{
  "K_C2_2_finite_simplicial_levels": [
    {
      "predicted_2_power_binomial_q_2": 1,
      "simplex_count": 1,
      "simplicial_degree": 0
    },
    {
      "predicted_2_power_binomial_q_2": 1,
      "simplex_count": 1,
      "simplicial_degree": 1
    },
    {
      "predicted_2_power_binomial_q_2": 2,
      "simplex_count": 2,
      "simplicial_degree": 2
    },
    {
      "predicted_2_power_binomial_q_2": 8,
      "simplex_count": 8,
      "simplicial_degree": 3
    },
    {
      "predicted_2_power_binomial_q_2": 64,
      "simplex_count": 64,
      "simplicial_degree": 4
    }
  ],
  "c2_nonzero_k_invariant": {
    "all_4_tuple_cocycle_conditions_hold": true,
    "coefficient_module": "C2 with trivial action",
    "distinct_3_coboundaries": [
      [
        0
      ]
    ],
    "group": "C2",
    "nontrivial_H3_class": true,
    "normalized_2_cochain_count": 2,
    "normalized_3_cocycle_nonzero_value": [
      1,
      1,
      1
    ]
  },
  "finite_crossed_module": {
    "boundary_values": [
      0,
      2,
      0,
      2
    ],
    "cokernel_order": 2,
    "crossed_module_axioms_hold": true,
    "kernel": [
      0,
      2
    ],
    "kernel_action_is_trivial": true,
    "nonzero_associativity_cocycle_values": [
      {
        "kernel_element": 2,
        "triple": [
          1,
          1,
          1
        ]
      }
    ],
    "source_group": "C4",
    "target_group": "C4"
  },
  "finite_totalization_sharpness": {
    "coefficient_module": "F3 with generator acting by (-1)^(r+1)",
    "group": "C2",
    "meaning_of_group_order_1": "The zero cohomology group.",
    "normalized_cochain_group_order_in_each_degree": 3,
    "rows": [
      {
        "delta_r_minus_1_mod_3": null,
        "delta_r_mod_3": 1,
        "epsilon_mod_3": 2,
        "full_H_r_order": 1,
        "full_pi_0_component_count": 1,
        "inverse_delta_r_mod_3": 1,
        "target_truncation_r": 0,
        "truncated_H_r_order": 3,
        "truncated_pi_0_component_count": 3
      },
      {
        "delta_r_minus_1_mod_3": 0,
        "delta_r_mod_3": 2,
        "epsilon_mod_3": 1,
        "full_H_r_order": 1,
        "full_pi_0_component_count": 1,
        "inverse_delta_r_mod_3": 2,
        "target_truncation_r": 1,
        "truncated_H_r_order": 3,
        "truncated_pi_0_component_count": 3
      },
      {
        "delta_r_minus_1_mod_3": 0,
        "delta_r_mod_3": 1,
        "epsilon_mod_3": 2,
        "full_H_r_order": 1,
        "full_pi_0_component_count": 1,
        "inverse_delta_r_mod_3": 1,
        "target_truncation_r": 2,
        "truncated_H_r_order": 3,
        "truncated_pi_0_component_count": 3
      },
      {
        "delta_r_minus_1_mod_3": 0,
        "delta_r_mod_3": 2,
        "epsilon_mod_3": 1,
        "full_H_r_order": 1,
        "full_pi_0_component_count": 1,
        "inverse_delta_r_mod_3": 2,
        "target_truncation_r": 3,
        "truncated_H_r_order": 3,
        "truncated_pi_0_component_count": 3
      },
      {
        "delta_r_minus_1_mod_3": 0,
        "delta_r_mod_3": 1,
        "epsilon_mod_3": 2,
        "full_H_r_order": 1,
        "full_pi_0_component_count": 1,
        "inverse_delta_r_mod_3": 1,
        "target_truncation_r": 4,
        "truncated_H_r_order": 3,
        "truncated_pi_0_component_count": 3
      },
      {
        "delta_r_minus_1_mod_3": 0,
        "delta_r_mod_3": 2,
        "epsilon_mod_3": 1,
        "full_H_r_order": 1,
        "full_pi_0_component_count": 1,
        "inverse_delta_r_mod_3": 2,
        "target_truncation_r": 5,
        "truncated_H_r_order": 3,
        "truncated_pi_0_component_count": 3
      },
      {
        "delta_r_minus_1_mod_3": 0,
        "delta_r_mod_3": 1,
        "epsilon_mod_3": 2,
        "full_H_r_order": 1,
        "full_pi_0_component_count": 1,
        "inverse_delta_r_mod_3": 1,
        "target_truncation_r": 6,
        "truncated_H_r_order": 3,
        "truncated_pi_0_component_count": 3
      },
      {
        "delta_r_minus_1_mod_3": 0,
        "delta_r_mod_3": 2,
        "epsilon_mod_3": 1,
        "full_H_r_order": 1,
        "full_pi_0_component_count": 1,
        "inverse_delta_r_mod_3": 2,
        "target_truncation_r": 7,
        "truncated_H_r_order": 3,
        "truncated_pi_0_component_count": 3
      },
      {
        "delta_r_minus_1_mod_3": 0,
        "delta_r_mod_3": 1,
        "epsilon_mod_3": 2,
        "full_H_r_order": 1,
        "full_pi_0_component_count": 1,
        "inverse_delta_r_mod_3": 1,
        "target_truncation_r": 8,
        "truncated_H_r_order": 3,
        "truncated_pi_0_component_count": 3
      }
    ],
    "verified_r_max": 8,
    "verified_r_min": 0
  },
  "method": "Exact exhaustive enumeration; Python standard library.",
  "pentagon_failure": {
    "coefficient_module": "C2 with trivial action",
    "failed_pentagon_inputs": [
      [
        1,
        1,
        1,
        2
      ],
      [
        1,
        1,
        2,
        2
      ],
      [
        1,
        2,
        2,
        1
      ],
      [
        2,
        1,
        1,
        1
      ],
      [
        2,
        2,
        1,
        1
      ]
    ],
    "group": "C3",
    "only_nonzero_associator": [
      1,
      1,
      1
    ]
  }
}