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  ],
  "fundamental_group_extensions": {
    "cases": [
      {
        "group": "Cp x Cp",
        "m": 0,
        "order_of_1_0": 3,
        "p": 3
      },
      {
        "group": "C(p^2)",
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        "order_of_1_0": 9,
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      },
      {
        "group": "C(p^2)",
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        "order_of_1_0": 9,
        "p": 3
      },
      {
        "group": "Cp x Cp",
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        "order_of_1_0": 5,
        "p": 5
      },
      {
        "group": "C(p^2)",
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        "order_of_1_0": 25,
        "p": 5
      },
      {
        "group": "C(p^2)",
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        "order_of_1_0": 25,
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      },
      {
        "group": "C(p^2)",
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        "order_of_1_0": 25,
        "p": 5
      },
      {
        "group": "C(p^2)",
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        "order_of_1_0": 25,
        "p": 5
      },
      {
        "group": "Cp x Cp",
        "m": 0,
        "order_of_1_0": 7,
        "p": 7
      },
      {
        "group": "C(p^2)",
        "m": 1,
        "order_of_1_0": 49,
        "p": 7
      },
      {
        "group": "C(p^2)",
        "m": 2,
        "order_of_1_0": 49,
        "p": 7
      },
      {
        "group": "C(p^2)",
        "m": 3,
        "order_of_1_0": 49,
        "p": 7
      },
      {
        "group": "C(p^2)",
        "m": 4,
        "order_of_1_0": 49,
        "p": 7
      },
      {
        "group": "C(p^2)",
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        "order_of_1_0": 49,
        "p": 7
      },
      {
        "group": "C(p^2)",
        "m": 6,
        "order_of_1_0": 49,
        "p": 7
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    ],
    "every_m_checked": true,
    "full_associativity_tables_checked": true,
    "primes": [
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      5,
      7
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  },
  "method": "Exact normalized bar matrices and modular Gaussian elimination; integer enumeration.",
  "padic_gauge_coefficients": {
    "all_coefficient_identities_hold": true,
    "all_nonzero_a_checked": true,
    "boundary_examples": [
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        "first_nonzero_exponent": 3,
        "j": 3,
        "p": 3,
        "retained_homotopy_degree": 5,
        "valuation": 1
      },
      {
        "first_nonzero_exponent": 3,
        "j": 6,
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        "retained_homotopy_degree": 5,
        "valuation": 1
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      {
        "first_nonzero_exponent": 9,
        "j": 9,
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        "retained_homotopy_degree": 17,
        "valuation": 2
      },
      {
        "first_nonzero_exponent": 5,
        "j": 5,
        "p": 5,
        "retained_homotopy_degree": 9,
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      {
        "first_nonzero_exponent": 5,
        "j": 10,
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      {
        "first_nonzero_exponent": 25,
        "j": 25,
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      {
        "first_nonzero_exponent": 7,
        "j": 7,
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        "retained_homotopy_degree": 13,
        "valuation": 1
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      {
        "first_nonzero_exponent": 7,
        "j": 14,
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        "retained_homotopy_degree": 13,
        "valuation": 1
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      {
        "first_nonzero_exponent": 49,
        "j": 49,
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        "retained_homotopy_degree": 97,
        "valuation": 2
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    ],
    "j_max": 100,
    "j_min": 2,
    "number_of_p_j_a_cases": 1188,
    "primes": [
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      7
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  },
  "scope_warning": "Finite consistency checks only. General theorems and space-level splittings require the manuscript proofs.",
  "script_sha256": "909f7b13298a0149851b6acdee237488bfc902d7fe7d02186dc88b7a7608e799",
  "twisted_C2_parity": {
    "band": "Z/4 with sign action",
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      {
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      {
        "boundary_image": [
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    "differential_degree_max": 10,
    "group": "C2",
    "lift_parity_r_max": 8,
    "lift_parity_r_min": 2,
    "lifts": [
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        "lift_exists": false,
        "obstruction_mod_2": 1,
        "r": 2
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      {
        "lift_exists": true,
        "obstruction_mod_2": 0,
        "r": 3
      },
      {
        "lift_exists": false,
        "obstruction_mod_2": 1,
        "r": 4
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      {
        "lift_exists": true,
        "obstruction_mod_2": 0,
        "r": 5
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      {
        "lift_exists": false,
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        "r": 6
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      {
        "lift_exists": true,
        "obstruction_mod_2": 0,
        "r": 7
      },
      {
        "lift_exists": false,
        "obstruction_mod_2": 1,
        "r": 8
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    ]
  }
}