{
  "artifact_id": "ONE_PATRON_HERALD_I_TOPOLOGY",
  "version": "1.0.0",
  "complex_type": "WEIGHTED_ORIENTED_CELL_COMPLEX",
  "coefficient_field": "RATIONAL",
  "vertices": [
    "v00", "v01", "v02", "v03", "v04", "v05", "v06",
    "v07", "v08", "v09", "v10", "v11", "v12", "v13",
    "v14", "v15", "v16", "v17", "v18", "v19", "v20"
  ],
  "boundary_channels": [
    {"id":"e00","source":"v00","target":"v01","family":"C1","position":1,"weight":1.00},
    {"id":"e01","source":"v01","target":"v02","family":"C1","position":2,"weight":1.08},
    {"id":"e02","source":"v02","target":"v03","family":"C1","position":3,"weight":1.16},
    {"id":"e03","source":"v03","target":"v04","family":"C1","position":4,"weight":1.24},
    {"id":"e04","source":"v04","target":"v05","family":"C1","position":5,"weight":1.16},
    {"id":"e05","source":"v05","target":"v06","family":"C1","position":6,"weight":1.08},
    {"id":"e06","source":"v06","target":"v07","family":"C1","position":7,"weight":1.00},
    {"id":"e07","source":"v07","target":"v08","family":"C2","position":1,"weight":0.92},
    {"id":"e08","source":"v08","target":"v09","family":"C2","position":2,"weight":1.00},
    {"id":"e09","source":"v09","target":"v10","family":"C2","position":3,"weight":1.08},
    {"id":"e10","source":"v10","target":"v11","family":"C2","position":4,"weight":1.16},
    {"id":"e11","source":"v11","target":"v12","family":"C2","position":5,"weight":1.08},
    {"id":"e12","source":"v12","target":"v13","family":"C2","position":6,"weight":1.00},
    {"id":"e13","source":"v13","target":"v14","family":"C2","position":7,"weight":0.92},
    {"id":"e14","source":"v14","target":"v15","family":"C3","position":1,"weight":1.04},
    {"id":"e15","source":"v15","target":"v16","family":"C3","position":2,"weight":1.12},
    {"id":"e16","source":"v16","target":"v17","family":"C3","position":3,"weight":1.20},
    {"id":"e17","source":"v17","target":"v18","family":"C3","position":4,"weight":1.28},
    {"id":"e18","source":"v18","target":"v19","family":"C3","position":5,"weight":1.20},
    {"id":"e19","source":"v19","target":"v20","family":"C3","position":6,"weight":1.12},
    {"id":"e20","source":"v20","target":"v00","family":"C3","position":7,"weight":1.04}
  ],
  "family_semantics": {
    "C1": "A_LOCAL_BOUNDARY_SEGMENT",
    "C2": "RELATIONAL_INTERFACE_SEGMENT",
    "C3": "B_LOCAL_BOUNDARY_SEGMENT"
  },
  "pre_event_cells_order_2": [],
  "closure_event": {
    "id": "ORDER_TRANSITION_22",
    "trigger": "VALID_FREE_EVENT_G0",
    "operation": "ATTACH_2_CELL",
    "cell": {
      "id": "c_closure",
      "order": 2,
      "oriented_boundary": [
        {"cell":"e00","coefficient":1},{"cell":"e01","coefficient":1},{"cell":"e02","coefficient":1},
        {"cell":"e03","coefficient":1},{"cell":"e04","coefficient":1},{"cell":"e05","coefficient":1},
        {"cell":"e06","coefficient":1},{"cell":"e07","coefficient":1},{"cell":"e08","coefficient":1},
        {"cell":"e09","coefficient":1},{"cell":"e10","coefficient":1},{"cell":"e11","coefficient":1},
        {"cell":"e12","coefficient":1},{"cell":"e13","coefficient":1},{"cell":"e14","coefficient":1},
        {"cell":"e15","coefficient":1},{"cell":"e16","coefficient":1},{"cell":"e17","coefficient":1},
        {"cell":"e18","coefficient":1},{"cell":"e19","coefficient":1},{"cell":"e20","coefficient":1}
      ]
    },
    "adds_boundary_channel": false,
    "expected_invariant_change": {
      "beta_0_before": 1,
      "beta_1_before": 1,
      "beta_0_after": 1,
      "beta_1_after": 0
    }
  },
  "cellular_sheaf": {
    "stalks": [
      {"id":"stalk_A","carrier":"A","space":"V_A","dimension":3},
      {"id":"stalk_B","carrier":"B","space":"V_B","dimension":2},
      {"id":"stalk_R","carrier":"R_AB","space":"V_R","dimension":2}
    ],
    "attachments": [
      {"stalk":"stalk_A","cells":["v00","v01","v02","v03","v04","v05","v06"]},
      {"stalk":"stalk_R","cells":["v07","v08","v09","v10","v11","v12","v13"]},
      {"stalk":"stalk_B","cells":["v14","v15","v16","v17","v18","v19","v20"]}
    ],
    "restriction_maps": [
      {"id":"rho_A_R","from_stalk":"stalk_A","to_stalk":"stalk_R","matrix":[[1,0,0],[0,1,0]]},
      {"id":"rho_B_R","from_stalk":"stalk_B","to_stalk":"stalk_R","matrix":[[1,1],[0,1]]}
    ],
    "global_section_condition": "rho_A_R(a)=rho_B_R(b)",
    "local_space_equality_required": false
  },
  "derived_operators": {
    "boundary_1": "SIGNED_VERTEX_EDGE_INCIDENCE",
    "boundary_2_before": "ZERO_COLUMN_SPACE",
    "boundary_2_after": "ORIENTED_BOUNDARY_OF_c_closure",
    "hodge_laplacian_0": "B1*W1*TRANSPOSE(B1)",
    "hodge_laplacian_1_before": "TRANSPOSE(B1)*B1",
    "hodge_laplacian_1_after": "TRANSPOSE(B1)*B1+B2*TRANSPOSE(B2)"
  }
}