{
  "canonical_lesson_id": "AN04-U047",
  "all_original_targets": 43,
  "targets": [
    {
      "original_id": "AN04-FIO-CAUCHY-001",
      "original_target": "Scalar homogeneous principal direction, arbitrary finite-matrix ordinary lower symbol, uniform time families and all-real Sobolev scale",
      "current_proofs": [
        "EC:H0",
        "EC:F0"
      ],
      "disposition": "Complete written proof at the original scalar-principal finite-matrix scope; exact current earlier providers and receiving arguments checked."
    },
    {
      "original_id": "AN04-FIO-CAUCHY-002",
      "original_target": "Two-sided Hermitian energy criterion, group law and uniform finite-time Sobolev bound",
      "current_proofs": [
        "EC:H1"
      ],
      "disposition": "Complete written proof at the original scalar-principal finite-matrix scope; exact current earlier providers and receiving arguments checked."
    },
    {
      "original_id": "AN04-FIO-CAUCHY-003",
      "original_target": "Oriented initial-time difference quotient and distinct left/right coefficient derivatives",
      "current_proofs": [
        "EC:H2"
      ],
      "disposition": "Complete written proof at the original scalar-principal finite-matrix scope; exact current earlier providers and receiving arguments checked."
    },
    {
      "original_id": "AN04-FIO-CAUCHY-004",
      "original_target": "Joint parameter derivatives with finite spatial-order loss and continuity of ordered products",
      "current_proofs": [
        "EC:H3",
        "EC:H4"
      ],
      "disposition": "Complete written proof at the original scalar-principal finite-matrix scope; exact current earlier providers and receiving arguments checked."
    },
    {
      "original_id": "AN04-FIO-CAUCHY-005",
      "original_target": "Global finite-time Hamilton flow by finite velocity, covector Gronwall and endpoint continuation",
      "current_proofs": [
        "EC:F1"
      ],
      "disposition": "Complete written proof at the original scalar-principal finite-matrix scope; exact current earlier providers and receiving arguments checked."
    },
    {
      "original_id": "AN04-FIO-CAUCHY-006",
      "original_target": "Homogeneity and uniform normalized flow derivatives including inverse flow",
      "current_proofs": [
        "EC:F3"
      ],
      "disposition": "Complete written proof at the original scalar-principal finite-matrix scope; exact current earlier providers and receiving arguments checked."
    },
    {
      "original_id": "AN04-FIO-CAUCHY-007",
      "original_target": "Uniform short-time derivative bound and one interval for every base point and unit covector",
      "current_proofs": [
        "EC:F4"
      ],
      "disposition": "Complete written proof at the original scalar-principal finite-matrix scope; exact current earlier providers and receiving arguments checked."
    },
    {
      "original_id": "AN04-FIO-CAUCHY-008",
      "original_target": "Global mixed base inverse by contraction, smooth implicit parameters and positive determinant",
      "current_proofs": [
        "EC:F4"
      ],
      "disposition": "Complete written proof at the original scalar-principal finite-matrix scope; exact current earlier providers and receiving arguments checked."
    },
    {
      "original_id": "AN04-FIO-CAUCHY-009",
      "original_target": "Full action variation with both moving endpoints and exact initial-parameter sign",
      "current_proofs": [
        "EC:F5"
      ],
      "disposition": "Complete written proof at the original scalar-principal finite-matrix scope; exact current earlier providers and receiving arguments checked."
    },
    {
      "original_id": "AN04-FIO-CAUCHY-010",
      "original_target": "Hamilton-Jacobi equation, exact initial phase and mixed Hessian invertibility",
      "current_proofs": [
        "EC:F5"
      ],
      "disposition": "Complete written proof at the original scalar-principal finite-matrix scope; exact current earlier providers and receiving arguments checked."
    },
    {
      "original_id": "AN04-FIO-CAUCHY-011",
      "original_target": "Nondegenerate homogeneous phase and reflected input kernel covector",
      "current_proofs": [
        "EC:F6"
      ],
      "disposition": "Complete written proof at the original scalar-principal finite-matrix scope; exact current earlier providers and receiving arguments checked."
    },
    {
      "original_id": "AN04-FIO-CAUCHY-012",
      "original_target": "Full ordinary phase derivative bounds on compact sets and globally for the phase difference",
      "current_proofs": [
        "EC:F3",
        "EC:F6"
      ],
      "disposition": "Complete written proof at the original scalar-principal finite-matrix scope; exact current earlier providers and receiving arguments checked."
    },
    {
      "original_id": "AN04-FIO-CAUCHY-013",
      "original_target": "Uniform cutoff excludes bounded frequency without losing any unit covector direction",
      "current_proofs": [
        "EC:F0"
      ],
      "disposition": "Complete written proof at the original scalar-principal finite-matrix scope; exact current earlier providers and receiving arguments checked."
    },
    {
      "original_id": "AN04-FIO-CAUCHY-014",
      "original_target": "Proper compact-base matrix initial operator and explicit low-frequency initial defect",
      "current_proofs": [
        "EC:A0"
      ],
      "disposition": "Complete written proof at the original scalar-principal finite-matrix scope; exact current earlier providers and receiving arguments checked."
    },
    {
      "original_id": "AN04-FIO-CAUCHY-015",
      "original_target": "Full ordinary amplitude action and order-lowering residual operator",
      "current_proofs": [
        "EC:A1",
        "EC:A2",
        "EC:A3",
        "EC:A4"
      ],
      "disposition": "Complete written proof at the original scalar-principal finite-matrix scope; exact current earlier providers and receiving arguments checked."
    },
    {
      "original_id": "AN04-FIO-CAUCHY-016",
      "original_target": "Normalized stationary critical point, unit Hessian determinant and zero signature",
      "current_proofs": [
        "EC:A2"
      ],
      "disposition": "Complete written proof at the original scalar-principal finite-matrix scope; exact current earlier providers and receiving arguments checked."
    },
    {
      "original_id": "AN04-FIO-CAUCHY-017",
      "original_target": "Nonclassical radial/angular differentiated stationary remainder and all normalized tails",
      "current_proofs": [
        "EC:A2",
        "EC:A4"
      ],
      "disposition": "Complete written proof at the original scalar-principal finite-matrix scope; exact current earlier providers and receiving arguments checked."
    },
    {
      "original_id": "AN04-FIO-CAUCHY-018",
      "original_target": "Left-symbol transport sign and retained full ordinary matrix coefficient",
      "current_proofs": [
        "EC:A3"
      ],
      "disposition": "Complete written proof at the original scalar-principal finite-matrix scope; exact current earlier providers and receiving arguments checked."
    },
    {
      "original_id": "AN04-FIO-CAUCHY-019",
      "original_target": "Support-preserving differential residual representatives and summation",
      "current_proofs": [
        "EC:A5"
      ],
      "disposition": "Complete written proof at the original scalar-principal finite-matrix scope; exact current earlier providers and receiving arguments checked."
    },
    {
      "original_id": "AN04-FIO-CAUCHY-020",
      "original_target": "Positive Jacobian half density, trace correction and ordered matrix equation",
      "current_proofs": [
        "EC:D0"
      ],
      "disposition": "Complete written proof at the original scalar-principal finite-matrix scope; exact current earlier providers and receiving arguments checked."
    },
    {
      "original_id": "AN04-FIO-CAUCHY-021",
      "original_target": "Full differentiated symbol bounds for ordered transport and its actual inverse",
      "current_proofs": [
        "EC:D1"
      ],
      "disposition": "Complete written proof at the original scalar-principal finite-matrix scope; exact current earlier providers and receiving arguments checked."
    },
    {
      "original_id": "AN04-FIO-CAUCHY-022",
      "original_target": "Zero-initial-value full residual recursion with oriented integrals and one-order improvement",
      "current_proofs": [
        "EC:D2"
      ],
      "disposition": "Complete written proof at the original scalar-principal finite-matrix scope; exact current earlier providers and receiving arguments checked."
    },
    {
      "original_id": "AN04-FIO-CAUCHY-023",
      "original_target": "Parameter-independent cutoff radii and all-order ordinary amplitude sum",
      "current_proofs": [
        "EC:D3"
      ],
      "disposition": "Complete written proof at the original scalar-principal finite-matrix scope; exact current earlier providers and receiving arguments checked."
    },
    {
      "original_id": "AN04-FIO-CAUCHY-024",
      "original_target": "Compact physical localization, exact initial normalization and strong graph continuity",
      "current_proofs": [
        "EC:D4"
      ],
      "disposition": "Complete written proof at the original scalar-principal finite-matrix scope; exact current earlier providers and receiving arguments checked."
    },
    {
      "original_id": "AN04-FIO-CAUCHY-025",
      "original_target": "Exterior PDO decay, additional oscillatory gains and global-output Sobolev smoothing",
      "current_proofs": [
        "EC:D5",
        "EC:D6"
      ],
      "disposition": "Complete written proof at the original scalar-principal finite-matrix scope; exact current earlier providers and receiving arguments checked."
    },
    {
      "original_id": "AN04-FIO-CAUCHY-026",
      "original_target": "Precise residual and initial family hypotheses, including operator-norm smoothing parameters",
      "current_proofs": [
        "EC:C0"
      ],
      "disposition": "Complete written proof at the original scalar-principal finite-matrix scope; exact current earlier providers and receiving arguments checked."
    },
    {
      "original_id": "AN04-FIO-CAUCHY-027",
      "original_target": "Exact Duhamel correction with both initial and equation errors in both time orientations",
      "current_proofs": [
        "EC:C1",
        "EC:C2"
      ],
      "disposition": "Complete written proof at the original scalar-principal finite-matrix scope; exact current earlier providers and receiving arguments checked."
    },
    {
      "original_id": "AN04-FIO-CAUCHY-028",
      "original_target": "Compact distribution data have some finite negative global Sobolev order",
      "current_proofs": [
        "EC:C2"
      ],
      "disposition": "Complete written proof at the original scalar-principal finite-matrix scope; exact current earlier providers and receiving arguments checked."
    },
    {
      "original_id": "AN04-FIO-CAUCHY-029",
      "original_target": "Delta columns and every input derivative in sufficiently negative Sobolev order",
      "current_proofs": [
        "EC:C4"
      ],
      "disposition": "Complete written proof at the original scalar-principal finite-matrix scope; exact current earlier providers and receiving arguments checked."
    },
    {
      "original_id": "AN04-FIO-CAUCHY-030",
      "original_target": "Arbitrary output Sobolev order gives joint spatial kernel evaluation and regularity",
      "current_proofs": [
        "EC:C3",
        "EC:C4"
      ],
      "disposition": "Complete written proof at the original scalar-principal finite-matrix scope; exact current earlier providers and receiving arguments checked."
    },
    {
      "original_id": "AN04-FIO-CAUCHY-031",
      "original_target": "Bochner delta reconstruction establishes the actual distribution kernel",
      "current_proofs": [
        "EC:C5"
      ],
      "disposition": "Complete written proof at the original scalar-principal finite-matrix scope; exact current earlier providers and receiving arguments checked."
    },
    {
      "original_id": "AN04-FIO-CAUCHY-032",
      "original_target": "Every parameter derivative, both endpoint terms and joint smooth kernel",
      "current_proofs": [
        "EC:C6",
        "EC:C7"
      ],
      "disposition": "Complete written proof at the original scalar-principal finite-matrix scope; exact current earlier providers and receiving arguments checked."
    },
    {
      "original_id": "AN04-FIO-CAUCHY-033",
      "original_target": "Exact localized graph class and elliptic reduced ordinary matrix symbol with kernel sign",
      "current_proofs": [
        "EC:D7",
        "EC:G0"
      ],
      "disposition": "Complete written proof at the original scalar-principal finite-matrix scope; exact current earlier providers and receiving arguments checked."
    },
    {
      "original_id": "AN04-FIO-CAUCHY-034",
      "original_target": "Finite time partition and entire physical output cutoffs, preserving exact insertion",
      "current_proofs": [
        "EC:G1",
        "EC:G2"
      ],
      "disposition": "Complete written proof at the original scalar-principal finite-matrix scope; exact current earlier providers and receiving arguments checked."
    },
    {
      "original_id": "AN04-FIO-CAUCHY-035",
      "original_target": "Zero-excess graph composition with actual bundle-map and Maslov product order",
      "current_proofs": [
        "EC:G3",
        "EC:G5"
      ],
      "disposition": "Complete written proof at the original scalar-principal finite-matrix scope; exact current earlier providers and receiving arguments checked."
    },
    {
      "original_id": "AN04-FIO-CAUCHY-036",
      "original_target": "Iterated full global smoothing estimates including finite parameter losses",
      "current_proofs": [
        "EC:G4"
      ],
      "disposition": "Complete written proof at the original scalar-principal finite-matrix scope; exact current earlier providers and receiving arguments checked."
    },
    {
      "original_id": "AN04-FIO-CAUCHY-037",
      "original_target": "Finite compatible chart assembly through caustics without trivial-holonomy assumption",
      "current_proofs": [
        "EC:G5"
      ],
      "disposition": "Complete written proof at the original scalar-principal finite-matrix scope; exact current earlier providers and receiving arguments checked."
    },
    {
      "original_id": "AN04-FIO-CAUCHY-038",
      "original_target": "Closed full graph excludes both covector axes via finite-time length comparison",
      "current_proofs": [
        "EC:G6"
      ],
      "disposition": "Complete written proof at the original scalar-principal finite-matrix scope; exact current earlier providers and receiving arguments checked."
    },
    {
      "original_id": "AN04-FIO-CAUCHY-039",
      "original_target": "Every matrix-kernel graph wavefront direction by the two-sided elliptic inverse contradiction",
      "current_proofs": [
        "EC:G7",
        "EC:G8"
      ],
      "disposition": "Complete written proof at the original scalar-principal finite-matrix scope; exact current earlier providers and receiving arguments checked."
    },
    {
      "original_id": "AN04-FIO-CAUCHY-040",
      "original_target": "Exact compact-distribution wavefront propagation by reverse evolution and global smooth tail",
      "current_proofs": [
        "EC:G9"
      ],
      "disposition": "Complete written proof at the original scalar-principal finite-matrix scope; exact current earlier providers and receiving arguments checked."
    },
    {
      "original_id": "AN04-FIO-CAUCHY-041",
      "original_target": "Solved initial-defect example: zero equation residual does not normalize initial data",
      "current_proofs": [
        "EC:X1"
      ],
      "disposition": "Complete written proof at the original scalar-principal finite-matrix scope; exact current earlier providers and receiving arguments checked."
    },
    {
      "original_id": "AN04-FIO-CAUCHY-042",
      "original_target": "Solved noncommuting pulse example with both endpoint derivative factor orders",
      "current_proofs": [
        "EC:X2"
      ],
      "disposition": "Complete written proof at the original scalar-principal finite-matrix scope; exact current earlier providers and receiving arguments checked."
    },
    {
      "original_id": "AN04-FIO-CAUCHY-043",
      "original_target": "Solved variable-speed flow, covector, density, ordered matrix and actual delta Jacobian",
      "current_proofs": [
        "EC:X3",
        "EC:V0",
        "EC:V1"
      ],
      "disposition": "Complete written proof at the original scalar-principal finite-matrix scope; exact current earlier providers and receiving arguments checked."
    }
  ],
  "all_original_solutions_preserved": true,
  "full_course_complete": false
}