{
  "canonical_lesson_id": "AN04-U050",
  "identity_basis": "All 45 original source-hash-bound private coverage atoms identify AN04-U050-private.",
  "all_original_targets": 45,
  "targets": [
    {
      "original_id": "AN04-U050-T001",
      "original_target": "Complete scalar mixed-problem hypotheses",
      "current_proofs": [
        "DC:T001"
      ],
      "disposition": "Complete independently written proof at the original all-real-order supported mixed Dirichlet scope, with exact current programme providers."
    },
    {
      "original_id": "AN04-U050-T002",
      "original_target": "Strict quadratic discriminant and Lorentz signature",
      "current_proofs": [
        "DC:T002"
      ],
      "disposition": "Complete independently written proof at the original all-real-order supported mixed Dirichlet scope, with exact current programme providers."
    },
    {
      "original_id": "AN04-U050-T003",
      "original_target": "Boundary transversality and tangent timelike vector",
      "current_proofs": [
        "DC:T003"
      ],
      "disposition": "Complete independently written proof at the original all-real-order supported mixed Dirichlet scope, with exact current programme providers."
    },
    {
      "original_id": "AN04-U050-T004",
      "original_target": "Global boundary-tangent temporal vector field",
      "current_proofs": [
        "DC:T004"
      ],
      "disposition": "Complete independently written proof at the original all-real-order supported mixed Dirichlet scope, with exact current programme providers."
    },
    {
      "original_id": "AN04-U050-T005",
      "original_target": "Local smooth flow with all parameter derivatives",
      "current_proofs": [
        "DC:T005"
      ],
      "disposition": "Complete independently written proof at the original all-real-order supported mixed Dirichlet scope, with exact current programme providers."
    },
    {
      "original_id": "AN04-U050-T006",
      "original_target": "Compact continuation and boundary-preserving product collars",
      "current_proofs": [
        "DC:T006"
      ],
      "disposition": "Complete independently written proof at the original all-real-order supported mixed Dirichlet scope, with exact current programme providers."
    },
    {
      "original_id": "AN04-U050-T007",
      "original_target": "Full Sobolev Dirichlet and zero-past theorem",
      "current_proofs": [
        "DC:T007"
      ],
      "disposition": "Complete independently written proof at the original all-real-order supported mixed Dirichlet scope, with exact current programme providers."
    },
    {
      "original_id": "AN04-U050-T008",
      "original_target": "Positive Lorentz flux and its exact converse",
      "current_proofs": [
        "DC:T008"
      ],
      "disposition": "Complete independently written proof at the original all-real-order supported mixed Dirichlet scope, with exact current programme providers."
    },
    {
      "original_id": "AN04-U050-T009",
      "original_target": "Differential operator sign and normalized model",
      "current_proofs": [
        "DC:T009"
      ],
      "disposition": "Complete independently written proof at the original all-real-order supported mixed Dirichlet scope, with exact current programme providers."
    },
    {
      "original_id": "AN04-U050-T010",
      "original_target": "Uniform inward timelike multiplier",
      "current_proofs": [
        "DC:T010"
      ],
      "disposition": "Complete independently written proof at the original all-real-order supported mixed Dirichlet scope, with exact current programme providers."
    },
    {
      "original_id": "AN04-U050-T011",
      "original_target": "Exact complex current and lower-order remainder",
      "current_proofs": [
        "DC:T011"
      ],
      "disposition": "Complete independently written proof at the original all-real-order supported mixed Dirichlet scope, with exact current programme providers."
    },
    {
      "original_id": "AN04-U050-T012",
      "original_target": "Temporal and artificial spacelike flux coercivity",
      "current_proofs": [
        "DC:T012"
      ],
      "disposition": "Complete independently written proof at the original all-real-order supported mixed Dirichlet scope, with exact current programme providers."
    },
    {
      "original_id": "AN04-U050-T013",
      "original_target": "Outward Dirichlet flux and free normal derivative",
      "current_proofs": [
        "DC:T013"
      ],
      "disposition": "Complete independently written proof at the original all-real-order supported mixed Dirichlet scope, with exact current programme providers."
    },
    {
      "original_id": "AN04-U050-T014",
      "original_target": "Weighted volume, terminal and boundary energy",
      "current_proofs": [
        "DC:T014"
      ],
      "disposition": "Complete independently written proof at the original all-real-order supported mixed Dirichlet scope, with exact current programme providers."
    },
    {
      "original_id": "AN04-U050-T015",
      "original_target": "Reverse-time inward multiplier and small-time scale",
      "current_proofs": [
        "DC:T015"
      ],
      "disposition": "Complete independently written proof at the original all-real-order supported mixed Dirichlet scope, with exact current programme providers."
    },
    {
      "original_id": "AN04-U050-T016",
      "original_target": "Retarded smoothing and all normal orders",
      "current_proofs": [
        "DC:T016"
      ],
      "disposition": "Complete independently written proof at the original all-real-order supported mixed Dirichlet scope, with exact current programme providers."
    },
    {
      "original_id": "AN04-U050-T017",
      "original_target": "Full Friedrichs commutator with correct coefficient sign",
      "current_proofs": [
        "DC:T017"
      ],
      "disposition": "Complete independently written proof at the original all-real-order supported mixed Dirichlet scope, with exact current programme providers."
    },
    {
      "original_id": "AN04-U050-T018",
      "original_target": "Rough uniqueness without second-derivative assumptions",
      "current_proofs": [
        "DC:T018"
      ],
      "disposition": "Complete independently written proof at the original all-real-order supported mixed Dirichlet scope, with exact current programme providers."
    },
    {
      "original_id": "AN04-U050-T019",
      "original_target": "One-sided complex powers and exact antidual",
      "current_proofs": [
        "DC:T019"
      ],
      "disposition": "Complete independently written proof at the original all-real-order supported mixed Dirichlet scope, with exact current programme providers."
    },
    {
      "original_id": "AN04-U050-T020",
      "original_target": "Isotropic symbol distinction and exact multiplier difference",
      "current_proofs": [
        "DC:T020"
      ],
      "disposition": "Complete independently written proof at the original all-real-order supported mixed Dirichlet scope, with exact current programme providers."
    },
    {
      "original_id": "AN04-U050-T021",
      "original_target": "Exact Fourier kernel and two Schur marginals",
      "current_proofs": [
        "DC:T021"
      ],
      "disposition": "Complete independently written proof at the original all-real-order supported mixed Dirichlet scope, with exact current programme providers."
    },
    {
      "original_id": "AN04-U050-T022",
      "original_target": "Full commutator representation on actual derivatives",
      "current_proofs": [
        "DC:T022"
      ],
      "disposition": "Complete independently written proof at the original all-real-order supported mixed Dirichlet scope, with exact current programme providers."
    },
    {
      "original_id": "AN04-U050-T023",
      "original_target": "Causal restriction and legitimate zero extension",
      "current_proofs": [
        "DC:T023"
      ],
      "disposition": "Complete independently written proof at the original all-real-order supported mixed Dirichlet scope, with exact current programme providers."
    },
    {
      "original_id": "AN04-U050-T024",
      "original_target": "All-real adjoint estimate with order-dependent time bound",
      "current_proofs": [
        "DC:T024"
      ],
      "disposition": "Complete independently written proof at the original all-real-order supported mixed Dirichlet scope, with exact current programme providers."
    },
    {
      "original_id": "AN04-U050-T025",
      "original_target": "Forcing as a supported tangential Hilbert input",
      "current_proofs": [
        "DC:T025"
      ],
      "disposition": "Complete independently written proof at the original all-real-order supported mixed Dirichlet scope, with exact current programme providers."
    },
    {
      "original_id": "AN04-U050-T026",
      "original_target": "Weak boundary functional and positive Green sign",
      "current_proofs": [
        "DC:T026"
      ],
      "disposition": "Complete independently written proof at the original all-real-order supported mixed Dirichlet scope, with exact current programme providers."
    },
    {
      "original_id": "AN04-U050-T027",
      "original_target": "Bound on an arbitrary image and complex extension",
      "current_proofs": [
        "DC:T027"
      ],
      "disposition": "Complete independently written proof at the original all-real-order supported mixed Dirichlet scope, with exact current programme providers."
    },
    {
      "original_id": "AN04-U050-T028",
      "original_target": "One global Hilbert representation and initial support",
      "current_proofs": [
        "DC:T028"
      ],
      "disposition": "Complete independently written proof at the original all-real-order supported mixed Dirichlet scope, with exact current programme providers."
    },
    {
      "original_id": "AN04-U050-T029",
      "original_target": "Three normal-recovery inequalities and full isotropic order",
      "current_proofs": [
        "DC:T029"
      ],
      "disposition": "Complete independently written proof at the original all-real-order supported mixed Dirichlet scope, with exact current programme providers."
    },
    {
      "original_id": "AN04-U050-T030",
      "original_target": "Weak Green identity justified at H1 regularity",
      "current_proofs": [
        "DC:T030"
      ],
      "disposition": "Complete independently written proof at the original all-real-order supported mixed Dirichlet scope, with exact current programme providers."
    },
    {
      "original_id": "AN04-U050-T031",
      "original_target": "Actual Dirichlet trace from arbitrary boundary tests",
      "current_proofs": [
        "DC:T031"
      ],
      "disposition": "Complete independently written proof at the original all-real-order supported mixed Dirichlet scope, with exact current programme providers."
    },
    {
      "original_id": "AN04-U050-T032",
      "original_target": "Shrinking-ball causal region and positive artificial faces",
      "current_proofs": [
        "DC:T032"
      ],
      "disposition": "Complete independently written proof at the original all-real-order supported mixed Dirichlet scope, with exact current programme providers."
    },
    {
      "original_id": "AN04-U050-T033",
      "original_target": "Domain of dependence for rough constructed solutions",
      "current_proofs": [
        "DC:T033"
      ],
      "disposition": "Complete independently written proof at the original all-real-order supported mixed Dirichlet scope, with exact current programme providers."
    },
    {
      "original_id": "AN04-U050-T034",
      "original_target": "Boundary bowl coordinates and legitimate global model",
      "current_proofs": [
        "DC:T034"
      ],
      "disposition": "Complete independently written proof at the original all-real-order supported mixed Dirichlet scope, with exact current programme providers."
    },
    {
      "original_id": "AN04-U050-T035",
      "original_target": "Local supported existence for the original curved time",
      "current_proofs": [
        "DC:T035"
      ],
      "disposition": "Complete independently written proof at the original all-real-order supported mixed Dirichlet scope, with exact current programme providers."
    },
    {
      "original_id": "AN04-U050-T036",
      "original_target": "One-sided local uniqueness and exact interior provider",
      "current_proofs": [
        "DC:T036"
      ],
      "disposition": "Complete independently written proof at the original all-real-order supported mixed Dirichlet scope, with exact current programme providers."
    },
    {
      "original_id": "AN04-U050-T037",
      "original_target": "Compatible finite level-set cover and overlap equality",
      "current_proofs": [
        "DC:T037"
      ],
      "disposition": "Complete independently written proof at the original all-real-order supported mixed Dirichlet scope, with exact current programme providers."
    },
    {
      "original_id": "AN04-U050-T038",
      "original_target": "Residual correction in the original P equation",
      "current_proofs": [
        "DC:T038"
      ],
      "disposition": "Complete independently written proof at the original all-real-order supported mixed Dirichlet scope, with exact current programme providers."
    },
    {
      "original_id": "AN04-U050-T039",
      "original_target": "Uniform finite-band width on each compact start interval",
      "current_proofs": [
        "DC:T039"
      ],
      "disposition": "Complete independently written proof at the original all-real-order supported mixed Dirichlet scope, with exact current programme providers."
    },
    {
      "original_id": "AN04-U050-T040",
      "original_target": "Locally finite global solution and uniqueness",
      "current_proofs": [
        "DC:T040"
      ],
      "disposition": "Complete independently written proof at the original all-real-order supported mixed Dirichlet scope, with exact current programme providers."
    },
    {
      "original_id": "AN04-U050-T041",
      "original_target": "Flat inward multiplier and both strict margins",
      "current_proofs": [
        "DC:T041"
      ],
      "disposition": "Complete independently written proof at the original all-real-order supported mixed Dirichlet scope, with exact current programme providers."
    },
    {
      "original_id": "AN04-U050-T042",
      "original_target": "Exact incoming Dirichlet wave and full local regularity",
      "current_proofs": [
        "DC:T042"
      ],
      "disposition": "Complete independently written proof at the original all-real-order supported mixed Dirichlet scope, with exact current programme providers."
    },
    {
      "original_id": "AN04-U050-T043",
      "original_target": "Boundary exponent is not the ordinary trace target",
      "current_proofs": [
        "DC:T043"
      ],
      "disposition": "Complete independently written proof at the original all-real-order supported mixed Dirichlet scope, with exact current programme providers."
    },
    {
      "original_id": "AN04-U050-T044",
      "original_target": "Moving wall, normalized metric and characteristic limit",
      "current_proofs": [
        "DC:T044"
      ],
      "disposition": "Complete independently written proof at the original all-real-order supported mixed Dirichlet scope, with exact current programme providers."
    },
    {
      "original_id": "AN04-U050-T045",
      "original_target": "Precise source, licence and remaining boundary scope",
      "current_proofs": [
        "DC:T045"
      ],
      "disposition": "Complete independently written proof at the original all-real-order supported mixed Dirichlet scope, with exact current programme providers."
    }
  ],
  "all_original_solutions_preserved": true,
  "full_course_complete": false
}