6,
     8
    ],
    "sigma": "0"
   },
   {
    "type": "integral stationary but not local max",
    "S1": [
     0,
     2,
     7,
     9
    ],
    "sigma": "0"
   },
   {
    "type": "integral stationary but not local max",
    "S1": [
     0,
     3,
     4,
     5
    ],
    "sigma": "0"
   },
   {
    "type": "integral stationary but not local max",
    "S1": [
     0,
     3,
     4,
     6
    ],
    "sigma": "0"
   },
   {
    "type": "integral stationary but not local max",
    "S1": [
     0,
     3,
     4,
     7
    ],
    "sigma": "0"
   },
   {
    "type": "integral stationary but not local max",
    "S1": [
     0,
     3,
     4,
     8
    ],
    "sigma": "0"
   },
   {
    "type": "integral stationary but not local max",
    "S1": [
     0,
     3,
     5,
     6
    ],
    "sigma": "0"
   },
   {
    "type": "integral stationary but not local max",
    "S1": [
     0,
     3,
     5,
     7
    ],
    "sigma": "0"
   },
   {
    "type": "integral stationary but not local max",
    "S1": [
     0,
     3,
     5,
     9
    ],
    "sigma": "0"
   },
   {
    "type": "integral stationary but not local max",
    "S1": [
     0,
     3,
     6,
     7
    ],
    "sigma": "0"
   },
   {
    "type": "integral stationary but not local max",
    "S1": [
     0,
     3,
     6,
     9
    ],
    "sigma": "0"
   },
   {
    "type": "integral stationary but not local max",
    "S1": [
     0,
     3,
     7,
     9
    ],
    "sigma": "0"
   },
   {
    "type": "integral stationary but not local max",
    "S1": [
     0,
     3,
     8,
     9
    ],
    "sigma": "0"
   },
   {
    "type": "integral stationary but not local max",
    "S1": [
     0,
     4,
     5,
     8
    ],
    "sigma": "0"
   },
   {
    "type": "integral stationary but not local max",
    "S1": [
     0,
     4,
     6,
     7
    ],
    "sigma": "0"
   },
   {
    "type": "integral stationary but not local max",
    "S1": [
     0,
     4,
     6,
     9
    ],
    "sigma": "0"
   },
   {
    "type": "integral stationary but not local max",
    "S1": [
     0,
     4,
     7,
     8
    ],
    "sigma": "0"
   },
   {
    "type": "integral stationary but not local max",
    "S1": [
     0,
     4,
     7,
     9
    ],
    "sigma": "0"
   },
   {
    "type": "integral stationary but not local max",
    "S1": [
     0,
     5,
     6,
     7
    ],
    "sigma": "0"
   },
   {
    "type": "integral stationary but not local max",
    "S1": [
     0,
     5,
     6,
     8
    ],
    "sigma": "0"
   },
   {
    "type": "integral stationary but not local max",
    "S1": [
     0,
     5,
     7,
     8
    ],
    "sigma": "0"
   },
   {
    "type": "integral stationary but not local max",
    "S1": [
     0,
     5,
     8,
     9
    ],
    "sigma": "0"
   },
   {
    "type": "integral stationary but not local max",
    "S1": [
     0,
     6,
     7,
     9
    ],
    "sigma": "0"
   },
   {
    "type": "integral stationary but not local max",
    "S1": [
     0,
     7,
     8,
     9
    ],
    "sigma": "0"
   },
   {
    "type": "integral stationary but not local max",
    "S1": [
     1,
     2,
     3,
     4
    ],
    "sigma": "0"
   },
   {
    "type": "integral stationary but not local max",
    "S1": [
     1,
     2,
     3,
     6
    ],
    "sigma": "0"
   },
   {
    "type": "integral stationary but not local max",
    "S1": [
     1,
     2,
     3,
     7
    ],
    "sigma": "0"
   },
   {
    "type": "integral stationary but not local max",
    "S1": [
     1,
     2,
     3,
     8
    ],
    "sigma": "0"
   },
   {
    "type": "integral stationary but not local max",
    "S1": [
     1,
     2,
     4,
     8
    ],
    "sigma": "0"
   },
   {
    "type": "integral stationary but not local max",
    "S1": [
     1,
     2,
     6,
     7
    ],
    "sigma": "0"
   },
   {
    "type": "integral stationary but not local max",
    "S1": [
     1,
     2,
     6,
     8
    ],
    "sigma": "0"
   },
   {
    "type": "integral stationary but not local max",
    "S1": [
     1,
     2,
     7,
     8
    ],
    "sigma": "0"
   },
   {
    "type": "integral stationary but not local max",
    "S1": [
     1,
     3,
     4,
     6
    ],
    "sigma": "0"
   },
   {
    "type": "integral stationary but not local max",
    "S1": [
     1,
     3,
     4,
     7
    ],
    "sigma": "0"
   },
   {
    "type": "integral stationary but not local max",
    "S1": [
     1,
     3,
     4,
     8
    ],
    "sigma": "0"
   },
   {
    "type": "integral stationary but not local max",
    "S1": [
     1,
     3,
     5,
     6
    ],
    "sigma": "0"
   },
   {
    "type": "integral stationary but not local max",
    "S1": [
     1,
     3,
     5,
     7
    ],
    "sigma": "0"
   },
   {
    "type": "integral stationary but not local max",
    "S1": [
     1,
     3,
     5,
     8
    ],
    "sigma": "0"
   },
   {
    "type": "integral stationary but not local max",
    "S1": [
     1,
     3,
     6,
     9
    ],
    "sigma": "0"
   },
   {
    "type": "integral stationary but not local max",
    "S1": [
     1,
     3,
     7,
     9
    ],
    "sigma": "0"
   },
   {
    "type": "integral stationary but not local max",
    "S1": [
     1,
     3,
     8,
     9
    ],
    "sigma": "0"
   },
   {
    "type": "integral stationary but not local max",
    "S1": [
     1,
     4,
     5,
     6
    ],
    "sigma": "0"
   },
   {
    "type": "integral stationary but not local max",
    "S1": [
     1,
     4,
     5,
     7
    ],
    "sigma": "0"
   },
   {
    "type": "integral stationary but not local max",
    "S1": [
     1,
     4,
     5,
     8
    ],
    "sigma": "0"
   },
   {
    "type": "integral stationary but not local max",
    "S1": [
     1,
     4,
     6,
     7
    ],
    "sigma": "0"
   },
   {
    "type": "integral stationary but not local max",
    "S1": [
     1,
     4,
     6,
     9
    ],
    "sigma": "0"
   },
   {
    "type": "integral stationary but not local max",
    "S1": [
     1,
     4,
     7,
     8
    ],
    "sigma": "0"
   },
   {
    "type": "integral stationary but not local max",
    "S1": [
     1,
     4,
     7,
     9
    ],
    "sigma": "0"
   },
   {
    "type": "integral stationary but not local max",
    "S1": [
     1,
     5,
     6,
     7
    ],
    "sigma": "0"
   },
   {
    "type": "integral stationary but not local max",
    "S1": [
     1,
     5,
     6,
     8
    ],
    "sigma": "0"
   },
   {
    "type": "integral stationary but not local max",
    "S1": [
     1,
     5,
     7,
     8
    ],
    "sigma": "0"
   },
   {
    "type": "integral stationary but not local max",
    "S1": [
     1,
     6,
     7,
     9
    ],
    "sigma": "0"
   },
   {
    "type": "integral stationary but not local max",
    "S1": [
     1,
     6,
     8,
     9
    ],
    "sigma": "0"
   },
   {
    "type": "integral stationary but not local max",
    "S1": [
     1,
     7,
     8,
     9
    ],
    "sigma": "0"
   },
   {
    "type": "integral stationary but not local max",
    "S1": [
     2,
     3,
     4,
     6
    ],
    "sigma": "0"
   },
   {
    "type": "integral stationary but not local max",
    "S1": [
     2,
     3,
     4,
     7
    ],
    "sigma": "0"
   },
   {
    "type": "integral stationary but not local max",
    "S1": [
     2,
     3,
     4,
     8
    ],
    "sigma": "0"
   },
   {
    "type": "integral stationary but not local max",
    "S1": [
     2,
     3,
     5,
     6
    ],
    "sigma": "0"
   },
   {
    "type": "integral stationary but not local max",
    "S1": [
     2,
     3,
     5,
     8
    ],
    "sigma": "0"
   },
   {
    "type": "integral stationary but not local max",
    "S1": [
     2,
     3,
     6,
     9
    ],
    "sigma": "0"
   },
   {
    "type": "integral stationary but not local max",
    "S1": [
     2,
     3,
     7,
     9
    ],
    "sigma": "0"
   },
   {
    "type": "integral stationary but not local max",
    "S1": [
     2,
     3,
     8,
     9
    ],
    "sigma": "0"
   },
   {
    "type": "integral stationary but not local max",
    "S1": [
     2,
     4,
     5,
     6
    ],
    "sigma": "0"
   },
   {
    "type": "integral stationary but not local max",
    "S1": [
     2,
     4,
     5,
     8
    ],
    "sigma": "0"
   },
   {
    "type": "integral stationary but not local max",
    "S1": [
     2,
     4,
     6,
     9
    ],
    "sigma": "0"
   },
   {
    "type": "integral stationary but not local max",
    "S1": [
     2,
     4,
     7,
     8
    ],
    "sigma": "0"
   },
   {
    "type": "integral stationary but not local max",
    "S1": [
     2,
     5,
     6,
     7
    ],
    "sigma": "0"
   },
   {
    "type": "integral stationary but not local max",
    "S1": [
     2,
     5,
     6,
     8
    ],
    "sigma": "0"
   },
   {
    "type": "integral stationary but not local max",
    "S1": [
     2,
     5,
     7,
     8
    ],
    "sigma": "0"
   },
   {
    "type": "integral stationary but not local max",
    "S1": [
     2,
     5,
     7,
     9
    ],
    "sigma": "0"
   },
   {
    "type": "integral stationary but not local max",
    "S1": [
     2,
     6,
     7,
     9
    ],
    "sigma": "0"
   },
   {
    "type": "integral stationary but not local max",
    "S1": [
     2,
     6,
     8,
     9
    ],
    "sigma": "0"
   },
   {
    "type": "integral stationary but not local max",
    "S1": [
     2,
     7,
     8,
     9
    ],
    "sigma": "0"
   },
   {
    "type": "integral stationary but not local max",
    "S1": [
     3,
     4,
     5,
     6
    ],
    "sigma": "0"
   },
   {
    "type": "integral stationary but not local max",
    "S1": [
     3,
     4,
     5,
     7
    ],
    "sigma": "0"
   },
   {
    "type": "integral stationary but not local max",
    "S1": [
     3,
     4,
     5,
     8
    ],
    "sigma": "0"
   },
   {
    "type": "integral stationary but not local max",
    "S1": [
     3,
     4,
     6,
     7
    ],
    "sigma": "0"
   },
   {
    "type": "integral stationary but not local max",
    "S1": [
     3,
     4,
     6,
     8
    ],
    "sigma": "0"
   },
   {
    "type": "integral stationary but not local max",
    "S1": [
     3,
     4,
     7,
     8
    ],
    "sigma": "0"
   },
   {
    "type": "integral stationary but not local max",
    "S1": [
     3,
     5,
     6,
     9
    ],
    "sigma": "0"
   },
   {
    "type": "integral stationary but not local max",
    "S1": [
     3,
     5,
     7,
     9
    ],
    "sigma": "0"
   },
   {
    "type": "integral stationary but not local max",
    "S1": [
     3,
     5,
     8,
     9
    ],
    "sigma": "0"
   },
   {
    "type": "integral stationary but not local max",
    "S1": [
     3,
     6,
     7,
     9
    ],
    "sigma": "0"
   },
   {
    "type": "integral stationary but not local max",
    "S1": [
     3,
     6,
     8,
     9
    ],
    "sigma": "0"
   },
   {
    "type": "integral stationary but not local max",
    "S1": [
     3,
     7,
     8,
     9
    ],
    "sigma": "0"
   },
   {
    "type": "integral stationary but not local max",
    "S1": [
     4,
     5,
     6,
     7
    ],
    "sigma": "0"
   },
   {
    "type": "integral stationary but not local max",
    "S1": [
     4,
     5,
     6,
     9
    ],
    "sigma": "0"
   },
   {
    "type": "integral stationary but not local max",
    "S1": [
     4,
     5,
     7,
     8
    ],
    "sigma": "0"
   },
   {
    "type": "integral stationary but not local max",
    "S1": [
     4,
     5,
     7,
     9
    ],
    "sigma": "0"
   },
   {
    "type": "integral stationary but not local max",
    "S1": [
     4,
     6,
     7,
     8
    ],
    "sigma": "0"
   },
   {
    "type": "integral stationary but not local max",
    "S1": [
     4,
     6,
     7,
     9
    ],
    "sigma": "0"
   },
   {
    "type": "integral stationary but not local max",
    "S1": [
     4,
     6,
     8,
     9
    ],
    "sigma": "0"
   },
   {
    "type": "integral stationary but not local max",
    "S1": [
     5,
     6,
     7,
     9
    ],
    "sigma": "0"
   },
   {
    "type": "integral stationary but not local max",
    "S1": [
     5,
     7,
     8,
     9
    ],
    "sigma": "0"
   },
   {
    "type": "integral stationary but not local max",
    "S1": [
     6,
     7,
     8,
     9
    ],
    "sigma": "0"
   }
  ],
  "curvature_ge_2lam_minus_2": true,
  "sigma_ge_lam_minus_1": false,
  "graph": "G(10,0.3) seed=17",
  "n": 10,
  "k": 4,
  "lam": "2",
  "arm": "M1_lam_integral"
 },
 {
  "n_stationary_isolated": 22,
  "n_integral": 4,
  "n_nonintegral": 18,
  "integral_localmax_thm36": 4,
  "integral_localmax_D4": 4,
  "integral_NOT_localmax": 0,
  "certs_disagree": 0,
  "ascent_found_inside_radius": 0,
  "ascent_found_at_4x_radius": 0,
  "localmax_probed": 4,
  "nonintegral_strict_saddle": 18,
  "nonintegral_no_saddle_cert": 0,
  "min_saddle_curvature": "1",
  "min_localmax_sigma": "1/2",
  "min_localmax_radius": 0.09090909090909091,
  "n_families": 40,
  "n_unhandled": 0,
  "families_all_nonintegral_with_cert": true,
  "counterexamples": [],
  "curvature_ge_2lam_minus_2": true,
  "sigma_ge_lam_minus_1": true,
  "graph": "G(10,0.3) seed=17",
  "n": 10,
  "k": 4,
  "lam": "1/2",
  "arm": "M2_lam_lt_1"
 },
 {
  "n_stationary_isolated": 1701,
  "n_integral": 60,
  "n_nonintegral": 1641,
  "integral_localmax_thm36": 60,
  "integral_localmax_D4": 60,
  "integral_NOT_localmax": 0,
  "certs_disagree": 0,
  "ascent_found_inside_radius": 0,
  "ascent_found_at_4x_radius": 0,
  "localmax_probed": 60,
  "nonintegral_strict_saddle": 1641,
  "nonintegral_no_saddle_cert": 0,
  "min_saddle_curvature": "1",
  "min_localmax_sigma": "1/2",
  "min_localmax_radius": 0.14285714285714285,
  "n_families": 0,
  "n_unhandled": 0,
  "families_all_nonintegral_with_cert": true,
  "counterexamples": [],
  "curvature_ge_2lam_minus_2": true,
  "sigma_ge_lam_minus_1": true,
  "graph": "cycle C10",
  "n": 10,
  "k": 3,
  "lam": "3/2",
  "arm": "main"
 },
 {
  "n_stationary_isolated": 2807,
  "n_integral": 120,
  "n_nonintegral": 2687,
  "integral_localmax_thm36": 60,
  "integral_localmax_D4": 60,
  "integral_NOT_localmax": 60,
  "certs_disagree": 0,
  "ascent_found_inside_radius": 0,
  "ascent_found_at_4x_radius": 0,
  "localmax_probed": 60,
  "nonintegral_strict_saddle": 2687,
  "nonintegral_no_saddle_cert": 0,
  "min_saddle_curvature": "2",
  "min_localmax_sigma": "0",
  "min_localmax_radius": 0.25,
  "n_families": 1,
  "n_unhandled": 0,
  "families_all_nonintegral_with_cert": true,
  "counterexamples": [
   {
    "type": "integral stationary but not local max",
    "S1": [
     0,
     1,
     3
    ],
    "sigma": "0"
   },
   {
    "type": "integral stationary but not local max",
    "S1": [
     0,
     1,
     8
    ],
    "sigma": "0"
   },
   {
    "type": "integral stationary but not local max",
    "S1": [
     0,
     2,
     3
    ],
    "sigma": "0"
   },
   {
    "type": "integral stationary but not local max",
    "S1": [
     0,
     2,
     4
    ],
    "sigma": "0"
   },
   {
    "type": "integral stationary but not local max",
    "S1": [
     0,
     2,
     5
    ],
    "sigma": "0"
   },
   {
    "type": "integral stationary but not local max",
    "S1": [
     0,
     2,
     6
    ],
    "sigma": "0"
   },
   {
    "type": "integral stationary but not local max",
    "S1": [
     0,
     2,
     7
    ],
    "sigma": "0"
   },
   {
    "type": "integral stationary but not local max",
    "S1": [
     0,
     2,
     8
    ],
    "sigma": "0"
   },
   {
    "type": "integral stationary but not local max",
    "S1": [
     0,
     2,
     9
    ],
    "sigma": "0"
   },
   {
    "type": "integral stationary but not local max",
    "S1": [
     0,
     3,
     5
    ],
    "sigma": "0"
   },
   {
    "type": "integral stationary but not local max",
    "S1": [
     0,
     3,
     8
    ],
    "sigma": "0"
   },
   {
    "type": "integral stationary but not local max",
    "S1": [
     0,
     4,
     6
    ],
    "sigma": "0"
   },
   {
    "type": "integral stationary but not local max",
    "S1": [
     0,
     4,
     8
    ],
    "sigma": "0"
   },
   {
    "type": "integral stationary but not local max",
    "S1": [
     0,
     5,
     7
    ],
    "sigma": "0"
   },
   {
    "type": "integral stationary but not local max",
    "S1": [
     0,
     5,
     8
    ],
    "sigma": "0"
   },
   {
    "type": "integral stationary but not local max",
    "S1": [
     0,
     6,
     8
    ],
    "sigma": "0"
   },
   {
    "type": "integral stationary but not local max",
    "S1": [
     0,
     7,
     8
    ],
    "sigma": "0"
   },
   {
    "type": "integral stationary but not local max",
    "S1": [
     0,
     7,
     9
    ],
    "sigma": "0"
   },
   {
    "type": "integral stationary but not local max",
    "S1": [
     1,
     2,
     4
    ],
    "sigma": "0"
   },
   {
    "type": "integral stationary but not local max",
    "S1": [
     1,
     2,
     9
    ],
    "sigma": "0"
   },
   {
    "type": "integral stationary but not local max",
    "S1": [
     1,
     3,
     4
    ],
    "sigma": "0"
   },
   {
    "type": "integral stationary but not local max",
    "S1": [
     1,
     3,
     5
    ],
    "sigma": "0"
   },
   {
    "type": "integral stationary but not local max",
    "S1": [
     1,
     3,
     6
    ],
    "sigma": "0"
   },
   {
    "type": "integral stationary but not local max",
    "S1": [
     1,
     3,
     7
    ],
    "sigma": "0"
   },
   {
    "type": "integral stationary but not local max",
    "S1": [
     1,
     3,
     8
    ],
    "sigma": "0"
   },
   {
    "type": "integral stationary but not local max",
    "S1": [
     1,
     3,
     9
    ],
    "sigma": "0"
   },
   {
    "type": "integral stationary but not local max",
    "S1": [
     1,
     4,
     6
    ],
    "sigma": "0"
   },
   {
    "type": "integral stationary but not local max",
    "S1": [
     1,
     4,
     9
    ],
    "sigma": "0"
   },
   {
    "type": "integral stationary but not local max",
    "S1": [
     1,
     5,
     7
    ],
    "sigma": "0"
   },
   {
    "type": "integral stationary but not local max",
    "S1": [
     1,
     5,
     9
    ],
    "sigma": "0"
   },
   {
    "type": "integral stationary but not local max",
    "S1": [
     1,
     6,
     8
    ],
    "sigma": "0"
   },
   {
    "type": "integral stationary but not local max",
    "S1": [
     1,
     6,
     9
    ],
    "sigma": "0"
   },
   {
    "type": "integral stationary but not local max",
    "S1": [
     1,
     7,
     9
    ],
    "sigma": "0"
   },
   {
    "type": "integral stationary but not local max",
    "S1": [
     1,
     8,
     9
    ],
    "sigma": "0"
   },
   {
    "type": "integral stationary but not local max",
    "S1": [
     2,
     3,
     5
    ],
    "sigma": "0"
   },
   {
    "type": "integral stationary but not local max",
    "S1": [
     2,
     4,
     5
    ],
    "sigma": "0"
   },
   {
    "type": "integral stationary but not local max",
    "S1": [
     2,
     4,
     6
    ],
    "sigma": "0"
   },
   {
    "type": "integral stationary but not local max",
    "S1": [
     2,
     4,
     7
    ],
    "sigma": "0"
   },
   {
    "type": "integral stationary but not local max",
    "S1": [
     2,
     4,
     8
    ],
    "sigma": "0"
   },
   {
    "type": "integral stationary but not local max",
    "S1": [
     2,
     4,
     9
    ],
    "sigma": "0"
   },
   {
    "type": "integral stationary but not local max",
    "S1": [
     2,
     5,
     7
    ],
    "sigma": "0"
   },
   {
    "type": "integral stationary but not local max",
    "S1": [
     2,
     6,
     8
    ],
    "sigma": "0"
   },
   {
    "type": "integral stationary but not local max",
    "S1": [
     2,
     7,
     9
    ],
    "sigma": "0"
   },
   {
    "type": "integral stationary but not local max",
    "S1": [
     3,
     4,
     6
    ],
    "sigma": "0"
   },
   {
    "type": "integral stationary but not local max",
    "S1": [
     3,
     5,
     6
    ],
    "sigma": "0"
   },
   {
    "type": "integral stationary but not local max",
    "S1": [
     3,
     5,
     7
    ],
    "sigma": "0"
   },
   {
    "type": "integral stationary but not local max",
    "S1": [
     3,
     5,
     8
    ],
    "sigma": "0"
   },
   {
    "type": "integral stationary but not local max",
    "S1": [
     3,
     5,
     9
    ],
    "sigma": "0"
   },
   {
    "type": "integral stationary but not local max",
    "S1": [
     3,
     6,
     8
    ],
    "sigma": "0"
   },
   {
    "type": "integral stationary but not local max",
    "S1": [
     3,
     7,
     9
    ],
    "sigma": "0"
   },
   {
    "type": "integral stationary but not local max",
    "S1": [
     4,
     5,
     7
    ],
    "sigma": "0"
   },
   {
    "type": "integral stationary but not local max",
    "S1": [
     4,
     6,
     7
    ],
    "sigma": "0"
   },
   {
    "type": "integral stationary but not local max",
    "S1": [
     4,
     6,
     8
    ],
    "sigma": "0"
   },
   {
    "type": "integral stationary but not local max",
    "S1": [
     4,
     6,
     9
    ],
    "sigma": "0"
   },
   {
    "type": "integral stationary but not local max",
    "S1": [
     4,
     7,
     9
    ],
    "sigma": "0"
   },
   {
    "type": "integral stationary but not local max",
    "S1": [
     5,
     6,
     8
    ],
    "sigma": "0"
   },
   {
    "type": "integral stationary but not local max",
    "S1": [
     5,
     7,
     8
    ],
    "sigma": "0"
   },
   {
    "type": "integral stationary but not local max",
    "S1": [
     5,
     7,
     9
    ],
    "sigma": "0"
   },
   {
    "type": "integral stationary but not local max",
    "S1": [
     6,
     7,
     9
    ],
    "sigma": "0"
   },
   {
    "type": "integral stationary but not local max",
    "S1": [
     6,
     8,
     9
    ],
    "sigma": "0"
   }
  ],
  "curvature_ge_2lam_minus_2": true,
  "sigma_ge_lam_minus_1": false,
  "graph": "cycle C10",
  "n": 10,
  "k": 3,
  "lam": "2",
  "arm": "M1_lam_integral"
 },
 {
  "n_stationary_isolated": 101,
  "n_integral": 10,
  "n_nonintegral": 91,
  "integral_localmax_thm36": 10,
  "integral_localmax_D4": 10,
  "integral_NOT_localmax": 0,
  "certs_disagree": 0,
  "ascent_found_inside_radius": 0,
  "ascent_found_at_4x_radius": 0,
  "localmax_probed": 10,
  "nonintegral_strict_saddle": 91,
  "nonintegral_no_saddle_cert": 0,
  "min_saddle_curvature": "1",
  "min_localmax_sigma": "1/2",
  "min_localmax_radius": 0.2,
  "n_families": 20,
  "n_unhandled": 0,
  "families_all_nonintegral_with_cert": true,
  "counterexamples": [],
  "curvature_ge_2lam_minus_2": true,
  "sigma_ge_lam_minus_1": true,
  "graph": "cycle C10",
  "n": 10,
  "k": 3,
  "lam": "1/2",
  "arm": "M2_lam_lt_1"
 },
 {
  "n_stationary_isolated": 1991,
  "n_integral": 75,
  "n_nonintegral": 1916,
  "integral_localmax_thm36": 75,
  "integral_localmax_D4": 75,
  "integral_NOT_localmax": 0,
  "certs_disagree": 0,
  "ascent_found_inside_radius": 0,
  "ascent_found_at_4x_radius": 0,
  "localmax_probed": 75,
  "nonintegral_strict_saddle": 1916,
  "nonintegral_no_saddle_cert": 0,
  "min_saddle_curvature": "1",
  "min_localmax_sigma": "1/2",
  "min_localmax_radius": 0.14285714285714285,
  "n_families": 0,
  "n_unhandled": 0,
  "families_all_nonintegral_with_cert": true,
  "counterexamples": [],
  "curvature_ge_2lam_minus_2": true,
  "sigma_ge_lam_minus_1": true,
  "graph": "cycle C10",
  "n": 10,
  "k": 4,
  "lam": "3/2",
  "arm": "main"
 },
 {
  "n_stationary_isolated": 4232,
  "n_integral": 210,
  "n_nonintegral": 4022,
  "integral_localmax_thm36": 75,
  "integral_localmax_D4": 75,
  "integral_NOT_localmax": 135,
  "certs_disagree": 0,
  "ascent_found_inside_radius": 0,
  "ascent_found_at_4x_radius": 0,
  "localmax_probed": 75,
  "nonintegral_strict_saddle": 4022,
  "nonintegral_no_saddle_cert": 0,
  "min_saddle_curvature": "2",
  "min_localmax_sigma": "0",
  "min_localmax_radius": 0.25,
  "n_families": 1,
  "n_unhandled": 0,
  "families_all_nonintegral_with_cert": true,
  "counterexamples": [
   {
    "type": "integral stationary but not local max",
    "S1": [
     0,
     1,
     2,
     4
    ],
    "sigma": "0"
   },
   {
    "type": "integral stationary but not local max",
    "S1": [
     0,
     1,
     2,
     8
    ],
    "sigma": "0"
   },
   {
    "type": "integral stationary but not local max",
    "S1": [
     0,
     1,
     3,
     5
    ],
    "sigma": "0"
   },
   {
    "type": "integral stationary but not local max",
    "S1": [
     0,
     1,
     3,
     6
    ],
    "sigma": "0"
   },
   {
    "type": "integral stationary but not local max",
    "S1": [
     0,
     1,
     3,
     7
    ],
    "sigma": "0"
   },
   {
    "type": "integral stationary but not local max",
    "S1": [
     0,
     1,
     3,
     8
    ],
    "sigma": "0"
   },
   {
    "type": "integral stationary but not local max",
    "S1": [
     0,
     1,
     3,
     9
    ],
    "sigma": "0"
   },
   {
    "type": "integral stationary but not local max",
    "S1": [
     0,
     1,
     4,
     6
    ],
    "sigma": "0"
   },
   {
    "type": "integral stationary but not local max",
    "S1": [
     0,
     1,
     4,
     8
    ],
    "sigma": "0"
   },
   {
    "type": "integral stationary but not local max",
    "S1": [
     0,
     1,
     5,
     7
    ],
    "sigma": "0"
   },
   {
    "type": "integral stationary but not local max",
    "S1": [
     0,
     1,
     5,
     8
    ],
    "sigma": "0"
   },
   {
    "type": "integral stationary but not local max",
    "S1": [
     0,
     1,
     6,
     8
    ],
    "sigma": "0"
   },
   {
    "type": "integral stationary but not local max",
    "S1": [
     0,
     1,
     7,
     9
    ],
    "sigma": "0"
   },
   {
    "type": "integral stationary but not local max",
    "S1": [
     0,
     2,
     3,
     4
    ],
    "sigma": "0"
   },
   {
    "type": "integral stationary but not local max",
    "S1": [
     0,
     2,
     3,
     5
    ],
    "sigma": "0"
   },
   {
    "type": "integral stationary but not local max",
    "S1": [
     0,
     2,
     3,
     6
    ],
    "sigma": "0"
   },
   {
    "type": "integral stationary but not local max",
    "S1": [
     0,
     2,
     3,
     7
    ],
    "sigma": "0"
   },
   {
    "type": "integral stationary but not local max",
    "S1": [
     0,
     2,
     3,
     8
    ],
    "sigma": "0"
   },
   {
    "type": "integral stationary but not local max",
    "S1": [
     0,
     2,
     4,
     5
    ],
    "sigma": "0"
   },
   {
    "type": "integral stationary but not local max",
    "S1": [
     0,
     2,
     4,
     6
    ],
    "sigma": "0"
   },
   {
    "type": "integral stationary but not local max",
    "S1": [
     0,
     2,
     4,
     7
    ],
    "sigma": "0"
   },
   {
    "type": "integral stationary but not local max",
    "S1": [
     0,
     2,
     4,
     8
    ],
    "sigma": "0"
   },
   {
    "type": "integral stationary but not local max",
    "S1": [
     0,
     2,
     4,
     9
    ],
    "sigma": "0"
   },
   {
    "type": "integral stationary but not local max",
    "S1": [
     0,
     2,
     5,
     6
    ],
    "sigma": "0"
   },
   {
    "type": "integral stationary but not local max",
    "S1": [
     0,
     2,
     5,
     7
    ],
    "sigma": "0"
   },
   {
    "type": "integral stationary but not local max",
    "S1": [
     0,
     2,
     5,
     8
    ],
    "sigma": "0"
   },
   {
    "type": "integral stationary but not local max",
    "S1": [
     0,
     2,
     5,
     9
    ],
    "sigma": "0"
   },
   {
    "type": "integral stationary but not local max",
    "S1": [
     0,
     2,
     6,
     7
    ],
    "sigma": "0"
   },
   {
    "type": "integral stationary but not local max",
    "S1": [
     0,
     2,
     6,
     8
    ],
    "sigma": "0"
   },
   {
    "type": "integral stationary but not local max",
    "S1": [
     0,
     2,
     6,
     9
    ],
    "sigma": "0"
   },
   {
    "type": "integral stationary but not local max",
    "S1": [
     0,
     2,
     7,
     8
    ],
    "sigma": "0"
   },
   {
    "type": "integral stationary but not local max",
    "S1": [
     0,
     2,
     7,
     9
    ],
    "sigma": "0"
   },
   {
    "type": "integral stationary but not local max",
    "S1": [
     0,
     2,
     8,
     9
    ],
    "sigma": "0"
   },
   {
    "type": "integral stationary but not local max",
    "S1": [
     0,
     3,
     4,
     6
    ],
    "sigma": "0"
   },
   {
    "type": "integral stationary but not local max",
    "S1": [
     0,
     3,
     4,
     8
    ],
    "sigma": "0"
   },
   {
    "type": "integral stationary but not local max",
    "S1": [
     0,
     3,
     5,
     6
    ],
    "sigma": "0"
   },
   {
    "type": "integral stationary but not local max",
    "S1": [
     0,
     3,
     5,
     7
    ],
    "sigma": "0"
   },
   {
    "type": "integral stationary but not local max",
    "S1": [
     0,
     3,
     5,
     8
    ],
    "sigma": "0"
   },
   {
    "type": "integral stationary but not local max",
    "S1": [
     0,
     3,
     5,
     9
    ],
    "sigma": "0"
   },
   {
    "type": "integral stationary but not local max",
    "S1": [
     0,
     3,
     6,
     8
    ],
    "sigma": "0"
   },
   {
    "type": "integral stationary but not local max",
    "S1": [
     0,
     3,
     7,
     8
    ],
    "sigma": "0"
   },
   {
    "type": "integral stationary but not local max",
    "S1": [
     0,
     3,
     7,
     9
    ],
    "sigma": "0"
   },
   {
    "type": "integral stationary but not local max",
    "S1": [
     0,
     4,
     5,
     7
    ],
    "sigma": "0"
   },
   {
    "type": "integral stationary but not local max",
    "S1": [
     0,
     4,
     5,
     8
    ],
    "sigma": "0"
   },
   {
    "type": "integral stationary but not local max",
    "S1": [
     0,
     4,
     6,
     7
    ],
    "sigma": "0"
   },
   {
    "type": "integral stationary but not local max",
    "S1": [
     0,
     4,
     6,
     8
    ],
    "sigma": "0"
   },
   {
    "type": "integral stationary but not local max",
    "S1": [
     0,
     4,
     6,
     9
    ],
    "sigma": "0"
   },
   {
    "type": "integral stationary but not local max",
    "S1": [
     0,
     4,
     7,
     8
    ],
    "sigma": "0"
   },
   {
    "type": "integral stationary but not local max",
    "S1": [
     0,
     4,
     7,
     9
    ],
    "sigma": "0"
   },
   {
    "type": "integral stationary but not local max",
    "S1": [
     0,
     5,
     6,
     8
    ],
    "sigma": "0"
   },
   {
    "type": "integral stationary but not local max",
    "S1": [
     0,
     5,
     7,
     8
    ],
    "sigma": "0"
   },
   {
    "type": "integral stationary but not local max",
    "S1": [
     0,
     5,
     7,
     9
    ],
    "sigma": "0"
   },
   {
    "type": "integral stationary but not local max",
    "S1": [
     0,
     6,
     7,
     8
    ],
    "sigma": "0"
   },
   {
    "type": "integral stationary but not local max",
    "S1": [
     0,
     6,
     8,
     9
    ],
    "sigma": "0"
   },
   {
    "type": "integral stationary but not local max",
    "S1": [
     1,
     2,
     3,
     5
    ],
    "sigma": "0"
   },
   {
    "type": "integral stationary but not local max",
    "S1": [
     1,
     2,
     3,
     9
    ],
    "sigma": "0"
   },
   {
    "type": "integral stationary but not local max",
    "S1": [
     1,
     2,
     4,
     6
    ],
    "sigma": "0"
   },
   {
    "type": "integral stationary but not local max",
    "S1": [
     1,
     2,
     4,
     7
    ],
    "sigma": "0"
   },
   {
    "type": "integral stationary but not local max",
    "S1": [
     1,
     2,
     4,
     8
    ],
    "sigma": "0"
   },
   {
    "type": "integral stationary but not local max",
    "S1": [
     1,
     2,
     4,
     9
    ],
    "sigma": "0"
   },
   {
    "type": "integral stationary but not local max",
    "S1": [
     1,
     2,
     5,
     7
    ],
    "sigma": "0"
   },
   {
    "type": "integral stationary but not local max",
    "S1": [
     1,
     2,
     5,
     9
    ],
    "sigma": "0"
   },
   {
    "type": "integral stationary but not local max",
    "S1": [
     1,
     2,
     6,
     8
    ],
    "sigma": "0"
   },
   {
    "type": "integral stationary but not local max",
    "S1": [
     1,
     2,
     6,
     9
    ],
    "sigma": "0"
   },
   {
    "type": "integral stationary but not local max",
    "S1": [
     1,
     2,
     7,
     9
    ],
    "sigma": "0"
   },
   {
    "type": "integral stationary but not local max",
    "S1": [
     1,
     3,
     4,
     5
    ],
    "sigma": "0"
   },
   {
    "type": "integral stationary but not local max",
    "S1": [
     1,
     3,
     4,
     6
    ],
    "sigma": "0"
   },
   {
    "type": "integral stationary but not local max",
    "S1": [
     1,
     3,
     4,
     7
    ],
    "sigma": "0"
   },
   {
    "type": "integral stationary but not local max",
    "S1": [
     1,
     3,
     4,
     8
    ],
    "sigma": "0"
   },
   {
    "type": "integral stationary but not local max",
    "S1": [
     1,
     3,
     4,
     9
    ],
    "sigma": "0"
   },
   {
    "type": "integral stationary but not local max",
    "S1": [
     1,
     3,
     5,
     6
    ],
    "sigma": "0"
   },
   {
    "type": "integral stationary but not local max",
    "S1": [
     1,
     3,
     5,
     7
    ],
    "sigma": "0"
   },
   {
    "type": "integral stationary but not local max",
    "S1": [
     1,
     3,
     5,
     8
    ],
    "sigma": "0"
   },
   {
    "type": "integral stationary but not local max",
    "S1": [
     1,
     3,
     5,
     9
    ],
    "sigma": "0"
   },
   {
    "type": "integral stationary but not local max",
    "S1": [
     1,
     3,
     6,
     7
    ],
    "sigma": "0"
   },
   {
    "type": "integral stationary but not local max",
    "S1": [
     1,
     3,
     6,
     8
    ],
    "sigma": "0"
   },
   {
    "type": "integral stationary but not local max",
    "S1": [
     1,
     3,
     6,
     9
    ],
    "sigma": "0"
   },
   {
    "type": "integral stationary but not local max",
    "S1": [
     1,
     3,
     7,
     8
    ],
    "sigma": "0"
   },
   {
    "type": "integral stationary but not local max",
    "S1": [
     1,
     3,
     7,
     9
    ],
    "sigma": "0"
   },
   {
    "type": "integral stationary but not local max",
    "S1": [
     1,
     3,
     8,
     9
    ],
    "sigma": "0"
   },
   {
    "type": "integral stationary but not local max",
    "S1": [
     1,
     4,
     5,
     7
    ],
    "sigma": "0"
   },
   {
    "type": "integral stationary but not local max",
    "S1": [
     1,
     4,
     5,
     9
    ],
    "sigma": "0"
   },
   {
    "type": "integral stationary but not local max",
    "S1": [
     1,
     4,
     6,
     7
    ],
    "sigma": "0"
   },
   {
    "type": "integral stationary but not local max",
    "S1": [
     1,
     4,
     6,
     8
    ],
    "sigma": "0"
   },
   {
    "type": "integral stationary but not local max",
    "S1": [
     1,
     4,
     6,
     9
    ],
    "sigma": "0"
   },
   {
    "type": "integral stationary but not local max",
    "S1": [
     1,
     4,
     7,
     9
    ],
    "sigma": "0"
   },
   {
    "type": "integral stationary but not local max",
    "S1": [
     1,
     4,
     8,
     9
    ],
    "sigma": "0"
   },
   {
    "type": "integral stationary but not local max",
    "S1": [
     1,
     5,
     6,
     8
    ],
    "sigma": "0"
   },
   {
    "type": "integral stationary but not local max",
    "S1": [
     1,
     5,
     6,
     9
    ],
    "sigma": "0"
   },
   {
    "type": "integral stationary but not local max",
    "S1": [
     1,
     5,
     7,
     8
    ],
    "sigma": "0"
   },
   {
    "type": "integral stationary but not local max",
    "S1": [
     1,
     5,
     7,
     9
    ],
    "sigma": "0"
   },
   {
    "type": "integral stationary but not local max",
    "S1": [
     1,
     5,
     8,
     9
    ],
    "sigma": "0"
   },
   {
    "type": "integral stationary but not local max",
    "S1": [
     1,
     6,
     7,
     9
    ],
    "sigma": "0"
   },
   {
    "type": "integral stationary but not local max",
    "S1": [
     1,
     6,
     8,
     9
    ],
    "sigma": "0"
   },
   {
    "type": "integral stationary but not local max",
    "S1": [
     1,
     7,
     8,
     9
    ],
    "sigma": "0"
   },
   {
    "type": "integral stationary but not local max",
    "S1": [
     2,
     3,
     4,
     6
    ],
    "sigma": "0"
   },
   {
    "type": "integral stationary but not local max",
    "S1": [
     2,
     3,
     5,
     7
    ],
    "sigma": "0"
   },
   {
    "type": "integral stationary but not local max",
    "S1": [
     2,
     3,
     5,
     8
    ],
    "sigma": "0"
   },
   {
    "type": "integral stationary but not local max",
    "S1": [
     2,
     3,
     5,
     9
    ],
    "sigma": "0"
   },
   {
    "type": "integral stationary but not local max",
    "S1": [
     2,
     3,
     6,
     8
    ],
    "sigma": "0"
   },
   {
    "type": "integral stationary but not local max",
    "S1": [
     2,
     3,
     7,
     9
    ],
    "sigma": "0"
   },
   {
    "type": "integral stationary but not local max",
    "S1": [
     2,
     4,
     5,
     6
    ],
    "sigma": "0"
   },
   {
    "type": "integral stationary but not local max",
    "S1": [
     2,
     4,
     5,
     7
    ],
    "sigma": "0"
   },
   {
    "type": "integral stationary but not local max",
    "S1": [
     2,
     4,
     5,
     8
    ],
    "sigma": "0"
   },
   {
    "type": "integral stationary but not local max",
    "S1": [
     2,
     4,
     5,
     9
    ],
    "sigma": "0"
   },
   {
    "type": "integral stationary but not local max",
    "S1": [
     2,
     4,
     6,
     7
    ],
    "sigma": "0"
   },
   {
    "type": "integral stationary but not local max",
    "S1": [
     2,
     4,
     6,
     8
    ],
    "sigma": "0"
   },
   {
    "type": "integral stationary but not local max",
    "S1": [
     2,
     4,
     6,
     9
    ],
    "sigma": "0"
   },
   {
    "type": "integral stationary but not local max",
    "S1": [
     2,
     4,
     7,
     8
    ],
    "sigma": "0"
   },
   {
    "type": "integral stationary but not local max",
    "S1": [
     2,
     4,
     7,
     9
    ],
    "sigma": "0"
   },
   {
    "type": "integral stationary but not local max",
    "S1": [
     2,
     4,
     8,
     9
    ],
    "sigma": "0"
   },
   {
    "type": "integral stationary but not local max",
    "S1": [
     2,
     5,
     6,
     8
    ],
    "sigma": "0"
   },
   {
    "type": "integral stationary but not local max",
    "S1": [
     2,
     5,
     7,
     8
    ],
    "sigma": "0"
   },
   {
    "type": "integral stationary but not local max",
    "S1": [
     2,
     5,
     7,
     9
    ],
    "sigma": "0"
   },
   {
    "type": "integral stationary but not local max",
    "S1": [
     2,
     6,
     7,
     9
    ],
    "sigma": "0"
   },
   {
    "type": "integral stationary but not local max",
    "S1": [
     2,
     6,
     8,
     9
    ],
    "sigma": "0"
   },
   {
    "type": "integral stationary but not local max",
    "S1": [
     3,
     4,
     5,
     7
    ],
    "sigma": "0"
   },
   {
    "type": "integral stationary but not local max",
    "S1": [
     3,
     4,
     6,
     8
    ],
    "sigma": "0"
   },
   {
    "type": "integral stationary but not local max",
    "S1": [
     3,
     4,
     6,
     9
    ],
    "sigma": "0"
   },
   {
    "type": "integral stationary but not local max",
    "S1": [
     3,
     4,
     7,
     9
    ],
    "sigma": "0"
   },
   {
    "type": "integral stationary but not local max",
    "S1": [
     3,
     5,
     6,
     7
    ],
    "sigma": "0"
   },
   {
    "type": "integral stationary but not local max",
    "S1": [
     3,
     5,
     6,
     8
    ],
    "sigma": "0"
   },
   {
    "type": "integral stationary but not local max",
    "S1": [
     3,
     5,
     6,
     9
    ],
    "sigma": "0"
   },
   {
    "type": "integral stationary but not local max",
    "S1": [
     3,
     5,
     7,
     8
    ],
    "sigma": "0"
   },
   {
    "type": "integral stationary but not local max",
    "S1": [
     3,
     5,
     7,
     9
    ],
    "sigma": "0"
   },
   {
    "type": "integral stationary but not local max",
    "S1": [
     3,
     5,
     8,
     9
    ],
    "sigma": "0"
   },
   {
    "type": "integral stationary but not local max",
    "S1": [
     3,
     6,
     7,
     9
    ],
    "sigma": "0"
   },
   {
    "type": "integral stationary but not local max",
    "S1": [
     3,
     6,
     8,
     9
    ],
    "sigma": "0"
   },
   {
    "type": "integral stationary but not local max",
    "S1": [
     4,
     5,
     6,
     8
    ],
    "sigma": "0"
   },
   {
    "type": "integral stationary but not local max",
    "S1": [
     4,
     5,
     7,
     9
    ],
    "sigma": "0"
   },
   {
    "type": "integral stationary but not local max",
    "S1": [
     4,
     6,
     7,
     8
    ],
    "sigma": "0"
   },
   {
    "type": "integral stationary but not local max",
    "S1": [
     4,
     6,
     7,
     9
    ],
    "sigma": "0"
   },
   {
    "type": "integral stationary but not local max",
    "S1": [
     4,
     6,
     8,
     9
    ],
    "sigma": "0"
   },
   {
    "type": "integral stationary but not local max",
    "S1": [
     5,
     6,
     7,
     9
    ],
    "sigma": "0"
   },
   {
    "type": "integral stationary but not local max",
    "S1": [
     5,
     7,
     8,
     9
    ],
    "sigma": "0"
   }
  ],
  "curvature_ge_2lam_minus_2": true,
  "sigma_ge_lam_minus_1": false,
  "graph": "cycle C10",
  "n": 10,
  "k": 4,
  "lam": "2",
  "arm": "M1_lam_integral"
 },
 {
  "n_stationary_isolated": 271,
  "n_integral": 25,
  "n_nonintegral": 246,
  "integral_localmax_thm36": 25,
  "integral_localmax_D4": 25,
  "integral_NOT_localmax": 0,
  "certs_disagree": 0,
  "ascent_found_inside_radius": 0,
  "ascent_found_at_4x_radius": 0,
  "localmax_probed": 25,
  "nonintegral_strict_saddle": 246,
  "nonintegral_no_saddle_cert": 0,
  "min_saddle_curvature": "1",
  "min_localmax_sigma": "1/2",
  "min_localmax_radius": 0.2,
  "n_families": 80,
  "n_unhandled": 0,
  "families_all_nonintegral_with_cert": true,
  "counterexamples": [],
  "curvature_ge_2lam_minus_2": true,
  "sigma_ge_lam_minus_1": true,
  "graph": "cycle C10",
  "n": 10,
  "k": 4,
  "lam": "1/2",
  "arm": "M2_lam_lt_1"
 },
 {
  "n_stationary_isolated": 2261,
  "n_integral": 70,
  "n_nonintegral": 2191,
  "integral_localmax_thm36": 70,
  "integral_localmax_D4": 70,
  "integral_NOT_localmax": 0,
  "certs_disagree": 0,
  "ascent_found_inside_radius": 0,
  "ascent_found_at_4x_radius": 0,
  "localmax_probed": 70,
  "nonintegral_strict_saddle": 2191,
  "nonintegral_no_saddle_cert": 0,
  "min_saddle_curvature": "1",
  "min_localmax_sigma": "1/2",
  "min_localmax_radius": 0.14285714285714285,
  "n_families": 0,
  "n_unhandled": 0,
  "families_all_nonintegral_with_cert": true,
  "counterexamples": [],
  "curvature_ge_2lam_minus_2": true,
  "sigma_ge_lam_minus_1": true,
  "graph": "cycle C10",
  "n": 10,
  "k": 5,
  "lam": "3/2",
  "arm": "main"
 },
 {
  "n_stationary_isolated": 5032,
  "n_integral": 252,
  "n_nonintegral": 4780,
  "integral_localmax_thm36": 70,
  "integral_localmax_D4": 70,
  "integral_NOT_localmax": 182,
  "certs_disagree": 0,
  "ascent_found_inside_radius": 0,
  "ascent_found_at_4x_radius": 0,
  "localmax_probed": 70,
  "nonintegral_strict_saddle": 4780,
  "nonintegral_no_saddle_cert": 0,
  "min_saddle_curvature": "2",
  "min_localmax_sigma": "0",
  "min_localmax_radius": 0.25,
  "n_families": 1,
  "n_unhandled": 0,
  "families_all_nonintegral_with_cert": true,
  "counterexamples": [
   {
    "type": "integral stationary but not local max",
    "S1": [
     0,
     1,
     2,
     3,
     5
    ],
    "sigma": "0"
   },
   {
    "type": "integral stationary but not local max",
    "S1": [
     0,
     1,
     2,
     3,
     8
    ],
    "sigma": "0"
   },
   {
    "type": "integral stationary but not local max",
    "S1": [
     0,
     1,
     2,
     4,
     6
    ],
    "sigma": "0"
   },
   {
    "type": "integral stationary but not local max",
    "S1": [
     0,
     1,
     2,
     4,
     7
    ],
    "sigma": "0"
   },
   {
    "type": "integral stationary but not local max",
    "S1": [
     0,
     1,
     2,
     4,
     8
    ],
    "sigma": "0"
   },
   {
    "type": "integral stationary but not local max",
    "S1": [
     0,
     1,
     2,
     4,
     9
    ],
    "sigma": "0"
   },
   {
    "type": "integral stationary but not local max",
    "S1": [
     0,
     1,
     2,
     5,
     7
    ],
    "sigma": "0"
   },
   {
    "type": "integral stationary but not local max",
    "S1": [
     0,
     1,
     2,
     5,
     8
    ],
    "sigma": "0"
   },
   {
    "type": "integral stationary but not local max",
    "S1": [
     0,
     1,
     2,
     6,
     8
    ],
    "sigma": "0"
   },
   {
    "type": "integral stationary but not local max",
    "S1": [
     0,
     1,
     2,
     7,
     9
    ],
    "sigma": "0"
   },
   {
    "type": "integral stationary but not local max",
    "S1": [
     0,
     1,
     3,
     4,
     6
    ],
    "sigma": "0"
   },
   {
    "type": "integral stationary but not local max",
    "S1": [
     0,
     1,
     3,
     4,
     7
    ],
    "sigma": "0"
   },
   {
    "type": "integral stationary but not local max",
    "S1": [
     0,
     1,
     3,
     4,
     8
    ],
    "sigma": "0"
   },
   {
    "type": "integral stationary but not local max",
    "S1": [
     0,
     1,
     3,
     5,
     6
    ],
    "sigma": "0"
   },
   {
    "type": "integral stationary but not local max",
    "S1": [
     0,
     1,
     3,
     5,
     7
    ],
    "sigma": "0"
   },
   {
    "type": "integral stationary but not local max",
    "S1": [
     0,
     1,
     3,
     5,
     8
    ],
    "sigma": "0"
   },
   {
    "type": "integral stationary but not local max",
    "S1": [
     0,
     1,
     3,
     5,
     9
    ],
    "sigma": "0"
   },
   {
    "type": "integral stationary but not local max",
    "S1": [
     0,
     1,
     3,
     6,
     7
    ],
    "sigma": "0"
   },
   {
    "type": "integral stationary but not local max",
    "S1": [
     0,
     1,
     3,
     6,
     8
    ],
    "sigma": "0"
   },
   {
    "type": "integral stationary but not local max",
    "S1": [
     0,
     1,
     3,
     6,
     9
    ],
    "sigma": "0"
   },
   {
    "type": "integral stationary but not local max",
    "S1": [
     0,
     1,
     3,
     7,
     8
    ],
    "sigma": "0"
   },
   {
    "type": "integral stationary but not local max",
    "S1": [
     0,
     1,
     3,
     7,
     9
    ],
    "sigma": "0"
   },
   {
    "type": "integral stationary but not local max",
    "S1": [
     0,
     1,
     3,
     8,
     9
    ],
    "sigma": "0"
   },
   {
    "type": "integral stationary but not local max",
    "S1": [
     0,
     1,
     4,
     5,
     7
    ],
    "sigma": "0"
   },
   {
    "type": "integral stationary but not local max",
    "S1": [
     0,
     1,
     4,
     5,
     8
    ],
    "sigma": "0"
   },
   {
    "type": "integral stationary but not local max",
    "S1": [
     0,
     1,
     4,
     6,
     7
    ],
    "sigma": "0"
   },
   {
    "type": "integral stationary but not local max",
    "S1": [
     0,
     1,
     4,
     6,
     8
    ],
    "sigma": "0"
   },
   {
    "type": "integral stationary but not local max",
    "S1": [
     0,
     1,
     4,
     6,
     9
    ],
    "sigma": "0"
   },
   {
    "type": "integral stationary but not local max",
    "S1": [
     0,
     1,
     4,
     7,
     8
    ],
    "sigma": "0"
   },
   {
    "type": "integral stationary but not local max",
    "S1": [
     0,
     1,
     4,
     7,
     9
    ],
    "sigma": "0"
   },
   {
    "type": "integral stationary but not local max",
    "S1": [
     0,
     1,
     5,
     6,
     8
    ],
    "sigma": "0"
   },
   {
    "type": "integral stationary but not local max",
    "S1": [
     0,
     1,
     5,
     7,
     8
    ],
    "sigma": "0"
   },
   {
    "type": "integral stationary but not local max",
    "S1": [
     0,
     1,
     5,
     7,
     9
    ],
    "sigma": "0"
   },
   {
    "type": "integral stationary but not local max",
    "S1": [
     0,
     1,
     6,
     8,
     9
    ],
    "sigma": "0"
   },
   {
    "type": "integral stationary but not local max",
    "S1": [
     0,
     2,
     3,
     4,
     5
    ],
    "sigma": "0"
   },
   {
    "type": "integral stationary but not local max",
    "S1": [
     0,
     2,
     3,
     4,
     6
    ],
    "sigma": "0"
   },
   {
    "type": "integral stationary but not local max",
    "S1": [
     0,
     2,
     3,
     4,
     7
    ],
    "sigma": "0"
   },
   {
    "type": "integral stationary but not local max",
    "S1": [
     0,
     2,
     3,
     4,
     8
    ],
    "sigma": "0"
   },
   {
    "type": "integral stationary but not local max",
    "S1": [
     0,
     2,
     3,
     5,
     6
    ],
    "sigma": "0"
   },
   {
    "type": "integral stationary but not local max",
    "S1": [
     0,
     2,
     3,
     5,
     7
    ],
    "sigma": "0"
   },
   {
    "type": "integral stationary but not local max",
    "S1": [
     0,
     2,
     3,
     5,
     8
    ],
    "sigma": "0"
   },
   {
    "type": "integral stationary but not local max",
    "S1": [
     0,
     2,
     3,
     5,
     9
    ],
    "sigma": "0"
   },
   {
    "type": "integral stationary but not local max",
    "S1": [
     0,
     2,
     3,
     6,
     7
    ],
    "sigma": "0"
   },
   {
    "type": "integral stationary but not local max",
    "S1": [
     0,
     2,
     3,
     6,
     8
    ],
    "sigma": "0"
   },
   {
    "type": "integral stationary but not local max",
    "S1": [
     0,
     2,
     3,
     6,
     9
    ],
    "sigma": "0"
   },
   {
    "type": "integral stationary but not local max",
    "S1": [
     0,
     2,
     3,
     7,
     8
    ],
    "sigma": "0"
   },
   {
    "type": "integral stationary but not local max",
    "S1": [
     0,
     2,
     3,
     7,
     9
    ],
    "sigma": "0"
   },
   {
    "type": "integral stationary but not local max",
    "S1": [
     0,
     2,
     4,
     5,
     6
    ],
    "sigma": "0"
   },
   {
    "type": "integral stationary but not local max",
    "S1": [
     0,
     2,
     4,
     5,
     7
    ],
    "sigma": "0"
   },
   {
    "type": "integral stationary but not local max",
    "S1": [
     0,
     2,
     4,
     5,
     8
    ],
    "sigma": "0"
   },
   {
    "type": "integral stationary but not local max",
    "S1": [
     0,
     2,
     4,
     5,
     9
    ],
    "sigma": "0"
   },
   {
    "type": "integral stationary but not local max",
    "S1": [
     0,
     2,
     4,
     6,
     7
    ],
    "sigma": "0"
   },
   {
    "type": "integral stationary but not local max",
    "S1": [
     0,
     2,
     4,
     6,
     8
    ],
    "sigma": "0"
   },
   {
    "type": "integral stationary but not local max",
    "S1": [
     0,
     2,
     4,
     6,
     9
    ],
    "sigma": "0"
   },
   {
    "type": "integral stationary but not local max",
    "S1": [
     0,
     2,
     4,
     7,
     8
    ],
    "sigma": "0"
   },
   {
    "type": "integral stationary but not local max",
    "S1": [
     0,
     2,
     4,
     7,
     9
    ],
    "sigma": "0"
   },
   {
    "type": "integral stationary but not local max",
    "S1": [
     0,
     2,
     4,
     8,
     9
    ],
    "sigma": "0"
   },
   {
    "type": "integral stationary but not local max",
    "S1": [
     0,
     2,
     5,
     6,
     7
    ],
    "sigma": "0"
   },
   {
    "type": "integral stationary but not local max",
    "S1": [
     0,
     2,
     5,
     6,
     8
    ],
    "sigma": "0"
   },
   {
    "type": "integral stationary but not local max",
    "S1": [
     0,
     2,
     5,
     6,
     9
    ],
    "sigma": "0"
   },
   {
    "type": "integral stationary but not local max",
    "S1": [
     0,
     2,
     5,
     7,
     8
    ],
    "sigma": "0"
   },
   {
    "type": "integral stationary but not local max",
    "S1": [
     0,
     2,
     5,
     7,
     9
    ],
    "sigma": "0"
   },
   {
    "type": "integral stationary but not local max",
    "S1": [
     0,
     2,
     5,
     8,
     9
    ],
    "sigma": "0"
   },
   {
    "type": "integral stationary but not local max",
    "S1": [
     0,
     2,
     6,
     7,
     8
    ],
    "sigma": "0"
   },
   {
    "type": "integral stationary but not local max",
    "S1": [
     0,
     2,
     6,
     7,
     9
    ],
    "sigma": "0"
   },
   {
    "type": "integral stationary but not local max",
    "S1": [
     0,
     2,
     6,
     8,
     9
    ],
    "sigma": "0"
   },
   {
    "type": "integral stationary but not local max",
    "S1": [
     0,
     2,
     7,
     8,
     9
    ],
    "sigma": "0"
   },
   {
    "type": "integral stationary but not local max",
    "S1": [
     0,
     3,
     4,
     5,
     7
    ],
    "sigma": "0"
   },
   {
    "type": "integral stationary but not local max",
    "S1": [
     0,
     3,
     4,
     5,
     8
    ],
    "sigma": "0"
   },
   {
    "type": "integral stationary but not local max",
    "S1": [
     0,
     3,
     4,
     6,
     7
    ],
    "sigma": "0"
   },
   {
    "type": "integral stationary but not local max",
    "S1": [
     0,
     3,
     4,
     6,
     8
    ],
    "sigma": "0"
   },
   {
    "type": "integral stationary but not local max",
    "S1": [
     0,
     3,
     4,
     6,
     9
    ],
    "sigma": "0"
   },
   {
    "type": "integral stationary but not local max",
    "S1": [
     0,
     3,
     4,
     7,
     8
    ],
    "sigma": "0"
   },
   {
    "type": "integral stationary but not local max",
    "S1": [
     0,
     3,
     4,
     7,
     9
    ],
    "sigma": "0"
   },
   {
    "type": "integral stationary but not local max",
    "S1": [
     0,
     3,
     5,
     6,
     7
    ],
    "sigma": "0"
   },
   {
    "type": "integral stationary but not local max",
    "S1": [
     0,
     3,
     5,
     6,
     8
    ],
    "sigma": "0"
   },
   {
    "type": "integral stationary but not local max",
    "S1": [
     0,
     3,
     5,
     6,
     9
    ],
    "sigma": "0"
   },
   {
    "type": "integral stationary but not local max",
    "S1": [
     0,
     3,
     5,
     7,
     8
    ],
    "sigma": "0"
   },
   {
    "type": "integral stationary but not local max",
    "S1": [
     0,
     3,
     5,
     7,
     9
    ],
    "sigma": "0"
   },
   {
    "type": "integral stationary but not local max",
    "S1": [
     0,
     3,
     5,
     8,
     9
    ],
    "sigma": "0"
   },
   {
    "type": "integral stationary but not local max",
    "S1": [
     0,
     3,
     6,
     7,
     8
    ],
    "sigma": "0"
   },
   {
    "type": "integral stationary but not local max",
    "S1": [
     0,
     3,
     6,
     7,
     9
    ],
    "sigma": "0"
   },
   {
    "type": "integral stationary but not local max",
    "S1": [
     0,
     3,
     6,
     8,
     9
    ],
    "sigma": "0"
   },
   {
    "type": "integral stationary but not local max",
    "S1": [
     0,
     4,
     5,
     6,
     8
    ],
    "sigma": "0"
   },
   {
    "type": "integral stationary but not local max",
    "S1": [
     0,
     4,
     5,
     7,
     8
    ],
    "sigma": "0"
   },
   {
    "type": "integral stationary but not local max",
    "S1": [
     0,
     4,
     5,
     7,
     9
    ],
    "sigma": "0"
   },
   {
    "type": "integral stationary but not local max",
    "S1": [
     0,
     4,
     6,
     7,
     8
    ],
    "sigma": "0"
   },
   {
    "type": "integral stationary but not local max",
    "S1": [
     0,
     4,
     6,
     7,
     9
    ],
    "sigma": "0"
   },
   {
    "type": "integral stationary but not local max",
    "S1": [
     0,
     4,
     6,
     8,
     9
    ],
    "sigma": "0"
   },
   {
    "type": "integral stationary but not local max",
    "S1": [
     0,
     5,
     6,
     7,
     8
    ],
    "sigma": "0"
   },
   {
    "type": "integral stationary but not local max",
    "S1": [
     0,
     5,
     7,
     8,
     9
    ],
    "sigma": "0"
   },
   {
    "type": "integral stationary but not local max",
    "S1": [
     1,
     2,
     3,
     4,
     6
    ],
    "sigma": "0"
   },
   {
    "type": "integral stationary but not local max",
    "S1": [
     1,
     2,
     3,
     4,
     9
    ],
    "sigma": "0"
   },
   {
    "type": "integral stationary but not local max",
    "S1": [
     1,
     2,
     3,
     5,
     7
    ],
    "sigma": "0"
   },
   {
    "type": "integral stationary but not local max",
    "S1": [
     1,
     2,
     3,
     5,
     8
    ],
    "sigma": "0"
   },
   {
    "type": "integral stationary but not local max",
    "S1": [
     1,
     2,
     3,
     5,
     9
    ],
    "sigma": "0"
   },
   {
    "type": "integral stationary but not local max",
    "S1": [
     1,
     2,
     3,
     6,
     8
    ],
    "sigma": "0"
   },
   {
    "type": "integral stationary but not local max",
    "S1": [
     1,
     2,
     3,
     6,
     9
    ],
    "sigma": "0"
   },
   {
    "type": "integral stationary but not local max",
    "S1": [
     1,
     2,
     3,
     7,
     9
    ],
    "sigma": "0"
   },
   {
    "type": "integral stationary but not local max",
    "S1": [
     1,
     2,
     4,
     5,
     7
    ],
    "sigma": "0"
   },
   {
    "type": "integral stationary but not local max",
    "S1": [
     1,
     2,
     4,
     5,
     8
    ],
    "sigma": "0"
   },
   {
    "type": "integral stationary but not local max",
    "S1": [
     1,
     2,
     4,
     5,
     9
    ],
    "sigma": "0"
   },
   {
    "type": "integral stationary but not local max",
    "S1": [
     1,
     2,
     4,
     6,
     7
    ],
    "sigma": "0"
   },
   {
    "type": "integral stationary but not local max",
    "S1": [
     1,
     2,
     4,
     6,
     8
    ],
    "sigma": "0"
   },
   {
    "type": "integral stationary but not local max",
    "S1": [
     1,
     2,
     4,
     6,
     9
    ],
    "sigma": "0"
   },
   {
    "type": "integral stationary but not local max",
    "S1": [
     1,
     2,
     4,
     7,
     8
    ],
    "sigma": "0"
   },
   {
    "type": "integral stationary but not local max",
    "S1": [
     1,
     2,
     4,
     7,
     9
    ],
    "sigma": "0"
   },
   {
    "type": "integral stationary but not local max",
    "S1": [
     1,
     2,
     4,
     8,
     9
    ],
    "sigma": "0"
   },
   {
    "type": "integral stationary but not local max",
    "S1": [
     1,
     2,
     5,
     6,
     8
    ],
    "sigma": "0"
   },
   {
    "type": "integral stationary but not local max",
    "S1": [
     1,
     2,
     5,
     6,
     9
    ],
    "sigma": "0"
   },
   {
    "type": "integral stationary but not local max",
    "S1": [
     1,
     2,
     5,
     7,
     8
    ],
    "sigma": "0"
   },
   {
    "type": "integral stationary but not local max",
    "S1": [
     1,
     2,
     5,
     7,
     9
    ],
    "sigma": "0"
   },
   {
    "type": "integral stationary but not local max",
    "S1": [
     1,
     2,
     5,
     8,
     9
    ],
    "sigma": "0"
   },
   {
    "type": "integral stationary but not local max",
    "S1": [
     1,
     2,
     6,
     7,
     9
    ],
    "sigma": "0"
   },
   {
    "type": "integral stationary but not local max",
    "S1": [
     1,
     2,
     6,
     8,
     9
    ],
    "sigma": "0"
   },
   {
    "type": "integral stationary but not local max",
    "S1": [
     1,
     3,
     4,
     5,
     6
    ],
    "sigma": "0"
   },
   {
    "type": "integral stationary but not local max",
    "S1": [
     1,
     3,
     4,
     5,
     7
    ],
    "sigma": "0"
   },
   {
    "type": "integral stationary but not local max",
    "S1": [
     1,
     3,
     4,
     5,
     8
    ],
    "sigma": "0"
   },
   {
    "type": "integral stationary but not local max",
    "S1": [
     1,
     3,
     4,
     5,
     9
    ],
    "sigma": "0"
   },
   {
    "type": "integral stationary but not local max",
    "S1": [
     1,
     3,
     4,
     6,
     7
    ],
    "sigma": "0"
   },
   {
    "type": "integral stationary but not local max",
    "S1": [
     1,
     3,
     4,
     6,
     8
    ],
    "sigma": "0"
   },
   {
    "type": "integral stationary but not local max",
    "S1": [
     1,
     3,
     4,
     6,
     9
    ],
    "sigma": "0"
   },
   {
    "type": "integral stationary but not local max",
    "S1": [
     1,
     3,
     4,
     7,
     8
    ],
    "sigma": "0"
   },
   {
    "type": "integral stationary but not local max",
    "S1": [
     1,
     3,
     4,
     7,
     9
    ],
    "sigma": "0"
   },
   {
    "type": "integral stationary but not local max",
    "S1": [
     1,
     3,
     4,
     8,
     9
    ],
    "sigma": "0"
   },
   {
    "type": "integral stationary but not local max",
    "S1": [
     1,
     3,
     5,
     6,
     7
    ],
    "sigma": "0"
   },
   {
    "type": "integral stationary but not local max",
    "S1": [
     1,
     3,
     5,
     6,
     8
    ],
    "sigma": "0"
   },
   {
    "type": "integral stationary but not local max",
    "S1": [
     1,
     3,
     5,
     6,
     9
    ],
    "sigma": "0"
   },
   {
    "type": "integral stationary but not local max",
    "S1": [
     1,
     3,
     5,
     7,
     8
    ],
    "sigma": "0"
   },
   {
    "type": "integral stationary but not local max",
    "S1": [
     1,
     3,
     5,
     7,
     9
    ],
    "sigma": "0"
   },
   {
    "type": "integral stationary but not local max",
    "S1": [
     1,
     3,
     5,
     8,
     9
    ],
    "sigma": "0"
   },
   {
    "type": "integral stationary but not local max",
    "S1": [
     1,
     3,
     6,
     7,
     8
    ],
    "sigma": "0"
   },
   {
    "type": "integral stationary but not local max",
    "S1": [
     1,
     3,
     6,
     7,
     9
    ],
    "sigma": "0"
   },
   {
    "type": "integral stationary but not local max",
    "S1": [
     1,
     3,
     6,
     8,
     9
    ],
    "sigma": "0"
   },
   {
    "type": "integral stationary but not local max",
    "S1": [
     1,
     3,
     7,
     8,
     9
    ],
    "sigma": "0"
   },
   {
    "type": "integral stationary but not local max",
    "S1": [
     1,
     4,
     5,
     6,
     8
    ],
    "sigma": "0"
   },
   {
    "type": "integral stationary but not local max",
    "S1": [
     1,
     4,
     5,
     6,
     9
    ],
    "sigma": "0"
   },
   {
    "type": "integral stationary but not local max",
    "S1": [
     1,
     4,
     5,
     7,
     8
    ],
    "sigma": "0"
   },
   {
    "type": "integral stationary but not local max",
    "S1": [
     1,
     4,
     5,
     7,
     9
    ],
    "sigma": "0"
   },
   {
    "type": "integral stationary but not local max",
    "S1": [
     1,
     4,
     5,
     8,
     9
    ],
    "sigma": "0"
   },
   {
    "type": "integral stationary but not local max",
    "S1": [
     1,
     4,
     6,
     7,
     8
    ],
    "sigma": "0"
   },
   {
    "type": "integral stationary but not local max",
    "S1": [
     1,
     4,
     6,
     7,
     9
    ],
    "sigma": "0"
   },
   {
    "type": "integral stationary but not local max",
    "S1": [
     1,
     4,
     6,
     8,
     9
    ],
    "sigma": "0"
   },
   {
    "type": "integral stationary but not local max",
    "S1": [
     1,
     4,
     7,
     8,
     9
    ],
    "sigma": "0"
   },
   {
    "type": "integral stationary but not local max",
    "S1": [
     1,
     5,
     6,
     7,
     9
    ],
    "sigma": "0"
   },
   {
    "type": "integral stationary but not local max",
    "S1": [
     1,
     5,
     6,
     8,
     9
    ],
    "sigma": "0"
   },
   {
    "type": "integral stationary but not local max",
    "S1": [
     1,
     5,
     7,
     8,
     9
    ],
    "sigma": "0"
   },
   {
    "type": "integral stationary but not local max",
    "S1": [
     1,
     6,
     7,
     8,
     9
    ],
    "sigma": "0"
   },
   {
    "type": "integral stationary but not local max",
    "S1": [
     2,
     3,
     4,
     5,
     7
    ],
    "sigma": "0"
   },
   {
    "type": "integral stationary but not local max",
    "S1": [
     2,
     3,
     4,
     6,
     8
    ],
    "sigma": "0"
   },
   {
    "type": "integral stationary but not local max",
    "S1": [
     2,
     3,
     4,
     6,
     9
    ],
    "sigma": "0"
   },
   {
    "type": "integral stationary but not local max",
    "S1": [
     2,
     3,
     4,
     7,
     9
    ],
    "sigma": "0"
   },
   {
    "type": "integral stationary but not local max",
    "S1": [
     2,
     3,
     5,
     6,
     8
    ],
    "sigma": "0"
   },
   {
    "type": "integral stationary but not local max",
    "S1": [
     2,
     3,
     5,
     6,
     9
    ],
    "sigma": "0"
   },
   {
    "type": "integral stationary but not local max",
    "S1": [
     2,
     3,
     5,
     7,
     8
    ],
    "sigma": "0"
   },
   {
    "type": "integral stationary but not local max",
    "S1": [
     2,
     3,
     5,
     7,
     9
    ],
    "sigma": "0"
   },
   {
    "type": "integral stationary but not local max",
    "S1": [
     2,
     3,
     5,
     8,
     9
    ],
    "sigma": "0"
   },
   {
    "type": "integral stationary but not local max",
    "S1": [
     2,
     3,
     6,
     7,
     9
    ],
    "sigma": "0"
   },
   {
    "type": "integral stationary but not local max",
    "S1": [
     2,
     3,
     6,
     8,
     9
    ],
    "sigma": "0"
   },
   {
    "type": "integral stationary but not local max",
    "S1": [
     2,
     4,
     5,
     6,
     7
    ],
    "sigma": "0"
   },
   {
    "type": "integral stationary but not local max",
    "S1": [
     2,
     4,
     5,
     6,
     8
    ],
    "sigma": "0"
   },
   {
    "type": "integral stationary but not local max",
    "S1": [
     2,
     4,
     5,
     6,
     9
    ],
    "sigma": "0"
   },
   {
    "type": "integral stationary but not local max",
    "S1": [
     2,
     4,
     5,
     7,
     8
    ],
    "sigma": "0"
   },
   {
    "type": "integral stationary but not local max",
    "S1": [
     2,
     4,
     5,
     7,
     9
    ],
    "sigma": "0"
   },
   {
    "type": "integral stationary but not local max",
    "S1": [
     2,
     4,
     5,
     8,
     9
    ],
    "sigma": "0"
   },
   {
    "type": "integral stationary but not local max",
    "S1": [
     2,
     4,
     6,
     7,
     8
    ],
    "sigma": "0"
   },
   {
    "type": "integral stationary but not local max",
    "S1": [
     2,
     4,
     6,
     7,
     9
    ],
    "sigma": "0"
   },
   {
    "type": "integral stationary but not local max",
    "S1": [
     2,
     4,
     6,
     8,
     9
    ],
    "sigma": "0"
   },
   {
    "type": "integral stationary but not local max",
    "S1": [
     2,
     4,
     7,
     8,
     9
    ],
    "sigma": "0"
   },
   {
    "type": "integral stationary but not local max",
    "S1": [
     2,
     5,
     6,
     7,
     9
    ],
    "sigma": "0"
   },
   {
    "type": "integral stationary but not local max",
    "S1": [
     2,
     5,
     6,
     8,
     9
    ],
    "sigma": "0"
   },
   {
    "type": "integral stationary but not local max",
    "S1": [
     2,
     5,
     7,
     8,
     9
    ],
    "sigma": "0"
   },
   {
    "type": "integral stationary but not local max",
    "S1": [
     3,
     4,
     5,
     6,
     8
    ],
    "sigma": "0"
   },
   {
    "type": "integral stationary but not local max",
    "S1": [
     3,
     4,
     5,
     7,
     9
    ],
    "sigma": "0"
   },
   {
    "type": "integral stationary but not local max",
    "S1": [
     3,
     4,
     6,
     7,
     9
    ],
    "sigma": "0"
   },
   {
    "type": "integral stationary but not local max",
    "S1": [
     3,
     4,
     6,
     8,
     9
    ],
    "sigma": "0"
   },
   {
    "type": "integral stationary but not local max",
    "S1": [
     3,
     5,
     6,
     7,
     8
    ],
    "sigma": "0"
   },
   {
    "type": "integral stationary but not local max",
    "S1": [
     3,
     5,
     6,
     7,
     9
    ],
    "sigma": "0"
   },
   {
    "type": "integral stationary but not local max",
    "S1": [
     3,
     5,
     6,
     8,
     9
    ],
    "sigma": "0"
   },
   {
    "type": "integral stationary but not local max",
    "S1": [
     3,
     5,
     7,
     8,
     9
    ],
    "sigma": "0"
   },
   {
    "type": "integral stationary but not local max",
    "S1": [
     4,
     5,
     6,
     7,
     9
    ],
    "sigma": "0"
   },
   {
    "type": "integral stationary but not local max",
    "S1": [
     4,
     6,
     7,
     8,
     9
    ],
    "sigma": "0"
   }
  ],
  "curvature_ge_2lam_minus_2": true,
  "sigma_ge_lam_minus_1": false,
  "graph": "cycle C10",
  "n": 10,
  "k": 5,
  "lam": "2",
  "arm": "M1_lam_integral"
 },
 {
  "n_stationary_isolated": 361,
  "n_integral": 30,
  "n_nonintegral": 331,
  "integral_localmax_thm36": 30,
  "integral_localmax_D4": 30,
  "integral_NOT_localmax": 0,
  "certs_disagree": 0,
  "ascent_found_inside_radius": 0,
  "ascent_found_at_4x_radius": 0,
  "localmax_probed": 30,
  "nonintegral_strict_saddle": 331,
  "nonintegral_no_saddle_cert": 0,
  "min_saddle_curvature": "1",
  "min_localmax_sigma": "1/2",
  "min_localmax_radius": 0.2,
  "n_families": 130,
  "n_unhandled": 0,
  "families_all_nonintegral_with_cert": true,
  "counterexamples": [],
  "curvature_ge_2lam_minus_2": true,
  "sigma_ge_lam_minus_1": true,
  "graph": "cycle C10",
  "n": 10,
  "k": 5,
  "lam": "1/2",
  "arm": "M2_lam_lt_1"
 }
]