{
  "canonical_lesson_id": "AN04-U049",
  "identity_basis": "All 53 original source-hash-bound private coverage atoms identify AN04-U049-private.",
  "all_original_targets": 53,
  "targets": [
    {
      "original_id": "AN04-U049-S001",
      "original_target": "Full ordinary symbol and all-time parameter hypotheses",
      "current_proofs": [
        "SM:R001"
      ],
      "disposition": "Complete independently written proof at the original global positive-metric and local separated-trajectory scope, with exact current programme providers."
    },
    {
      "original_id": "AN04-U049-S002",
      "original_target": "Uniform positive principal metric",
      "current_proofs": [
        "SM:R002"
      ],
      "disposition": "Complete independently written proof at the original global positive-metric and local separated-trajectory scope, with exact current programme providers."
    },
    {
      "original_id": "AN04-U049-S003",
      "original_target": "Both time directions and integrable forcing",
      "current_proofs": [
        "SM:R003"
      ],
      "disposition": "Complete independently written proof at the original global positive-metric and local separated-trajectory scope, with exact current programme providers."
    },
    {
      "original_id": "AN04-U049-S004",
      "original_target": "Gap-free energy versus separated kernel scope",
      "current_proofs": [
        "SM:R004"
      ],
      "disposition": "Complete independently written proof at the original global positive-metric and local separated-trajectory scope, with exact current programme providers."
    },
    {
      "original_id": "AN04-U049-S005",
      "original_target": "Low-frequency convex metric extension",
      "current_proofs": [
        "SM:R005"
      ],
      "disposition": "Complete independently written proof at the original global positive-metric and local separated-trajectory scope, with exact current programme providers."
    },
    {
      "original_id": "AN04-U049-S006",
      "original_target": "Scalar binomial coefficients and matrix root",
      "current_proofs": [
        "SM:R006"
      ],
      "disposition": "Complete independently written proof at the original global positive-metric and local separated-trajectory scope, with exact current programme providers."
    },
    {
      "original_id": "AN04-U049-S007",
      "original_target": "Every differentiated root seminorm",
      "current_proofs": [
        "SM:R007"
      ],
      "disposition": "Complete independently written proof at the original global positive-metric and local separated-trajectory scope, with exact current programme providers."
    },
    {
      "original_id": "AN04-U049-S008",
      "original_target": "Homogeneous principal metric distinguished from its extension",
      "current_proofs": [
        "SM:R008"
      ],
      "disposition": "Complete independently written proof at the original global positive-metric and local separated-trajectory scope, with exact current programme providers."
    },
    {
      "original_id": "AN04-U049-S009",
      "original_target": "Pointwise metric and real diagonalizability equivalence",
      "current_proofs": [
        "SM:R009"
      ],
      "disposition": "Complete independently written proof at the original global positive-metric and local separated-trajectory scope, with exact current programme providers."
    },
    {
      "original_id": "AN04-U049-S010",
      "original_target": "Sobolev conjugation changes only order zero",
      "current_proofs": [
        "SM:R010"
      ],
      "disposition": "Complete independently written proof at the original global positive-metric and local separated-trajectory scope, with exact current programme providers."
    },
    {
      "original_id": "AN04-U049-S011",
      "original_target": "Quantized principal energy cancellation",
      "current_proofs": [
        "SM:R011"
      ],
      "disposition": "Complete independently written proof at the original global positive-metric and local separated-trajectory scope, with exact current programme providers."
    },
    {
      "original_id": "AN04-U049-S012",
      "original_target": "Coercivity from an approximate inverse",
      "current_proofs": [
        "SM:R012"
      ],
      "disposition": "Complete independently written proof at the original global positive-metric and local separated-trajectory scope, with exact current programme providers."
    },
    {
      "original_id": "AN04-U049-S013",
      "original_target": "Equivalent corrected Sobolev energy",
      "current_proofs": [
        "SM:R013"
      ],
      "disposition": "Complete independently written proof at the original global positive-metric and local separated-trajectory scope, with exact current programme providers."
    },
    {
      "original_id": "AN04-U049-S014",
      "original_target": "Complete energy derivative",
      "current_proofs": [
        "SM:R014"
      ],
      "disposition": "Complete independently written proof at the original global positive-metric and local separated-trajectory scope, with exact current programme providers."
    },
    {
      "original_id": "AN04-U049-S015",
      "original_target": "Scalar inequality, zero energy and time reversal",
      "current_proofs": [
        "SM:R015"
      ],
      "disposition": "Complete independently written proof at the original global positive-metric and local separated-trajectory scope, with exact current programme providers."
    },
    {
      "original_id": "AN04-U049-S016",
      "original_target": "Uniform scalar Fourier regularizers",
      "current_proofs": [
        "SM:R016"
      ],
      "disposition": "Complete independently written proof at the original global positive-metric and local separated-trajectory scope, with exact current programme providers."
    },
    {
      "original_id": "AN04-U049-S017",
      "original_target": "Bounded regularized ODE in every Sobolev space",
      "current_proofs": [
        "SM:R017"
      ],
      "disposition": "Complete independently written proof at the original global positive-metric and local separated-trajectory scope, with exact current programme providers."
    },
    {
      "original_id": "AN04-U049-S018",
      "original_target": "Uniform energy for regularized operators",
      "current_proofs": [
        "SM:R018"
      ],
      "disposition": "Complete independently written proof at the original global positive-metric and local separated-trajectory scope, with exact current programme providers."
    },
    {
      "original_id": "AN04-U049-S019",
      "original_target": "Order-losing convergence estimate",
      "current_proofs": [
        "SM:R019"
      ],
      "disposition": "Complete independently written proof at the original global positive-metric and local separated-trajectory scope, with exact current programme providers."
    },
    {
      "original_id": "AN04-U049-S020",
      "original_target": "Strong convergence of smooth-data solutions",
      "current_proofs": [
        "SM:R020"
      ],
      "disposition": "Complete independently written proof at the original global positive-metric and local separated-trajectory scope, with exact current programme providers."
    },
    {
      "original_id": "AN04-U049-S021",
      "original_target": "Data and Bochner forcing approximation",
      "current_proofs": [
        "SM:R021"
      ],
      "disposition": "Complete independently written proof at the original global positive-metric and local separated-trajectory scope, with exact current programme providers."
    },
    {
      "original_id": "AN04-U049-S022",
      "original_target": "Commutator convergence uniformly in time",
      "current_proofs": [
        "SM:R022"
      ],
      "disposition": "Complete independently written proof at the original global positive-metric and local separated-trajectory scope, with exact current programme providers."
    },
    {
      "original_id": "AN04-U049-S023",
      "original_target": "Energy and uniqueness for every rough solution",
      "current_proofs": [
        "SM:R023"
      ],
      "disposition": "Complete independently written proof at the original global positive-metric and local separated-trajectory scope, with exact current programme providers."
    },
    {
      "original_id": "AN04-U049-S024",
      "original_target": "Evolution composition and invertibility",
      "current_proofs": [
        "SM:R024"
      ],
      "disposition": "Complete independently written proof at the original global positive-metric and local separated-trajectory scope, with exact current programme providers."
    },
    {
      "original_id": "AN04-U049-S025",
      "original_target": "Joint strong endpoint continuity",
      "current_proofs": [
        "SM:R025"
      ],
      "disposition": "Complete independently written proof at the original global positive-metric and local separated-trajectory scope, with exact current programme providers."
    },
    {
      "original_id": "AN04-U049-S026",
      "original_target": "Both ordered endpoint derivatives",
      "current_proofs": [
        "SM:R026"
      ],
      "disposition": "Complete independently written proof at the original global positive-metric and local separated-trajectory scope, with exact current programme providers."
    },
    {
      "original_id": "AN04-U049-S027",
      "original_target": "Oriented forcing integral",
      "current_proofs": [
        "SM:R027"
      ],
      "disposition": "Complete independently written proof at the original global positive-metric and local separated-trajectory scope, with exact current programme providers."
    },
    {
      "original_id": "AN04-U049-S028",
      "original_target": "Full parameter-aware two-sided inverse",
      "current_proofs": [
        "SM:R028"
      ],
      "disposition": "Complete independently written proof at the original global positive-metric and local separated-trajectory scope, with exact current programme providers."
    },
    {
      "original_id": "AN04-U049-S029",
      "original_target": "Spatial intertwining with a Hermitian principal part",
      "current_proofs": [
        "SM:R029"
      ],
      "disposition": "Complete independently written proof at the original global positive-metric and local separated-trajectory scope, with exact current programme providers."
    },
    {
      "original_id": "AN04-U049-S030",
      "original_target": "Ordered inverse first correction",
      "current_proofs": [
        "SM:R030"
      ],
      "disposition": "Complete independently written proof at the original global positive-metric and local separated-trajectory scope, with exact current programme providers."
    },
    {
      "original_id": "AN04-U049-S031",
      "original_target": "Complete order-zero transformed coefficient",
      "current_proofs": [
        "SM:R031"
      ],
      "disposition": "Complete independently written proof at the original global positive-metric and local separated-trajectory scope, with exact current programme providers."
    },
    {
      "original_id": "AN04-U049-S032",
      "original_target": "Ordinary remainder and time-coefficient qualification",
      "current_proofs": [
        "SM:R032"
      ],
      "disposition": "Complete independently written proof at the original global positive-metric and local separated-trajectory scope, with exact current programme providers."
    },
    {
      "original_id": "AN04-U049-S033",
      "original_target": "Separate equation and initial defects",
      "current_proofs": [
        "SM:R033"
      ],
      "disposition": "Complete independently written proof at the original global positive-metric and local separated-trajectory scope, with exact current programme providers."
    },
    {
      "original_id": "AN04-U049-S034",
      "original_target": "Actual-system Duhamel correction",
      "current_proofs": [
        "SM:R034"
      ],
      "disposition": "Complete independently written proof at the original global positive-metric and local separated-trajectory scope, with exact current programme providers."
    },
    {
      "original_id": "AN04-U049-S035",
      "original_target": "Joint smooth compact-input kernel",
      "current_proofs": [
        "SM:R035"
      ],
      "disposition": "Complete independently written proof at the original global positive-metric and local separated-trajectory scope, with exact current programme providers."
    },
    {
      "original_id": "AN04-U049-S036",
      "original_target": "Transformed input localization with full exterior tails",
      "current_proofs": [
        "SM:R036"
      ],
      "disposition": "Complete independently written proof at the original global positive-metric and local separated-trajectory scope, with exact current programme providers."
    },
    {
      "original_id": "AN04-U049-S037",
      "original_target": "Separated non-Hermitian branch kernels",
      "current_proofs": [
        "SM:R037"
      ],
      "disposition": "Complete independently written proof at the original global positive-metric and local separated-trajectory scope, with exact current programme providers."
    },
    {
      "original_id": "AN04-U049-S038",
      "original_target": "Nonorthogonal spectral metrics and full projectors",
      "current_proofs": [
        "SM:R038"
      ],
      "disposition": "Complete independently written proof at the original global positive-metric and local separated-trajectory scope, with exact current programme providers."
    },
    {
      "original_id": "AN04-U049-S039",
      "original_target": "Full projector identities and correct time sign",
      "current_proofs": [
        "SM:R039"
      ],
      "disposition": "Complete independently written proof at the original global positive-metric and local separated-trajectory scope, with exact current programme providers."
    },
    {
      "original_id": "AN04-U049-S040",
      "original_target": "Elliptic maps of original eigenbundles",
      "current_proofs": [
        "SM:R040"
      ],
      "disposition": "Complete independently written proof at the original global positive-metric and local separated-trajectory scope, with exact current programme providers."
    },
    {
      "original_id": "AN04-U049-S041",
      "original_target": "Exact full-matrix branch wavefront union",
      "current_proofs": [
        "SM:R041"
      ],
      "disposition": "Complete independently written proof at the original global positive-metric and local separated-trajectory scope, with exact current programme providers."
    },
    {
      "original_id": "AN04-U049-S042",
      "original_target": "Precisely localized projected data equivalence",
      "current_proofs": [
        "SM:R042"
      ],
      "disposition": "Complete independently written proof at the original global positive-metric and local separated-trajectory scope, with exact current programme providers."
    },
    {
      "original_id": "AN04-U049-S043",
      "original_target": "Necessary uniform projector bound",
      "current_proofs": [
        "SM:R043"
      ],
      "disposition": "Complete independently written proof at the original global positive-metric and local separated-trajectory scope, with exact current programme providers."
    },
    {
      "original_id": "AN04-U049-S044",
      "original_target": "Stable nonnormal resolvent contours",
      "current_proofs": [
        "SM:R044"
      ],
      "disposition": "Complete independently written proof at the original global positive-metric and local separated-trajectory scope, with exact current programme providers."
    },
    {
      "original_id": "AN04-U049-S045",
      "original_target": "All differentiated nonorthogonal projectors",
      "current_proofs": [
        "SM:R045"
      ],
      "disposition": "Complete independently written proof at the original global positive-metric and local separated-trajectory scope, with exact current programme providers."
    },
    {
      "original_id": "AN04-U049-S046",
      "original_target": "Global metric without a global frame",
      "current_proofs": [
        "SM:R046"
      ],
      "disposition": "Complete independently written proof at the original global positive-metric and local separated-trajectory scope, with exact current programme providers."
    },
    {
      "original_id": "AN04-U049-S047",
      "original_target": "Pointwise, uniform and crossing distinctions",
      "current_proofs": [
        "SM:R047"
      ],
      "disposition": "Complete independently written proof at the original global positive-metric and local separated-trajectory scope, with exact current programme providers."
    },
    {
      "original_id": "AN04-U049-S048",
      "original_target": "Sheared square root and nonorthogonal eigenvectors",
      "current_proofs": [
        "SM:R048"
      ],
      "disposition": "Complete independently written proof at the original global positive-metric and local separated-trajectory scope, with exact current programme providers."
    },
    {
      "original_id": "AN04-U049-S049",
      "original_target": "Exact component-energy ellipse",
      "current_proofs": [
        "SM:R049"
      ],
      "disposition": "Complete independently written proof at the original global positive-metric and local separated-trajectory scope, with exact current programme providers."
    },
    {
      "original_id": "AN04-U049-S050",
      "original_target": "Changing frame exact Cauchy kernel",
      "current_proofs": [
        "SM:R050"
      ],
      "disposition": "Complete independently written proof at the original global positive-metric and local separated-trajectory scope, with exact current programme providers."
    },
    {
      "original_id": "AN04-U049-S051",
      "original_target": "Uniform-condition failure at a closing gap",
      "current_proofs": [
        "SM:R051"
      ],
      "disposition": "Complete independently written proof at the original global positive-metric and local separated-trajectory scope, with exact current programme providers."
    },
    {
      "original_id": "AN04-U049-S052",
      "original_target": "Jordan roots and sharp derivative loss",
      "current_proofs": [
        "SM:R052"
      ],
      "disposition": "Complete independently written proof at the original global positive-metric and local separated-trajectory scope, with exact current programme providers."
    },
    {
      "original_id": "AN04-U049-S053",
      "original_target": "Frequency metric with no constant replacement",
      "current_proofs": [
        "SM:R053"
      ],
      "disposition": "Complete independently written proof at the original global positive-metric and local separated-trajectory scope, with exact current programme providers."
    }
  ],
  "all_original_solutions_preserved": true,
  "full_course_complete": false
}