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      "tolerance": 4e-12
    },
    {
      "name": "sweep 119 continuity",
      "passed": true,
      "absolute_error": 1.1102230246251565e-16,
      "scaled_error": 1.1102230246251565e-16,
      "tolerance": 4e-12
    },
    {
      "name": "sweep 119 incident current",
      "passed": true,
      "absolute_error": 0.0,
      "scaled_error": 0.0,
      "tolerance": 4e-12
    },
    {
      "name": "sweep 119 reflected unit-mode current",
      "passed": true,
      "absolute_error": 0.0,
      "scaled_error": 0.0,
      "tolerance": 4e-12
    },
    {
      "name": "sweep 119 outgoing or gap current",
      "passed": true,
      "absolute_error": 3.3306690738754696e-16,
      "scaled_error": 3.3306690738754696e-16,
      "tolerance": 4e-12
    },
    {
      "name": "sweep 119 incident eigen-equation",
      "passed": true,
      "absolute_error": 1.1102230246251565e-16,
      "scaled_error": 5.958081967793454e-17,
      "tolerance": 4e-12
    },
    {
      "name": "sweep 119 incident positive density",
      "passed": true
    },
    {
      "name": "sweep 119 incident current/group-velocity ratio",
      "passed": true,
      "absolute_error": 0.0,
      "scaled_error": 0.0,
      "tolerance": 4e-12
    },
    {
      "name": "sweep 119 incident independent eigensolver projector",
      "passed": true,
      "absolute_error": 0.0,
      "scaled_error": 0.0,
      "tolerance": 4e-12
    },
    {
      "name": "sweep 119 reflected eigen-equation",
      "passed": true,
      "absolute_error": 1.1102230246251565e-16,
      "scaled_error": 5.958081967793454e-17,
      "tolerance": 4e-12
    },
    {
      "name": "sweep 119 reflected positive density",
      "passed": true
    },
    {
      "name": "sweep 119 reflected current/group-velocity ratio",
      "passed": true,
      "absolute_error": 0.0,
      "scaled_error": 0.0,
      "tolerance": 4e-12
    },
    {
      "name": "sweep 119 reflected independent eigensolver projector",
      "passed": true,
      "absolute_error": 0.0,
      "scaled_error": 0.0,
      "tolerance": 4e-12
    },
    {
      "name": "sweep 119 right eigen-equation",
      "passed": true,
      "absolute_error": 6.280369834735101e-16,
      "scaled_error": 1.4793615479892973e-16,
      "tolerance": 4e-12
    },
    {
      "name": "sweep 119 right positive density",
      "passed": true
    },
    {
      "name": "sweep 119 right current/group-velocity ratio",
      "passed": true,
      "absolute_error": 0.0,
      "scaled_error": 0.0,
      "tolerance": 4e-12
    },
    {
      "name": "sweep 119 right independent eigensolver projector",
      "passed": true,
      "absolute_error": 4.710277376051325e-16,
      "scaled_error": 4.710277376051325e-16,
      "tolerance": 4e-12
    },
    {
      "name": "sweep 119 independently closed r",
      "passed": true,
      "absolute_error": 5.551115123125783e-17,
      "scaled_error": 5.551115123125783e-17,
      "tolerance": 4e-12
    },
    {
      "name": "sweep 119 independently closed normalized tau",
      "passed": true,
      "absolute_error": 3.3306690738754696e-16,
      "scaled_error": 3.3306690738754696e-16,
      "tolerance": 4e-12
    },
    {
      "name": "sweep 119 conserved R+T",
      "passed": true,
      "absolute_error": 0.0,
      "scaled_error": 0.0,
      "tolerance": 4e-12
    },
    {
      "name": "sweep 119 nonnegative bounded R,T",
      "passed": true
    },
    {
      "name": "sweep 119 left current at -3.1",
      "passed": true,
      "absolute_error": 0.0,
      "scaled_error": 0.0,
      "tolerance": 4e-12
    },
    {
      "name": "sweep 119 left current at -0.73",
      "passed": true,
      "absolute_error": 0.0,
      "scaled_error": 0.0,
      "tolerance": 4e-12
    },
    {
      "name": "sweep 119 left current at -0.01",
      "passed": true,
      "absolute_error": 0.0,
      "scaled_error": 0.0,
      "tolerance": 4e-12
    },
    {
      "name": "sweep 119 right current at 0.01",
      "passed": true,
      "absolute_error": 1.1102230246251565e-16,
      "scaled_error": 1.1102230246251565e-16,
      "tolerance": 4e-12
    },
    {
      "name": "sweep 119 right current at 0.73",
      "passed": true,
      "absolute_error": 2.220446049250313e-16,
      "scaled_error": 2.220446049250313e-16,
      "tolerance": 4e-12
    },
    {
      "name": "sweep 119 right current at 3.1",
      "passed": true,
      "absolute_error": 2.220446049250313e-16,
      "scaled_error": 2.220446049250313e-16,
      "tolerance": 4e-12
    },
    {
      "name": "sweep 119 two-port S unitarity",
      "passed": true,
      "absolute_error": 4.44103664781926e-16,
      "scaled_error": 3.1402871291709717e-16,
      "tolerance": 4e-12
    },
    {
      "name": "sweep 119 two-port left-incident column",
      "passed": true,
      "absolute_error": 0.0,
      "scaled_error": 0.0,
      "tolerance": 4e-12
    },
    {
      "name": "sweep 120 continuity",
      "passed": true,
      "absolute_error": 1.1102230246251565e-16,
      "scaled_error": 1.1102230246251565e-16,
      "tolerance": 4e-12
    },
    {
      "name": "sweep 120 incident current",
      "passed": true,
      "absolute_error": 0.0,
      "scaled_error": 0.0,
      "tolerance": 4e-12
    },
    {
      "name": "sweep 120 reflected unit-mode current",
      "passed": true,
      "absolute_error": 0.0,
      "scaled_error": 0.0,
      "tolerance": 4e-12
    },
    {
      "name": "sweep 120 outgoing or gap current",
      "passed": true,
      "absolute_error": 0.0,
      "scaled_error": 0.0,
      "tolerance": 4e-12
    },
    {
      "name": "sweep 120 incident eigen-equation",
      "passed": true,
      "absolute_error": 1.1102230246251565e-16,
      "scaled_error": 5.958081967793454e-17,
      "tolerance": 4e-12
    },
    {
      "name": "sweep 120 incident positive density",
      "passed": true
    },
    {
      "name": "sweep 120 incident current/group-velocity ratio",
      "passed": true,
      "absolute_error": 0.0,
      "scaled_error": 0.0,
      "tolerance": 4e-12
    },
    {
      "name": "sweep 120 incident independent eigensolver projector",
      "passed": true,
      "absolute_error": 0.0,
      "scaled_error": 0.0,
      "tolerance": 4e-12
    },
    {
      "name": "sweep 120 reflected eigen-equation",
      "passed": true,
      "absolute_error": 1.1102230246251565e-16,
      "scaled_error": 5.958081967793454e-17,
      "tolerance": 4e-12
    },
    {
      "name": "sweep 120 reflected positive density",
      "passed": true
    },
    {
      "name": "sweep 120 reflected current/group-velocity ratio",
      "passed": true,
      "absolute_error": 0.0,
      "scaled_error": 0.0,
      "tolerance": 4e-12
    },
    {
      "name": "sweep 120 reflected independent eigensolver projector",
      "passed": true,
      "absolute_error": 0.0,
      "scaled_error": 0.0,
      "tolerance": 4e-12
    },
    {
      "name": "sweep 120 right eigen-equation",
      "passed": true,
      "absolute_error": 9.930136612989092e-16,
      "scaled_error": 2.3122710578711613e-16,
      "tolerance": 4e-12
    },
    {
      "name": "sweep 120 right positive density",
      "passed": true
    },
    {
      "name": "sweep 120 right current/group-velocity ratio",
      "passed": true,
      "absolute_error": 0.0,
      "scaled_error": 0.0,
      "tolerance": 4e-12
    },
    {
      "name": "sweep 120 right independent eigensolver projector",
      "passed": true,
      "absolute_error": 2.1499376424746292e-16,
      "scaled_error": 2.1499376424746292e-16,
      "tolerance": 4e-12
    },
    {
      "name": "sweep 120 independently closed r",
      "passed": true,
      "absolute_error": 5.551115123125783e-17,
      "scaled_error": 5.551115123125783e-17,
      "tolerance": 4e-12
    },
    {
      "name": "sweep 120 independently closed normalized tau",
      "passed": true,
      "absolute_error": 2.220446049250313e-16,
      "scaled_error": 2.220446049250313e-16,
      "tolerance": 4e-12
    },
    {
      "name": "sweep 120 conserved R+T",
      "passed": true,
      "absolute_error": 0.0,
      "scaled_error": 0.0,
      "tolerance": 4e-12
    },
    {
      "name": "sweep 120 nonnegative bounded R,T",
      "passed": true
    },
    {
      "name": "sweep 120 left current at -3.1",
      "passed": true,
      "absolute_error": 0.0,
      "scaled_error": 0.0,
      "tolerance": 4e-12
    },
    {
      "name": "sweep 120 left current at -0.73",
      "passed": true,
      "absolute_error": 0.0,
      "scaled_error": 0.0,
      "tolerance": 4e-12
    },
    {
      "name": "sweep 120 left current at -0.01",
      "passed": true,
      "absolute_error": 1.1102230246251565e-16,
      "scaled_error": 1.1102230246251565e-16,
      "tolerance": 4e-12
    },
    {
      "name": "sweep 120 right current at 0.01",
      "passed": true,
      "absolute_error": 1.1102230246251565e-16,
      "scaled_error": 1.1102230246251565e-16,
      "tolerance": 4e-12
    },
    {
      "name": "sweep 120 right current at 0.73",
      "passed": true,
      "absolute_error": 0.0,
      "scaled_error": 0.0,
      "tolerance": 4e-12
    },
    {
      "name": "sweep 120 right current at 3.1",
      "passed": true,
      "absolute_error": 0.0,
      "scaled_error": 0.0,
      "tolerance": 4e-12
    },
    {
      "name": "sweep 120 two-port S unitarity",
      "passed": true,
      "absolute_error": 2.632470973083967e-16,
      "scaled_error": 1.8614380763444224e-16,
      "tolerance": 4e-12
    },
    {
      "name": "sweep 120 two-port left-incident column",
      "passed": true,
      "absolute_error": 0.0,
      "scaled_error": 0.0,
      "tolerance": 4e-12
    },
    {
      "name": "sweep 121 continuity",
      "passed": true,
      "absolute_error": 1.1102230246251565e-16,
      "scaled_error": 1.1102230246251565e-16,
      "tolerance": 4e-12
    },
    {
      "name": "sweep 121 incident current",
      "passed": true,
      "absolute_error": 0.0,
      "scaled_error": 0.0,
      "tolerance": 4e-12
    },
    {
      "name": "sweep 121 reflected unit-mode current",
      "passed": true,
      "absolute_error": 0.0,
      "scaled_error": 0.0,
      "tolerance": 4e-12
    },
    {
      "name": "sweep 121 outgoing or gap current",
      "passed": true,
      "absolute_error": 0.0,
      "scaled_error": 0.0,
      "tolerance": 4e-12
    },
    {
      "name": "sweep 121 incident eigen-equation",
      "passed": true,
      "absolute_error": 1.1102230246251565e-16,
      "scaled_error": 5.958081967793454e-17,
      "tolerance": 4e-12
    },
    {
      "name": "sweep 121 incident positive density",
      "passed": true
    },
    {
      "name": "sweep 121 incident current/group-velocity ratio",
      "passed": true,
      "absolute_error": 0.0,
      "scaled_error": 0.0,
      "tolerance": 4e-12
    },
    {
      "name": "sweep 121 incident independent eigensolver projector",
      "passed": true,
      "absolute_error": 0.0,
      "scaled_error": 0.0,
      "tolerance": 4e-12
    },
    {
      "name": "sweep 121 reflected eigen-equation",
      "passed": true,
      "absolute_error": 1.1102230246251565e-16,
      "scaled_error": 5.958081967793454e-17,
      "tolerance": 4e-12
    },
    {
      "name": "sweep 121 reflected positive density",
      "passed": true
    },
    {
      "name": "sweep 121 reflected current/group-velocity ratio",
      "passed": true,
      "absolute_error": 0.0,
      "scaled_error": 0.0,
      "tolerance": 4e-12
    },
    {
      "name": "sweep 121 reflected independent eigensolver projector",
      "passed": true,
      "absolute_error": 0.0,
      "scaled_error": 0.0,
      "tolerance": 4e-12
    },
    {
      "name": "sweep 121 right eigen-equation",
      "passed": true,
      "absolute_error": 4.440892098500626e-16,
      "scaled_error": 1.0223583740762399e-16,
      "tolerance": 4e-12
    },
    {
      "name": "sweep 121 right positive density",
      "passed": true
    },
    {
      "name": "sweep 121 right current/group-velocity ratio",
      "passed": true,
      "absolute_error": 1.1102230246251565e-16,
      "scaled_error": 1.1102230246251565e-16,
      "tolerance": 4e-12
    },
    {
      "name": "sweep 121 right independent eigensolver projector",
      "passed": true,
      "absolute_error": 1.3597399555105182e-16,
      "scaled_error": 1.3597399555105182e-16,
      "tolerance": 4e-12
    },
    {
      "name": "sweep 121 independently closed r",
      "passed": true,
      "absolute_error": 1.6653345369377348e-16,
      "scaled_error": 1.6653345369377348e-16,
      "tolerance": 4e-12
    },
    {
      "name": "sweep 121 independently closed normalized tau",
      "passed": true,
      "absolute_error": 2.220446049250313e-16,
      "scaled_error": 2.220446049250313e-16,
      "tolerance": 4e-12
    },
    {
      "name": "sweep 121 conserved R+T",
      "passed": true,
      "absolute_error": 2.220446049250313e-16,
      "scaled_error": 2.220446049250313e-16,
      "tolerance": 4e-12
    },
    {
      "name": "sweep 121 nonnegative bounded R,T",
      "passed": true
    },
    {
      "name": "sweep 121 left current at -3.1",
      "passed": true,
      "absolute_error": 1.1102230246251565e-16,
      "scaled_error": 1.1102230246251565e-16,
      "tolerance": 4e-12
    },
    {
      "name": "sweep 121 left current at -0.73",
      "passed": true,
      "absolute_error": 0.0,
      "scaled_error": 0.0,
      "tolerance": 4e-12
    },
    {
      "name": "sweep 121 left current at -0.01",
      "passed": true,
      "absolute_error": 1.1102230246251565e-16,
      "scaled_error": 1.1102230246251565e-16,
      "tolerance": 4e-12
    },
    {
      "name": "sweep 121 right current at 0.01",
      "passed": true,
      "absolute_error": 0.0,
      "scaled_error": 0.0,
      "tolerance": 4e-12
    },
    {
      "name": "sweep 121 right current at 0.73",
      "passed": true,
      "absolute_error": 1.1102230246251565e-16,
      "scaled_error": 1.1102230246251565e-16,
      "tolerance": 4e-12
    },
    {
      "name": "sweep 121 right current at 3.1",
      "passed": true,
      "absolute_error": 1.1102230246251565e-16,
      "scaled_error": 1.1102230246251565e-16,
      "tolerance": 4e-12
    },
    {
      "name": "sweep 121 two-port S unitarity",
      "passed": true,
      "absolute_error": 2.0721691699645897e-16,
      "scaled_error": 1.4652448718476607e-16,
      "tolerance": 4e-12
    },
    {
      "name": "sweep 121 two-port left-incident column",
      "passed": true,
      "absolute_error": 0.0,
      "scaled_error": 0.0,
      "tolerance": 4e-12
    },
    {
      "name": "sweep 122 continuity",
      "passed": true,
      "absolute_error": 1.1102230246251565e-16,
      "scaled_error": 1.1102230246251565e-16,
      "tolerance": 4e-12
    },
    {
      "name": "sweep 122 incident current",
      "passed": true,
      "absolute_error": 0.0,
      "scaled_error": 0.0,
      "tolerance": 4e-12
    },
    {
      "name": "sweep 122 reflected unit-mode current",
      "passed": true,
      "absolute_error": 0.0,
      "scaled_error": 0.0,
      "tolerance": 4e-12
    },
    {
      "name": "sweep 122 outgoing or gap current",
      "passed": true,
      "absolute_error": 0.0,
      "scaled_error": 0.0,
      "tolerance": 4e-12
    },
    {
      "name": "sweep 122 incident eigen-equation",
      "passed": true,
      "absolute_error": 1.1102230246251565e-16,
      "scaled_error": 5.958081967793454e-17,
      "tolerance": 4e-12
    },
    {
      "name": "sweep 122 incident positive density",
      "passed": true
    },
    {
      "name": "sweep 122 incident current/group-velocity ratio",
      "passed": true,
      "absolute_error": 0.0,
      "scaled_error": 0.0,
      "tolerance": 4e-12
    },
    {
      "name": "sweep 122 incident independent eigensolver projector",
      "passed": true,
      "absolute_error": 0.0,
      "scaled_error": 0.0,
      "tolerance": 4e-12
    },
    {
      "name": "sweep 122 reflected eigen-equation",
      "passed": true,
      "absolute_error": 1.1102230246251565e-16,
      "scaled_error": 5.958081967793454e-17,
      "tolerance": 4e-12
    },
    {
      "name": "sweep 122 reflected positive density",
      "passed": true
    },
    {
      "name": "sweep 122 reflected current/group-velocity ratio",
      "passed": true,
      "absolute_error": 0.0,
      "scaled_error": 0.0,
      "tolerance": 4e-12
    },
    {
      "name": "sweep 122 reflected independent eigensolver projector",
      "passed": true,
      "absolute_error": 0.0,
      "scaled_error": 0.0,
      "tolerance": 4e-12
    },
    {
      "name": "sweep 122 right eigen-equation",
      "passed": true,
      "absolute_error": 8.881784197001252e-16,
      "scaled_error": 2.021791836905788e-16,
      "tolerance": 4e-12
    },
    {
      "name": "sweep 122 right positive density",
      "passed": true
    },
    {
      "name": "sweep 122 right current/group-velocity ratio",
      "passed": true,
      "absolute_error": 1.1102230246251565e-16,
      "scaled_error": 1.1102230246251565e-16,
      "tolerance": 4e-12
    },
    {
      "name": "sweep 122 right independent eigensolver projector",
      "passed": true,
      "absolute_error": 1.9229626863835638e-16,
      "scaled_error": 1.9229626863835638e-16,
      "tolerance": 4e-12
    },
    {
      "name": "sweep 122 independently closed r",
      "passed": true,
      "absolute_error": 5.551115123125783e-17,
      "scaled_error": 5.551115123125783e-17,
      "tolerance": 4e-12
    },
    {
      "name": "sweep 122 independently closed normalized tau",
      "passed": true,
      "absolute_error": 1.1102230246251565e-16,
      "scaled_error": 1.1102230246251565e-16,
      "tolerance": 4e-12
    },
    {
      "name": "sweep 122 conserved R+T",
      "passed": true,
      "absolute_error": 2.220446049250313e-16,
      "scaled_error": 2.220446049250313e-16,
      "tolerance": 4e-12
    },
    {
      "name": "sweep 122 nonnegative bounded R,T",
      "passed": true
    },
    {
      "name": "sweep 122 left current at -3.1",
      "passed": true,
      "absolute_error": 1.1102230246251565e-16,
      "scaled_error": 1.1102230246251565e-16,
      "tolerance": 4e-12
    },
    {
      "name": "sweep 122 left current at -0.73",
      "passed": true,
      "absolute_error": 1.1102230246251565e-16,
      "scaled_error": 1.1102230246251565e-16,
      "tolerance": 4e-12
    },
    {
      "name": "sweep 122 left current at -0.01",
      "passed": true,
      "absolute_error": 1.1102230246251565e-16,
      "scaled_error": 1.1102230246251565e-16,
      "tolerance": 4e-12
    },
    {
      "name": "sweep 122 right current at 0.01",
      "passed": true,
      "absolute_error": 1.1102230246251565e-16,
      "scaled_error": 1.1102230246251565e-16,
      "tolerance": 4e-12
    },
    {
      "name": "sweep 122 right current at 0.73",
      "passed": true,
      "absolute_error": 1.1102230246251565e-16,
      "scaled_error": 1.1102230246251565e-16,
      "tolerance": 4e-12
    },
    {
      "name": "sweep 122 right current at 3.1",
      "passed": true,
      "absolute_error": 0.0,
      "scaled_error": 0.0,
      "tolerance": 4e-12
    },
    {
      "name": "sweep 122 two-port S unitarity",
      "passed": true,
      "absolute_error": 3.5966108838969386e-16,
      "scaled_error": 2.543187945292868e-16,
      "tolerance": 4e-12
    },
    {
      "name": "sweep 122 two-port left-incident column",
      "passed": true,
      "absolute_error": 0.0,
      "scaled_error": 0.0,
      "tolerance": 4e-12
    }
  ],
  "interpretation": [
    "Natural units hbar=c=1; V is potential energy; fixed spin at normal incidence.",
    "Real asymptotic modes have unit absolute Dirac probability current; gap mode has unit interface density.",
    "The right outgoing negative-energy mode has negative momentum and positive current/group velocity.",
    "R+T=1 is a positive Dirac probability-current balance, not the scalar signed KG-current convention.",
    "These stationary one-body coefficients do not count produced pairs or specify a vacuum.",
    "Threshold rows are explicitly excluded because unit-flux normalization is singular there.",
    "Profiles are exact stationary solutions sampled on x; no mesh or propagation-step error is implied.",
    "Finite-difference dx refinement diagnoses the stationary derivative away from the discontinuous interface.",
    "The separate NR study holds physical mass, kinetic energy and potential fixed as c increases.",
    "An abrupt semi-infinite step does not model a smooth field, finite barrier or dynamical source."
  ],
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    "limits": "/data/relativistic-qm/klein-paradox/limits.csv",
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    "summary": "/data/relativistic-qm/klein-paradox/summary.json"
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    "normalization": "Absolute output locations replaced by site download paths; numerical results and CSV bytes unchanged.",
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