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      "name": "full vector set without decomposition multiplicity ('b', 'a'),('b', 'b'),lower=0,width=2,beta=-1",
      "passed": true
    },
    {
      "name": "forward/inverse and unique diagonal ('b', 'a'),('b', 'b'),lower=0,width=2,beta=-1",
      "passed": true
    },
    {
      "name": "direct arc-product count ('b', 'a'),('b', 'b'),lower=0,width=2,beta=0",
      "passed": true
    },
    {
      "name": "full vector set without decomposition multiplicity ('b', 'a'),('b', 'b'),lower=0,width=2,beta=0",
      "passed": true
    },
    {
      "name": "forward/inverse and unique diagonal ('b', 'a'),('b', 'b'),lower=0,width=2,beta=0",
      "passed": true
    },
    {
      "name": "direct arc-product count ('b', 'a'),('b', 'b'),lower=0,width=2,beta=1",
      "passed": true
    },
    {
      "name": "full vector set without decomposition multiplicity ('b', 'a'),('b', 'b'),lower=0,width=2,beta=1",
      "passed": true
    },
    {
      "name": "forward/inverse and unique diagonal ('b', 'a'),('b', 'b'),lower=0,width=2,beta=1",
      "passed": true
    },
    {
      "name": "direct arc-product count ('b', 'b'),('a', 'a'),lower=-1,width=1,beta=-1",
      "passed": true
    },
    {
      "name": "full vector set without decomposition multiplicity ('b', 'b'),('a', 'a'),lower=-1,width=1,beta=-1",
      "passed": true
    },
    {
      "name": "forward/inverse and unique diagonal ('b', 'b'),('a', 'a'),lower=-1,width=1,beta=-1",
      "passed": true
    },
    {
      "name": "direct arc-product count ('b', 'b'),('a', 'a'),lower=-1,width=1,beta=0",
      "passed": true
    },
    {
      "name": "full vector set without decomposition multiplicity ('b', 'b'),('a', 'a'),lower=-1,width=1,beta=0",
      "passed": true
    },
    {
      "name": "forward/inverse and unique diagonal ('b', 'b'),('a', 'a'),lower=-1,width=1,beta=0",
      "passed": true
    },
    {
      "name": "direct arc-product count ('b', 'b'),('a', 'a'),lower=-1,width=1,beta=1",
      "passed": true
    },
    {
      "name": "full vector set without decomposition multiplicity ('b', 'b'),('a', 'a'),lower=-1,width=1,beta=1",
      "passed": true
    },
    {
      "name": "forward/inverse and unique diagonal ('b', 'b'),('a', 'a'),lower=-1,width=1,beta=1",
      "passed": true
    },
    {
      "name": "direct arc-product count ('b', 'b'),('a', 'a'),lower=0,width=1,beta=-1",
      "passed": true
    },
    {
      "name": "full vector set without decomposition multiplicity ('b', 'b'),('a', 'a'),lower=0,width=1,beta=-1",
      "passed": true
    },
    {
      "name": "forward/inverse and unique diagonal ('b', 'b'),('a', 'a'),lower=0,width=1,beta=-1",
      "passed": true
    },
    {
      "name": "direct arc-product count ('b', 'b'),('a', 'a'),lower=0,width=1,beta=0",
      "passed": true
    },
    {
      "name": "full vector set without decomposition multiplicity ('b', 'b'),('a', 'a'),lower=0,width=1,beta=0",
      "passed": true
    },
    {
      "name": "forward/inverse and unique diagonal ('b', 'b'),('a', 'a'),lower=0,width=1,beta=0",
      "passed": true
    },
    {
      "name": "direct arc-product count ('b', 'b'),('a', 'a'),lower=0,width=1,beta=1",
      "passed": true
    },
    {
      "name": "full vector set without decomposition multiplicity ('b', 'b'),('a', 'a'),lower=0,width=1,beta=1",
      "passed": true
    },
    {
      "name": "forward/inverse and unique diagonal ('b', 'b'),('a', 'a'),lower=0,width=1,beta=1",
      "passed": true
    },
    {
      "name": "direct arc-product count ('b', 'b'),('a', 'a'),lower=0,width=2,beta=-1",
      "passed": true
    },
    {
      "name": "full vector set without decomposition multiplicity ('b', 'b'),('a', 'a'),lower=0,width=2,beta=-1",
      "passed": true
    },
    {
      "name": "forward/inverse and unique diagonal ('b', 'b'),('a', 'a'),lower=0,width=2,beta=-1",
      "passed": true
    },
    {
      "name": "direct arc-product count ('b', 'b'),('a', 'a'),lower=0,width=2,beta=0",
      "passed": true
    },
    {
      "name": "full vector set without decomposition multiplicity ('b', 'b'),('a', 'a'),lower=0,width=2,beta=0",
      "passed": true
    },
    {
      "name": "forward/inverse and unique diagonal ('b', 'b'),('a', 'a'),lower=0,width=2,beta=0",
      "passed": true
    },
    {
      "name": "direct arc-product count ('b', 'b'),('a', 'a'),lower=0,width=2,beta=1",
      "passed": true
    },
    {
      "name": "full vector set without decomposition multiplicity ('b', 'b'),('a', 'a'),lower=0,width=2,beta=1",
      "passed": true
    },
    {
      "name": "forward/inverse and unique diagonal ('b', 'b'),('a', 'a'),lower=0,width=2,beta=1",
      "passed": true
    },
    {
      "name": "direct arc-product count ('b', 'b'),('a', 'b'),lower=-1,width=1,beta=-1",
      "passed": true
    },
    {
      "name": "full vector set without decomposition multiplicity ('b', 'b'),('a', 'b'),lower=-1,width=1,beta=-1",
      "passed": true
    },
    {
      "name": "forward/inverse and unique diagonal ('b', 'b'),('a', 'b'),lower=-1,width=1,beta=-1",
      "passed": true
    },
    {
      "name": "direct arc-product count ('b', 'b'),('a', 'b'),lower=-1,width=1,beta=0",
      "passed": true
    },
    {
      "name": "full vector set without decomposition multiplicity ('b', 'b'),('a', 'b'),lower=-1,width=1,beta=0",
      "passed": true
    },
    {
      "name": "forward/inverse and unique diagonal ('b', 'b'),('a', 'b'),lower=-1,width=1,beta=0",
      "passed": true
    },
    {
      "name": "direct arc-product count ('b', 'b'),('a', 'b'),lower=-1,width=1,beta=1",
      "passed": true
    },
    {
      "name": "full vector set without decomposition multiplicity ('b', 'b'),('a', 'b'),lower=-1,width=1,beta=1",
      "passed": true
    },
    {
      "name": "forward/inverse and unique diagonal ('b', 'b'),('a', 'b'),lower=-1,width=1,beta=1",
      "passed": true
    },
    {
      "name": "direct arc-product count ('b', 'b'),('a', 'b'),lower=0,width=1,beta=-1",
      "passed": true
    },
    {
      "name": "full vector set without decomposition multiplicity ('b', 'b'),('a', 'b'),lower=0,width=1,beta=-1",
      "passed": true
    },
    {
      "name": "forward/inverse and unique diagonal ('b', 'b'),('a', 'b'),lower=0,width=1,beta=-1",
      "passed": true
    },
    {
      "name": "direct arc-product count ('b', 'b'),('a', 'b'),lower=0,width=1,beta=0",
      "passed": true
    },
    {
      "name": "full vector set without decomposition multiplicity ('b', 'b'),('a', 'b'),lower=0,width=1,beta=0",
      "passed": true
    },
    {
      "name": "forward/inverse and unique diagonal ('b', 'b'),('a', 'b'),lower=0,width=1,beta=0",
      "passed": true
    },
    {
      "name": "direct arc-product count ('b', 'b'),('a', 'b'),lower=0,width=1,beta=1",
      "passed": true
    },
    {
      "name": "full vector set without decomposition multiplicity ('b', 'b'),('a', 'b'),lower=0,width=1,beta=1",
      "passed": true
    },
    {
      "name": "forward/inverse and unique diagonal ('b', 'b'),('a', 'b'),lower=0,width=1,beta=1",
      "passed": true
    },
    {
      "name": "direct arc-product count ('b', 'b'),('a', 'b'),lower=0,width=2,beta=-1",
      "passed": true
    },
    {
      "name": "full vector set without decomposition multiplicity ('b', 'b'),('a', 'b'),lower=0,width=2,beta=-1",
      "passed": true
    },
    {
      "name": "forward/inverse and unique diagonal ('b', 'b'),('a', 'b'),lower=0,width=2,beta=-1",
      "passed": true
    },
    {
      "name": "direct arc-product count ('b', 'b'),('a', 'b'),lower=0,width=2,beta=0",
      "passed": true
    },
    {
      "name": "full vector set without decomposition multiplicity ('b', 'b'),('a', 'b'),lower=0,width=2,beta=0",
      "passed": true
    },
    {
      "name": "forward/inverse and unique diagonal ('b', 'b'),('a', 'b'),lower=0,width=2,beta=0",
      "passed": true
    },
    {
      "name": "direct arc-product count ('b', 'b'),('a', 'b'),lower=0,width=2,beta=1",
      "passed": true
    },
    {
      "name": "full vector set without decomposition multiplicity ('b', 'b'),('a', 'b'),lower=0,width=2,beta=1",
      "passed": true
    },
    {
      "name": "forward/inverse and unique diagonal ('b', 'b'),('a', 'b'),lower=0,width=2,beta=1",
      "passed": true
    },
    {
      "name": "direct arc-product count ('b', 'b'),('b', 'a'),lower=-1,width=1,beta=-1",
      "passed": true
    },
    {
      "name": "full vector set without decomposition multiplicity ('b', 'b'),('b', 'a'),lower=-1,width=1,beta=-1",
      "passed": true
    },
    {
      "name": "forward/inverse and unique diagonal ('b', 'b'),('b', 'a'),lower=-1,width=1,beta=-1",
      "passed": true
    },
    {
      "name": "direct arc-product count ('b', 'b'),('b', 'a'),lower=-1,width=1,beta=0",
      "passed": true
    },
    {
      "name": "full vector set without decomposition multiplicity ('b', 'b'),('b', 'a'),lower=-1,width=1,beta=0",
      "passed": true
    },
    {
      "name": "forward/inverse and unique diagonal ('b', 'b'),('b', 'a'),lower=-1,width=1,beta=0",
      "passed": true
    },
    {
      "name": "direct arc-product count ('b', 'b'),('b', 'a'),lower=-1,width=1,beta=1",
      "passed": true
    },
    {
      "name": "full vector set without decomposition multiplicity ('b', 'b'),('b', 'a'),lower=-1,width=1,beta=1",
      "passed": true
    },
    {
      "name": "forward/inverse and unique diagonal ('b', 'b'),('b', 'a'),lower=-1,width=1,beta=1",
      "passed": true
    },
    {
      "name": "direct arc-product count ('b', 'b'),('b', 'a'),lower=0,width=1,beta=-1",
      "passed": true
    },
    {
      "name": "full vector set without decomposition multiplicity ('b', 'b'),('b', 'a'),lower=0,width=1,beta=-1",
      "passed": true
    },
    {
      "name": "forward/inverse and unique diagonal ('b', 'b'),('b', 'a'),lower=0,width=1,beta=-1",
      "passed": true
    },
    {
      "name": "direct arc-product count ('b', 'b'),('b', 'a'),lower=0,width=1,beta=0",
      "passed": true
    },
    {
      "name": "full vector set without decomposition multiplicity ('b', 'b'),('b', 'a'),lower=0,width=1,beta=0",
      "passed": true
    },
    {
      "name": "forward/inverse and unique diagonal ('b', 'b'),('b', 'a'),lower=0,width=1,beta=0",
      "passed": true
    },
    {
      "name": "direct arc-product count ('b', 'b'),('b', 'a'),lower=0,width=1,beta=1",
      "passed": true
    },
    {
      "name": "full vector set without decomposition multiplicity ('b', 'b'),('b', 'a'),lower=0,width=1,beta=1",
      "passed": true
    },
    {
      "name": "forward/inverse and unique diagonal ('b', 'b'),('b', 'a'),lower=0,width=1,beta=1",
      "passed": true
    },
    {
      "name": "direct arc-product count ('b', 'b'),('b', 'a'),lower=0,width=2,beta=-1",
      "passed": true
    },
    {
      "name": "full vector set without decomposition multiplicity ('b', 'b'),('b', 'a'),lower=0,width=2,beta=-1",
      "passed": true
    },
    {
      "name": "forward/inverse and unique diagonal ('b', 'b'),('b', 'a'),lower=0,width=2,beta=-1",
      "passed": true
    },
    {
      "name": "direct arc-product count ('b', 'b'),('b', 'a'),lower=0,width=2,beta=0",
      "passed": true
    },
    {
      "name": "full vector set without decomposition multiplicity ('b', 'b'),('b', 'a'),lower=0,width=2,beta=0",
      "passed": true
    },
    {
      "name": "forward/inverse and unique diagonal ('b', 'b'),('b', 'a'),lower=0,width=2,beta=0",
      "passed": true
    },
    {
      "name": "direct arc-product count ('b', 'b'),('b', 'a'),lower=0,width=2,beta=1",
      "passed": true
    },
    {
      "name": "full vector set without decomposition multiplicity ('b', 'b'),('b', 'a'),lower=0,width=2,beta=1",
      "passed": true
    },
    {
      "name": "forward/inverse and unique diagonal ('b', 'b'),('b', 'a'),lower=0,width=2,beta=1",
      "passed": true
    },
    {
      "name": "direct arc-product count ('b', 'b'),('b', 'b'),lower=-1,width=1,beta=-1",
      "passed": true
    },
    {
      "name": "full vector set without decomposition multiplicity ('b', 'b'),('b', 'b'),lower=-1,width=1,beta=-1",
      "passed": true
    },
    {
      "name": "forward/inverse and unique diagonal ('b', 'b'),('b', 'b'),lower=-1,width=1,beta=-1",
      "passed": true
    },
    {
      "name": "direct arc-product count ('b', 'b'),('b', 'b'),lower=-1,width=1,beta=0",
      "passed": true
    },
    {
      "name": "full vector set without decomposition multiplicity ('b', 'b'),('b', 'b'),lower=-1,width=1,beta=0",
      "passed": true
    },
    {
      "name": "forward/inverse and unique diagonal ('b', 'b'),('b', 'b'),lower=-1,width=1,beta=0",
      "passed": true
    },
    {
      "name": "direct arc-product count ('b', 'b'),('b', 'b'),lower=-1,width=1,beta=1",
      "passed": true
    },
    {
      "name": "full vector set without decomposition multiplicity ('b', 'b'),('b', 'b'),lower=-1,width=1,beta=1",
      "passed": true
    },
    {
      "name": "forward/inverse and unique diagonal ('b', 'b'),('b', 'b'),lower=-1,width=1,beta=1",
      "passed": true
    },
    {
      "name": "direct arc-product count ('b', 'b'),('b', 'b'),lower=0,width=1,beta=-1",
      "passed": true
    },
    {
      "name": "full vector set without decomposition multiplicity ('b', 'b'),('b', 'b'),lower=0,width=1,beta=-1",
      "passed": true
    },
    {
      "name": "forward/inverse and unique diagonal ('b', 'b'),('b', 'b'),lower=0,width=1,beta=-1",
      "passed": true
    },
    {
      "name": "direct arc-product count ('b', 'b'),('b', 'b'),lower=0,width=1,beta=0",
      "passed": true
    },
    {
      "name": "full vector set without decomposition multiplicity ('b', 'b'),('b', 'b'),lower=0,width=1,beta=0",
      "passed": true
    },
    {
      "name": "forward/inverse and unique diagonal ('b', 'b'),('b', 'b'),lower=0,width=1,beta=0",
      "passed": true
    },
    {
      "name": "direct arc-product count ('b', 'b'),('b', 'b'),lower=0,width=1,beta=1",
      "passed": true
    },
    {
      "name": "full vector set without decomposition multiplicity ('b', 'b'),('b', 'b'),lower=0,width=1,beta=1",
      "passed": true
    },
    {
      "name": "forward/inverse and unique diagonal ('b', 'b'),('b', 'b'),lower=0,width=1,beta=1",
      "passed": true
    },
    {
      "name": "direct arc-product count ('b', 'b'),('b', 'b'),lower=0,width=2,beta=-1",
      "passed": true
    },
    {
      "name": "full vector set without decomposition multiplicity ('b', 'b'),('b', 'b'),lower=0,width=2,beta=-1",
      "passed": true
    },
    {
      "name": "forward/inverse and unique diagonal ('b', 'b'),('b', 'b'),lower=0,width=2,beta=-1",
      "passed": true
    },
    {
      "name": "direct arc-product count ('b', 'b'),('b', 'b'),lower=0,width=2,beta=0",
      "passed": true
    },
    {
      "name": "full vector set without decomposition multiplicity ('b', 'b'),('b', 'b'),lower=0,width=2,beta=0",
      "passed": true
    },
    {
      "name": "forward/inverse and unique diagonal ('b', 'b'),('b', 'b'),lower=0,width=2,beta=0",
      "passed": true
    },
    {
      "name": "direct arc-product count ('b', 'b'),('b', 'b'),lower=0,width=2,beta=1",
      "passed": true
    },
    {
      "name": "full vector set without decomposition multiplicity ('b', 'b'),('b', 'b'),lower=0,width=2,beta=1",
      "passed": true
    },
    {
      "name": "forward/inverse and unique diagonal ('b', 'b'),('b', 'b'),lower=0,width=2,beta=1",
      "passed": true
    },
    {
      "name": "parallel-unit-flow count",
      "passed": true
    },
    {
      "name": "parallel-unit-flow full original vectors",
      "passed": true
    },
    {
      "name": "parallel arcs remain distinct equiprobable coordinates",
      "passed": true
    },
    {
      "name": "two-route-unit-flow count",
      "passed": true
    },
    {
      "name": "two-route-unit-flow full original vectors",
      "passed": true
    },
    {
      "name": "signed-loop-flow count",
      "passed": true
    },
    {
      "name": "signed-loop-flow full original vectors",
      "passed": true
    },
    {
      "name": "loop cancels balances yet has five distinct values",
      "passed": true
    },
    {
      "name": "empty-network-flow count",
      "passed": true
    },
    {
      "name": "empty-network-flow full original vectors",
      "passed": true
    },
    {
      "name": "edgeless-infeasible-flow count",
      "passed": true
    },
    {
      "name": "edgeless-infeasible-flow full original vectors",
      "passed": true
    },
    {
      "name": "count budget leaves feasibility/count unknown {'count_work_budget': 1}",
      "passed": true
    },
    {
      "name": "count budget leaves feasibility/count unknown {'state_budget': 1}",
      "passed": true
    },
    {
      "name": "diagnostic exhaustion preserves completed count without partial law",
      "passed": true
    },
    {
      "name": "binary capacity reduction uses three vertices without unary expansion",
      "passed": true
    },
    {
      "name": "large valid reduction has unknown finite-reference count",
      "passed": true
    },
    {
      "name": "lower exceeding upper is known empty",
      "passed": true
    },
    {
      "name": "nonzero balance sum is known empty",
      "passed": true
    },
    {
      "name": "changed diagonal violates unique table correspondence",
      "passed": true
    },
    {
      "name": "out-of-bounds original vector refused",
      "passed": true
    },
    {
      "name": "wrong original balance refused",
      "passed": true
    },
    {
      "name": "duplicate arc ID refused",
      "passed": true
    },
    {
      "name": "unknown endpoint refused",
      "passed": true
    },
    {
      "name": "boolean capacity refused",
      "passed": true
    },
    {
      "name": "oversized integer refused before reduction",
      "passed": true
    },
    {
      "name": "duplicate vertex refused",
      "passed": true
    },
    {
      "name": "invalid budget refused even before reference-domain gate",
      "passed": true
    }
  ],
  "passed": 460,
  "failed": 0,
  "scope": "Direct arc-product enumeration, 144 signed/loop/parallel/balance cases, round trips, small fixtures, large binary reduction, damaged inputs and distinct count/diagnostic budget states. No source FPRAS, real network resilience/failure law, multicommodity model, independent proof/program or buyer value verified."
}