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    {
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    {
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      "obligation": "Low frequencies kept in lower residual",
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    {
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    {
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    {
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    {
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    {
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      "obligation": "L1 forcing for weak quotient solutions",
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    {
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      "obligation": "Initial quotient norms bounded by initial weighted jets",
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      "current_source_sha256": "b1b8dad95d3f7f5d90811d7f482585028efd3b9ec124b747eeaf3bcf773c01ba",
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    },
    {
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      "obligation": "Grönwall absorption without an extra derivative",
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      "current_source_sha256": "b1b8dad95d3f7f5d90811d7f482585028efd3b9ec124b747eeaf3bcf773c01ba",
      "disposition": "Complete retained and checked current proof under the stated exact hypotheses",
      "source_locator": "Lemma23.2.1 and23.2.3-23.2.4prime",
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    },
    {
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      "obligation": "Energy for every real Sobolev index",
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      "current_source_sha256": "b1b8dad95d3f7f5d90811d7f482585028efd3b9ec124b747eeaf3bcf773c01ba",
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    {
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      "obligation": "Finite time constant depends on s and T",
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      "current_source_sha256": "b1b8dad95d3f7f5d90811d7f482585028efd3b9ec124b747eeaf3bcf773c01ba",
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    {
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      "obligation": "Weighted lambda alternative and infinity convention",
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      "current_source_sha256": "b1b8dad95d3f7f5d90811d7f482585028efd3b9ec124b747eeaf3bcf773c01ba",
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    {
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      "obligation": "Uniqueness in the exact continuous weighted-jet class",
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      "historical_pdf_ranges_superseded_by_exact_approved_edition": true,
      "human_review_complete": false
    },
    {
      "id": "AN04-HO-G04-01",
      "obligation": "Formal adjoint reordered into normal-monic form",
      "current_proof_nodes": [
        "HC:M1",
        "HC:M2",
        "HC:M3",
        "HC:G1",
        "HC:G2",
        "HC:G3",
        "HC:G4"
      ],
      "current_source_sha256": "b1b8dad95d3f7f5d90811d7f482585028efd3b9ec124b747eeaf3bcf773c01ba",
      "disposition": "Complete retained and checked current proof under the stated exact hypotheses",
      "source_locator": "Theorem23.2.2 and23.2.5-23.2.6prime",
      "historical_pdf_ranges_superseded_by_exact_approved_edition": true,
      "human_review_complete": false
    },
    {
      "id": "AN04-HO-G04-02",
      "obligation": "Time reversal and top-coefficient sign normalization",
      "current_proof_nodes": [
        "HC:M1",
        "HC:M2",
        "HC:M3",
        "HC:G1",
        "HC:G2",
        "HC:G3",
        "HC:G4"
      ],
      "current_source_sha256": "b1b8dad95d3f7f5d90811d7f482585028efd3b9ec124b747eeaf3bcf773c01ba",
      "disposition": "Complete retained and checked current proof under the stated exact hypotheses",
      "source_locator": "Theorem23.2.2 and23.2.5-23.2.6prime",
      "historical_pdf_ranges_superseded_by_exact_approved_edition": true,
      "human_review_complete": false
    },
    {
      "id": "AN04-HO-G04-03",
      "obligation": "Exact Green initial-boundary sign",
      "current_proof_nodes": [
        "HC:M1",
        "HC:M2",
        "HC:M3",
        "HC:G1",
        "HC:G2",
        "HC:G3",
        "HC:G4"
      ],
      "current_source_sha256": "b1b8dad95d3f7f5d90811d7f482585028efd3b9ec124b747eeaf3bcf773c01ba",
      "disposition": "Complete retained and checked current proof under the stated exact hypotheses",
      "source_locator": "Theorem23.2.2 and23.2.5-23.2.6prime",
      "historical_pdf_ranges_superseded_by_exact_approved_edition": true,
      "human_review_complete": false
    },
    {
      "id": "AN04-HO-G04-04",
      "obligation": "Every coefficient Leibniz term",
      "current_proof_nodes": [
        "HC:M1",
        "HC:M2",
        "HC:M3",
        "HC:G1",
        "HC:G2",
        "HC:G3",
        "HC:G4"
      ],
      "current_source_sha256": "b1b8dad95d3f7f5d90811d7f482585028efd3b9ec124b747eeaf3bcf773c01ba",
      "disposition": "Complete retained and checked current proof under the stated exact hypotheses",
      "source_locator": "Theorem23.2.2 and23.2.5-23.2.6prime",
      "historical_pdf_ranges_superseded_by_exact_approved_edition": true,
      "human_review_complete": false
    },
    {
      "id": "AN04-HO-G04-05",
      "obligation": "Backward energy at1-m-s",
      "current_proof_nodes": [
        "HC:M1",
        "HC:M2",
        "HC:M3",
        "HC:G1",
        "HC:G2",
        "HC:G3",
        "HC:G4"
      ],
      "current_source_sha256": "b1b8dad95d3f7f5d90811d7f482585028efd3b9ec124b747eeaf3bcf773c01ba",
      "disposition": "Complete retained and checked current proof under the stated exact hypotheses",
      "source_locator": "Theorem23.2.2 and23.2.5-23.2.6prime",
      "historical_pdf_ranges_superseded_by_exact_approved_edition": true,
      "human_review_complete": false
    },
    {
      "id": "AN04-HO-G04-06",
      "obligation": "Sobolev pairing of every initial jet",
      "current_proof_nodes": [
        "HC:M1",
        "HC:M2",
        "HC:M3",
        "HC:G1",
        "HC:G2",
        "HC:G3",
        "HC:G4"
      ],
      "current_source_sha256": "b1b8dad95d3f7f5d90811d7f482585028efd3b9ec124b747eeaf3bcf773c01ba",
      "disposition": "Complete retained and checked current proof under the stated exact hypotheses",
      "source_locator": "Theorem23.2.2 and23.2.5-23.2.6prime",
      "historical_pdf_ranges_superseded_by_exact_approved_edition": true,
      "human_review_complete": false
    },
    {
      "id": "AN04-HO-G04-07",
      "obligation": "Well-defined anti-linear range functional",
      "current_proof_nodes": [
        "HC:M1",
        "HC:M2",
        "HC:M3",
        "HC:G1",
        "HC:G2",
        "HC:G3",
        "HC:G4"
      ],
      "current_source_sha256": "b1b8dad95d3f7f5d90811d7f482585028efd3b9ec124b747eeaf3bcf773c01ba",
      "disposition": "Complete retained and checked current proof under the stated exact hypotheses",
      "source_locator": "Theorem23.2.2 and23.2.5-23.2.6prime",
      "historical_pdf_ranges_superseded_by_exact_approved_edition": true,
      "human_review_complete": false
    },
    {
      "id": "AN04-HO-G04-08",
      "obligation": "Exact complex Hahn-Banach reuse",
      "current_proof_nodes": [
        "HC:M1",
        "HC:M2",
        "HC:M3",
        "HC:G1",
        "HC:G2",
        "HC:G3",
        "HC:G4"
      ],
      "current_source_sha256": "b1b8dad95d3f7f5d90811d7f482585028efd3b9ec124b747eeaf3bcf773c01ba",
      "disposition": "Complete retained and checked current proof under the stated exact hypotheses",
      "source_locator": "Theorem23.2.2 and23.2.5-23.2.6prime",
      "historical_pdf_ranges_superseded_by_exact_approved_edition": true,
      "human_review_complete": false
    },
    {
      "id": "AN04-HO-G04-09",
      "obligation": "Hilbert-valued L1 dual representation reuse",
      "current_proof_nodes": [
        "HC:M1",
        "HC:M2",
        "HC:M3",
        "HC:G1",
        "HC:G2",
        "HC:G3",
        "HC:G4"
      ],
      "current_source_sha256": "b1b8dad95d3f7f5d90811d7f482585028efd3b9ec124b747eeaf3bcf773c01ba",
      "disposition": "Complete retained and checked current proof under the stated exact hypotheses",
      "source_locator": "Theorem23.2.2 and23.2.5-23.2.6prime",
      "historical_pdf_ranges_superseded_by_exact_approved_edition": true,
      "human_review_complete": false
    },
    {
      "id": "AN04-HO-G04-10",
      "obligation": "Weak distributional equation",
      "current_proof_nodes": [
        "HC:M1",
        "HC:M2",
        "HC:M3",
        "HC:G1",
        "HC:G2",
        "HC:G3",
        "HC:G4"
      ],
      "current_source_sha256": "b1b8dad95d3f7f5d90811d7f482585028efd3b9ec124b747eeaf3bcf773c01ba",
      "disposition": "Complete retained and checked current proof under the stated exact hypotheses",
      "source_locator": "Theorem23.2.2 and23.2.5-23.2.6prime",
      "historical_pdf_ranges_superseded_by_exact_approved_edition": true,
      "human_review_complete": false
    },
    {
      "id": "AN04-HO-G04-11",
      "obligation": "Initial Green identity versus classical traces",
      "current_proof_nodes": [
        "HC:M1",
        "HC:M2",
        "HC:M3",
        "HC:G1",
        "HC:G2",
        "HC:G3",
        "HC:G4"
      ],
      "current_source_sha256": "b1b8dad95d3f7f5d90811d7f482585028efd3b9ec124b747eeaf3bcf773c01ba",
      "disposition": "Complete retained and checked current proof under the stated exact hypotheses",
      "source_locator": "Theorem23.2.2 and23.2.5-23.2.6prime",
      "historical_pdf_ranges_superseded_by_exact_approved_edition": true,
      "human_review_complete": false
    },
    {
      "id": "AN04-HO-G04-12",
      "obligation": "Exact anisotropic Fourier-weight definitions",
      "current_proof_nodes": [
        "HC:M1",
        "HC:M2",
        "HC:M3",
        "HC:G1",
        "HC:G2",
        "HC:G3",
        "HC:G4"
      ],
      "current_source_sha256": "b1b8dad95d3f7f5d90811d7f482585028efd3b9ec124b747eeaf3bcf773c01ba",
      "disposition": "Complete retained and checked current proof under the stated exact hypotheses",
      "source_locator": "Theorem23.2.2 and23.2.5-23.2.6prime",
      "historical_pdf_ranges_superseded_by_exact_approved_edition": true,
      "human_review_complete": false
    },
    {
      "id": "AN04-HO-G04-13",
      "obligation": "Supported versus restricted interval spaces",
      "current_proof_nodes": [
        "HC:M1",
        "HC:M2",
        "HC:M3",
        "HC:G1",
        "HC:G2",
        "HC:G3",
        "HC:G4"
      ],
      "current_source_sha256": "b1b8dad95d3f7f5d90811d7f482585028efd3b9ec124b747eeaf3bcf773c01ba",
      "disposition": "Complete retained and checked current proof under the stated exact hypotheses",
      "source_locator": "Theorem23.2.2 and23.2.5-23.2.6prime",
      "historical_pdf_ranges_superseded_by_exact_approved_edition": true,
      "human_review_complete": false
    },
    {
      "id": "AN04-HO-G04-14",
      "obligation": "Initial negative normal-order bounds",
      "current_proof_nodes": [
        "HC:M1",
        "HC:M2",
        "HC:M3",
        "HC:G1",
        "HC:G2",
        "HC:G3",
        "HC:G4"
      ],
      "current_source_sha256": "b1b8dad95d3f7f5d90811d7f482585028efd3b9ec124b747eeaf3bcf773c01ba",
      "disposition": "Complete retained and checked current proof under the stated exact hypotheses",
      "source_locator": "Theorem23.2.2 and23.2.5-23.2.6prime",
      "historical_pdf_ranges_superseded_by_exact_approved_edition": true,
      "human_review_complete": false
    },
    {
      "id": "AN04-HO-G04-15",
      "obligation": "Inductive normal/tangential redistribution",
      "current_proof_nodes": [
        "HC:M1",
        "HC:M2",
        "HC:M3",
        "HC:G1",
        "HC:G2",
        "HC:G3",
        "HC:G4"
      ],
      "current_source_sha256": "b1b8dad95d3f7f5d90811d7f482585028efd3b9ec124b747eeaf3bcf773c01ba",
      "disposition": "Complete retained and checked current proof under the stated exact hypotheses",
      "source_locator": "Theorem23.2.2 and23.2.5-23.2.6prime",
      "historical_pdf_ranges_superseded_by_exact_approved_edition": true,
      "human_review_complete": false
    },
    {
      "id": "AN04-HO-G04-16",
      "obligation": "Full normal recovery lemma at each decreasing jet index",
      "current_proof_nodes": [
        "HC:M1",
        "HC:M2",
        "HC:M3",
        "HC:G1",
        "HC:G2",
        "HC:G3",
        "HC:G4"
      ],
      "current_source_sha256": "b1b8dad95d3f7f5d90811d7f482585028efd3b9ec124b747eeaf3bcf773c01ba",
      "disposition": "Complete retained and checked current proof under the stated exact hypotheses",
      "source_locator": "Theorem23.2.2 and23.2.5-23.2.6prime",
      "historical_pdf_ranges_superseded_by_exact_approved_edition": true,
      "human_review_complete": false
    },
    {
      "id": "AN04-HO-G04-17",
      "obligation": "Trace theorem with provisional half-order loss",
      "current_proof_nodes": [
        "HC:M1",
        "HC:M2",
        "HC:M3",
        "HC:G1",
        "HC:G2",
        "HC:G3",
        "HC:G4"
      ],
      "current_source_sha256": "b1b8dad95d3f7f5d90811d7f482585028efd3b9ec124b747eeaf3bcf773c01ba",
      "disposition": "Complete retained and checked current proof under the stated exact hypotheses",
      "source_locator": "Theorem23.2.2 and23.2.5-23.2.6prime",
      "historical_pdf_ranges_superseded_by_exact_approved_edition": true,
      "human_review_complete": false
    },
    {
      "id": "AN04-HO-G04-18",
      "obligation": "Triangular tests recovering each initial jet",
      "current_proof_nodes": [
        "HC:M1",
        "HC:M2",
        "HC:M3",
        "HC:G1",
        "HC:G2",
        "HC:G3",
        "HC:G4"
      ],
      "current_source_sha256": "b1b8dad95d3f7f5d90811d7f482585028efd3b9ec124b747eeaf3bcf773c01ba",
      "disposition": "Complete retained and checked current proof under the stated exact hypotheses",
      "source_locator": "Theorem23.2.2 and23.2.5-23.2.6prime",
      "historical_pdf_ranges_superseded_by_exact_approved_edition": true,
      "human_review_complete": false
    },
    {
      "id": "AN04-HO-G04-19",
      "obligation": "High-level smooth data construction and lower-level uniqueness",
      "current_proof_nodes": [
        "HC:M1",
        "HC:M2",
        "HC:M3",
        "HC:G1",
        "HC:G2",
        "HC:G3",
        "HC:G4"
      ],
      "current_source_sha256": "b1b8dad95d3f7f5d90811d7f482585028efd3b9ec124b747eeaf3bcf773c01ba",
      "disposition": "Complete retained and checked current proof under the stated exact hypotheses",
      "source_locator": "Theorem23.2.2 and23.2.5-23.2.6prime",
      "historical_pdf_ranges_superseded_by_exact_approved_edition": true,
      "human_review_complete": false
    },
    {
      "id": "AN04-HO-G04-20",
      "obligation": "Smooth approximation of L1 forcing and weighted data",
      "current_proof_nodes": [
        "HC:M1",
        "HC:M2",
        "HC:M3",
        "HC:G1",
        "HC:G2",
        "HC:G3",
        "HC:G4"
      ],
      "current_source_sha256": "b1b8dad95d3f7f5d90811d7f482585028efd3b9ec124b747eeaf3bcf773c01ba",
      "disposition": "Complete retained and checked current proof under the stated exact hypotheses",
      "source_locator": "Theorem23.2.2 and23.2.5-23.2.6prime",
      "historical_pdf_ranges_superseded_by_exact_approved_edition": true,
      "human_review_complete": false
    },
    {
      "id": "AN04-HO-G04-21",
      "obligation": "Pass the exact equation and all continuous jets",
      "current_proof_nodes": [
        "HC:M1",
        "HC:M2",
        "HC:M3",
        "HC:G1",
        "HC:G2",
        "HC:G3",
        "HC:G4"
      ],
      "current_source_sha256": "b1b8dad95d3f7f5d90811d7f482585028efd3b9ec124b747eeaf3bcf773c01ba",
      "disposition": "Complete retained and checked current proof under the stated exact hypotheses",
      "source_locator": "Theorem23.2.2 and23.2.5-23.2.6prime",
      "historical_pdf_ranges_superseded_by_exact_approved_edition": true,
      "human_review_complete": false
    },
    {
      "id": "AN04-HO-G04-22",
      "obligation": "Preserve the requested Sobolev level without half-order loss",
      "current_proof_nodes": [
        "HC:M1",
        "HC:M2",
        "HC:M3",
        "HC:G1",
        "HC:G2",
        "HC:G3",
        "HC:G4"
      ],
      "current_source_sha256": "b1b8dad95d3f7f5d90811d7f482585028efd3b9ec124b747eeaf3bcf773c01ba",
      "disposition": "Complete retained and checked current proof under the stated exact hypotheses",
      "source_locator": "Theorem23.2.2 and23.2.5-23.2.6prime",
      "historical_pdf_ranges_superseded_by_exact_approved_edition": true,
      "human_review_complete": false
    },
    {
      "id": "AN04-HO-G05-01",
      "obligation": "Noncharacteristic defining differential",
      "current_proof_nodes": [
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        "HC:L2"
      ],
      "current_source_sha256": "b1b8dad95d3f7f5d90811d7f482585028efd3b9ec124b747eeaf3bcf773c01ba",
      "disposition": "Complete retained and checked current proof under the stated exact hypotheses",
      "source_locator": "Definition23.2.3 and local reduction",
      "historical_pdf_ranges_superseded_by_exact_approved_edition": true,
      "human_review_complete": false
    },
    {
      "id": "AN04-HO-G05-02",
      "obligation": "Exclude covectors parallel to the defining differential",
      "current_proof_nodes": [
        "HC:L1",
        "HC:L2"
      ],
      "current_source_sha256": "b1b8dad95d3f7f5d90811d7f482585028efd3b9ec124b747eeaf3bcf773c01ba",
      "disposition": "Complete retained and checked current proof under the stated exact hypotheses",
      "source_locator": "Definition23.2.3 and local reduction",
      "historical_pdf_ranges_superseded_by_exact_approved_edition": true,
      "human_review_complete": false
    },
    {
      "id": "AN04-HO-G05-03",
      "obligation": "Distinct roots relative to level sets",
      "current_proof_nodes": [
        "HC:L1",
        "HC:L2"
      ],
      "current_source_sha256": "b1b8dad95d3f7f5d90811d7f482585028efd3b9ec124b747eeaf3bcf773c01ba",
      "disposition": "Complete retained and checked current proof under the stated exact hypotheses",
      "source_locator": "Definition23.2.3 and local reduction",
      "historical_pdf_ranges_superseded_by_exact_approved_edition": true,
      "human_review_complete": false
    },
    {
      "id": "AN04-HO-G05-04",
      "obligation": "Local normalization of the leading normal coefficient",
      "current_proof_nodes": [
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        "HC:L2"
      ],
      "current_source_sha256": "b1b8dad95d3f7f5d90811d7f482585028efd3b9ec124b747eeaf3bcf773c01ba",
      "disposition": "Complete retained and checked current proof under the stated exact hypotheses",
      "source_locator": "Definition23.2.3 and local reduction",
      "historical_pdf_ranges_superseded_by_exact_approved_edition": true,
      "human_review_complete": false
    },
    {
      "id": "AN04-HO-G05-05",
      "obligation": "Choose a normal vector field with v phi1",
      "current_proof_nodes": [
        "HC:L1",
        "HC:L2"
      ],
      "current_source_sha256": "b1b8dad95d3f7f5d90811d7f482585028efd3b9ec124b747eeaf3bcf773c01ba",
      "disposition": "Complete retained and checked current proof under the stated exact hypotheses",
      "source_locator": "Definition23.2.3 and local reduction",
      "historical_pdf_ranges_superseded_by_exact_approved_edition": true,
      "human_review_complete": false
    },
    {
      "id": "AN04-HO-G05-06",
      "obligation": "Coordinate data and powers of i",
      "current_proof_nodes": [
        "HC:L1",
        "HC:L2"
      ],
      "current_source_sha256": "b1b8dad95d3f7f5d90811d7f482585028efd3b9ec124b747eeaf3bcf773c01ba",
      "disposition": "Complete retained and checked current proof under the stated exact hypotheses",
      "source_locator": "Definition23.2.3 and local reduction",
      "historical_pdf_ranges_superseded_by_exact_approved_edition": true,
      "human_review_complete": false
    },
    {
      "id": "AN04-HO-G05-07",
      "obligation": "Preserve full coordinate lower terms",
      "current_proof_nodes": [
        "HC:L1",
        "HC:L2"
      ],
      "current_source_sha256": "b1b8dad95d3f7f5d90811d7f482585028efd3b9ec124b747eeaf3bcf773c01ba",
      "disposition": "Complete retained and checked current proof under the stated exact hypotheses",
      "source_locator": "Definition23.2.3 and local reduction",
      "historical_pdf_ranges_superseded_by_exact_approved_edition": true,
      "human_review_complete": false
    },
    {
      "id": "AN04-HO-G05-08",
      "obligation": "Uniform ordered-root extension on compact charts",
      "current_proof_nodes": [
        "HC:L1",
        "HC:L2"
      ],
      "current_source_sha256": "b1b8dad95d3f7f5d90811d7f482585028efd3b9ec124b747eeaf3bcf773c01ba",
      "disposition": "Complete retained and checked current proof under the stated exact hypotheses",
      "source_locator": "Definition23.2.3 and local reduction",
      "historical_pdf_ranges_superseded_by_exact_approved_edition": true,
      "human_review_complete": false
    },
    {
      "id": "AN04-HO-G05-09",
      "obligation": "Convex-combination gap proof",
      "current_proof_nodes": [
        "HC:L1",
        "HC:L2"
      ],
      "current_source_sha256": "b1b8dad95d3f7f5d90811d7f482585028efd3b9ec124b747eeaf3bcf773c01ba",
      "disposition": "Complete retained and checked current proof under the stated exact hypotheses",
      "source_locator": "Definition23.2.3 and local reduction",
      "historical_pdf_ranges_superseded_by_exact_approved_edition": true,
      "human_review_complete": false
    },
    {
      "id": "AN04-HO-G05-10",
      "obligation": "Tangential pseudodifferential extension need not remain fully differential",
      "current_proof_nodes": [
        "HC:L1",
        "HC:L2"
      ],
      "current_source_sha256": "b1b8dad95d3f7f5d90811d7f482585028efd3b9ec124b747eeaf3bcf773c01ba",
      "disposition": "Complete retained and checked current proof under the stated exact hypotheses",
      "source_locator": "Definition23.2.3 and local reduction",
      "historical_pdf_ranges_superseded_by_exact_approved_edition": true,
      "human_review_complete": false
    },
    {
      "id": "AN04-HO-G05-11",
      "obligation": "Match full coefficients on the requested smaller set",
      "current_proof_nodes": [
        "HC:L1",
        "HC:L2"
      ],
      "current_source_sha256": "b1b8dad95d3f7f5d90811d7f482585028efd3b9ec124b747eeaf3bcf773c01ba",
      "disposition": "Complete retained and checked current proof under the stated exact hypotheses",
      "source_locator": "Definition23.2.3 and local reduction",
      "historical_pdf_ranges_superseded_by_exact_approved_edition": true,
      "human_review_complete": false
    },
    {
      "id": "AN04-HO-G06-01",
      "obligation": "Forcing restriction and nonnegative normal order",
      "current_proof_nodes": [
        "HC:L3",
        "HC:L4",
        "HC:L5",
        "HC:L6"
      ],
      "current_source_sha256": "b1b8dad95d3f7f5d90811d7f482585028efd3b9ec124b747eeaf3bcf773c01ba",
      "disposition": "Complete retained and checked current proof under the stated exact hypotheses",
      "source_locator": "Propositions23.2.5-23.2.6",
      "historical_pdf_ranges_superseded_by_exact_approved_edition": true,
      "human_review_complete": false
    },
    {
      "id": "AN04-HO-G06-02",
      "obligation": "Exact time-integrability implication",
      "current_proof_nodes": [
        "HC:L3",
        "HC:L4",
        "HC:L5",
        "HC:L6"
      ],
      "current_source_sha256": "b1b8dad95d3f7f5d90811d7f482585028efd3b9ec124b747eeaf3bcf773c01ba",
      "disposition": "Complete retained and checked current proof under the stated exact hypotheses",
      "source_locator": "Propositions23.2.5-23.2.6",
      "historical_pdf_ranges_superseded_by_exact_approved_edition": true,
      "human_review_complete": false
    },
    {
      "id": "AN04-HO-G06-03",
      "obligation": "All Cauchy-jet weights s+t+m-1-j",
      "current_proof_nodes": [
        "HC:L3",
        "HC:L4",
        "HC:L5",
        "HC:L6"
      ],
      "current_source_sha256": "b1b8dad95d3f7f5d90811d7f482585028efd3b9ec124b747eeaf3bcf773c01ba",
      "disposition": "Complete retained and checked current proof under the stated exact hypotheses",
      "source_locator": "Propositions23.2.5-23.2.6",
      "historical_pdf_ranges_superseded_by_exact_approved_edition": true,
      "human_review_complete": false
    },
    {
      "id": "AN04-HO-G06-04",
      "obligation": "Full mixed solution order m-1+s,t",
      "current_proof_nodes": [
        "HC:L3",
        "HC:L4",
        "HC:L5",
        "HC:L6"
      ],
      "current_source_sha256": "b1b8dad95d3f7f5d90811d7f482585028efd3b9ec124b747eeaf3bcf773c01ba",
      "disposition": "Complete retained and checked current proof under the stated exact hypotheses",
      "source_locator": "Propositions23.2.5-23.2.6",
      "historical_pdf_ranges_superseded_by_exact_approved_edition": true,
      "human_review_complete": false
    },
    {
      "id": "AN04-HO-G06-05",
      "obligation": "Normal recovery from the equation",
      "current_proof_nodes": [
        "HC:L3",
        "HC:L4",
        "HC:L5",
        "HC:L6"
      ],
      "current_source_sha256": "b1b8dad95d3f7f5d90811d7f482585028efd3b9ec124b747eeaf3bcf773c01ba",
      "disposition": "Complete retained and checked current proof under the stated exact hypotheses",
      "source_locator": "Propositions23.2.5-23.2.6",
      "historical_pdf_ranges_superseded_by_exact_approved_edition": true,
      "human_review_complete": false
    },
    {
      "id": "AN04-HO-G06-06",
      "obligation": "Supported negative-order decomposition",
      "current_proof_nodes": [
        "HC:L3",
        "HC:L4",
        "HC:L5",
        "HC:L6"
      ],
      "current_source_sha256": "b1b8dad95d3f7f5d90811d7f482585028efd3b9ec124b747eeaf3bcf773c01ba",
      "disposition": "Complete retained and checked current proof under the stated exact hypotheses",
      "source_locator": "Propositions23.2.5-23.2.6",
      "historical_pdf_ranges_superseded_by_exact_approved_edition": true,
      "human_review_complete": false
    },
    {
      "id": "AN04-HO-G06-07",
      "obligation": "Induction in real normal order",
      "current_proof_nodes": [
        "HC:L3",
        "HC:L4",
        "HC:L5",
        "HC:L6"
      ],
      "current_source_sha256": "b1b8dad95d3f7f5d90811d7f482585028efd3b9ec124b747eeaf3bcf773c01ba",
      "disposition": "Complete retained and checked current proof under the stated exact hypotheses",
      "source_locator": "Propositions23.2.5-23.2.6",
      "historical_pdf_ranges_superseded_by_exact_approved_edition": true,
      "human_review_complete": false
    },
    {
      "id": "AN04-HO-G06-08",
      "obligation": "Commutator total order m",
      "current_proof_nodes": [
        "HC:L3",
        "HC:L4",
        "HC:L5",
        "HC:L6"
      ],
      "current_source_sha256": "b1b8dad95d3f7f5d90811d7f482585028efd3b9ec124b747eeaf3bcf773c01ba",
      "disposition": "Complete retained and checked current proof under the stated exact hypotheses",
      "source_locator": "Propositions23.2.5-23.2.6",
      "historical_pdf_ranges_superseded_by_exact_approved_edition": true,
      "human_review_complete": false
    },
    {
      "id": "AN04-HO-G06-09",
      "obligation": "Commutator normal order at most m-1",
      "current_proof_nodes": [
        "HC:L3",
        "HC:L4",
        "HC:L5",
        "HC:L6"
      ],
      "current_source_sha256": "b1b8dad95d3f7f5d90811d7f482585028efd3b9ec124b747eeaf3bcf773c01ba",
      "disposition": "Complete retained and checked current proof under the stated exact hypotheses",
      "source_locator": "Propositions23.2.5-23.2.6",
      "historical_pdf_ranges_superseded_by_exact_approved_edition": true,
      "human_review_complete": false
    },
    {
      "id": "AN04-HO-G06-10",
      "obligation": "Correct residual correction sign",
      "current_proof_nodes": [
        "HC:L3",
        "HC:L4",
        "HC:L5",
        "HC:L6"
      ],
      "current_source_sha256": "b1b8dad95d3f7f5d90811d7f482585028efd3b9ec124b747eeaf3bcf773c01ba",
      "disposition": "Complete retained and checked current proof under the stated exact hypotheses",
      "source_locator": "Propositions23.2.5-23.2.6",
      "historical_pdf_ranges_superseded_by_exact_approved_edition": true,
      "human_review_complete": false
    },
    {
      "id": "AN04-HO-G06-11",
      "obligation": "Local scope and all finite or infinite regularity endpoints",
      "current_proof_nodes": [
        "HC:L3",
        "HC:L4",
        "HC:L5",
        "HC:L6"
      ],
      "current_source_sha256": "b1b8dad95d3f7f5d90811d7f482585028efd3b9ec124b747eeaf3bcf773c01ba",
      "disposition": "Complete retained and checked current proof under the stated exact hypotheses",
      "source_locator": "Propositions23.2.5-23.2.6",
      "historical_pdf_ranges_superseded_by_exact_approved_edition": true,
      "human_review_complete": false
    },
    {
      "id": "AN04-HO-G07-01",
      "obligation": "Closed forward-side support",
      "current_proof_nodes": [
        "HC:L7",
        "HC:L8"
      ],
      "current_source_sha256": "b1b8dad95d3f7f5d90811d7f482585028efd3b9ec124b747eeaf3bcf773c01ba",
      "disposition": "Complete retained and checked current proof under the stated exact hypotheses",
      "source_locator": "Theorems23.2.4 and23.2.7",
      "historical_pdf_ranges_superseded_by_exact_approved_edition": true,
      "human_review_complete": false
    },
    {
      "id": "AN04-HO-G07-02",
      "obligation": "Curved local time coordinates",
      "current_proof_nodes": [
        "HC:L7",
        "HC:L8"
      ],
      "current_source_sha256": "b1b8dad95d3f7f5d90811d7f482585028efd3b9ec124b747eeaf3bcf773c01ba",
      "disposition": "Complete retained and checked current proof under the stated exact hypotheses",
      "source_locator": "Theorems23.2.4 and23.2.7",
      "historical_pdf_ranges_superseded_by_exact_approved_edition": true,
      "human_review_complete": false
    },
    {
      "id": "AN04-HO-G07-03",
      "obligation": "Uniform hyperbolicity after a small spatial quadratic bend",
      "current_proof_nodes": [
        "HC:L7",
        "HC:L8"
      ],
      "current_source_sha256": "b1b8dad95d3f7f5d90811d7f482585028efd3b9ec124b747eeaf3bcf773c01ba",
      "disposition": "Complete retained and checked current proof under the stated exact hypotheses",
      "source_locator": "Theorems23.2.4 and23.2.7",
      "historical_pdf_ranges_superseded_by_exact_approved_edition": true,
      "human_review_complete": false
    },
    {
      "id": "AN04-HO-G07-04",
      "obligation": "Exact small-box geometry",
      "current_proof_nodes": [
        "HC:L7",
        "HC:L8"
      ],
      "current_source_sha256": "b1b8dad95d3f7f5d90811d7f482585028efd3b9ec124b747eeaf3bcf773c01ba",
      "disposition": "Complete retained and checked current proof under the stated exact hypotheses",
      "source_locator": "Theorems23.2.4 and23.2.7",
      "historical_pdf_ranges_superseded_by_exact_approved_edition": true,
      "human_review_complete": false
    },
    {
      "id": "AN04-HO-G07-05",
      "obligation": "Backward smooth adjoint construction",
      "current_proof_nodes": [
        "HC:L7",
        "HC:L8"
      ],
      "current_source_sha256": "b1b8dad95d3f7f5d90811d7f482585028efd3b9ec124b747eeaf3bcf773c01ba",
      "disposition": "Complete retained and checked current proof under the stated exact hypotheses",
      "source_locator": "Theorems23.2.4 and23.2.7",
      "historical_pdf_ranges_superseded_by_exact_approved_edition": true,
      "human_review_complete": false
    },
    {
      "id": "AN04-HO-G07-06",
      "obligation": "Compact support needed for distribution pairing",
      "current_proof_nodes": [
        "HC:L7",
        "HC:L8"
      ],
      "current_source_sha256": "b1b8dad95d3f7f5d90811d7f482585028efd3b9ec124b747eeaf3bcf773c01ba",
      "disposition": "Complete retained and checked current proof under the stated exact hypotheses",
      "source_locator": "Theorems23.2.4 and23.2.7",
      "historical_pdf_ranges_superseded_by_exact_approved_edition": true,
      "human_review_complete": false
    },
    {
      "id": "AN04-HO-G07-07",
      "obligation": "Retain all cutoff errors before pairing",
      "current_proof_nodes": [
        "HC:L7",
        "HC:L8"
      ],
      "current_source_sha256": "b1b8dad95d3f7f5d90811d7f482585028efd3b9ec124b747eeaf3bcf773c01ba",
      "disposition": "Complete retained and checked current proof under the stated exact hypotheses",
      "source_locator": "Theorems23.2.4 and23.2.7",
      "historical_pdf_ranges_superseded_by_exact_approved_edition": true,
      "human_review_complete": false
    },
    {
      "id": "AN04-HO-G07-08",
      "obligation": "Fundamental neighborhood system",
      "current_proof_nodes": [
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        "HC:L8"
      ],
      "current_source_sha256": "b1b8dad95d3f7f5d90811d7f482585028efd3b9ec124b747eeaf3bcf773c01ba",
      "disposition": "Complete retained and checked current proof under the stated exact hypotheses",
      "source_locator": "Theorems23.2.4 and23.2.7",
      "historical_pdf_ranges_superseded_by_exact_approved_edition": true,
      "human_review_complete": false
    },
    {
      "id": "AN04-HO-G07-09",
      "obligation": "Overlap identification by local uniqueness",
      "current_proof_nodes": [
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        "HC:L8"
      ],
      "current_source_sha256": "b1b8dad95d3f7f5d90811d7f482585028efd3b9ec124b747eeaf3bcf773c01ba",
      "disposition": "Complete retained and checked current proof under the stated exact hypotheses",
      "source_locator": "Theorems23.2.4 and23.2.7",
      "historical_pdf_ranges_superseded_by_exact_approved_edition": true,
      "human_review_complete": false
    },
    {
      "id": "AN04-HO-G07-10",
      "obligation": "Refinement with compatible pairwise overlaps",
      "current_proof_nodes": [
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        "HC:L8"
      ],
      "current_source_sha256": "b1b8dad95d3f7f5d90811d7f482585028efd3b9ec124b747eeaf3bcf773c01ba",
      "disposition": "Complete retained and checked current proof under the stated exact hypotheses",
      "source_locator": "Theorems23.2.4 and23.2.7",
      "historical_pdf_ranges_superseded_by_exact_approved_edition": true,
      "human_review_complete": false
    },
    {
      "id": "AN04-HO-G07-11",
      "obligation": "Cut off the already solved forcing near a level",
      "current_proof_nodes": [
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        "HC:L8"
      ],
      "current_source_sha256": "b1b8dad95d3f7f5d90811d7f482585028efd3b9ec124b747eeaf3bcf773c01ba",
      "disposition": "Complete retained and checked current proof under the stated exact hypotheses",
      "source_locator": "Theorems23.2.4 and23.2.7",
      "historical_pdf_ranges_superseded_by_exact_approved_edition": true,
      "human_review_complete": false
    },
    {
      "id": "AN04-HO-G07-12",
      "obligation": "Residual forcing starts above a positive level",
      "current_proof_nodes": [
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        "HC:L8"
      ],
      "current_source_sha256": "b1b8dad95d3f7f5d90811d7f482585028efd3b9ec124b747eeaf3bcf773c01ba",
      "disposition": "Complete retained and checked current proof under the stated exact hypotheses",
      "source_locator": "Theorems23.2.4 and23.2.7",
      "historical_pdf_ranges_superseded_by_exact_approved_edition": true,
      "human_review_complete": false
    },
    {
      "id": "AN04-HO-G07-13",
      "obligation": "One finite-level advance uniform on the chosen compact set",
      "current_proof_nodes": [
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        "HC:L8"
      ],
      "current_source_sha256": "b1b8dad95d3f7f5d90811d7f482585028efd3b9ec124b747eeaf3bcf773c01ba",
      "disposition": "Complete retained and checked current proof under the stated exact hypotheses",
      "source_locator": "Theorems23.2.4 and23.2.7",
      "historical_pdf_ranges_superseded_by_exact_approved_edition": true,
      "human_review_complete": false
    },
    {
      "id": "AN04-HO-G07-14",
      "obligation": "Finite iteration to cover the requested Y",
      "current_proof_nodes": [
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        "HC:L8"
      ],
      "current_source_sha256": "b1b8dad95d3f7f5d90811d7f482585028efd3b9ec124b747eeaf3bcf773c01ba",
      "disposition": "Complete retained and checked current proof under the stated exact hypotheses",
      "source_locator": "Theorems23.2.4 and23.2.7",
      "historical_pdf_ranges_superseded_by_exact_approved_edition": true,
      "human_review_complete": false
    },
    {
      "id": "AN04-HO-G07-15",
      "obligation": "Full output supported on the closed forward side",
      "current_proof_nodes": [
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        "HC:L8"
      ],
      "current_source_sha256": "b1b8dad95d3f7f5d90811d7f482585028efd3b9ec124b747eeaf3bcf773c01ba",
      "disposition": "Complete retained and checked current proof under the stated exact hypotheses",
      "source_locator": "Theorems23.2.4 and23.2.7",
      "historical_pdf_ranges_superseded_by_exact_approved_edition": true,
      "human_review_complete": false
    },
    {
      "id": "AN04-HO-G07-16",
      "obligation": "Equation guaranteed in Y rather than all X",
      "current_proof_nodes": [
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        "HC:L8"
      ],
      "current_source_sha256": "b1b8dad95d3f7f5d90811d7f482585028efd3b9ec124b747eeaf3bcf773c01ba",
      "disposition": "Complete retained and checked current proof under the stated exact hypotheses",
      "source_locator": "Theorems23.2.4 and23.2.7",
      "historical_pdf_ranges_superseded_by_exact_approved_edition": true,
      "human_review_complete": false
    },
    {
      "id": "AN04-HO-G07-17",
      "obligation": "Data prescription on X0 intersect Y",
      "current_proof_nodes": [
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        "HC:L8"
      ],
      "current_source_sha256": "b1b8dad95d3f7f5d90811d7f482585028efd3b9ec124b747eeaf3bcf773c01ba",
      "disposition": "Complete retained and checked current proof under the stated exact hypotheses",
      "source_locator": "Theorems23.2.4 and23.2.7",
      "historical_pdf_ranges_superseded_by_exact_approved_edition": true,
      "human_review_complete": false
    },
    {
      "id": "AN04-HO-G08-01",
      "obligation": "Residual order m-mu induction",
      "current_proof_nodes": [
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      ],
      "current_source_sha256": "b1b8dad95d3f7f5d90811d7f482585028efd3b9ec124b747eeaf3bcf773c01ba",
      "disposition": "Complete retained and checked current proof under the stated exact hypotheses",
      "source_locator": "Lemma23.2.8",
      "historical_pdf_ranges_superseded_by_exact_approved_edition": true,
      "human_review_complete": false
    },
    {
      "id": "AN04-HO-G08-02",
      "obligation": "Elliptic sum of quotients at a simple root",
      "current_proof_nodes": [
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      ],
      "current_source_sha256": "b1b8dad95d3f7f5d90811d7f482585028efd3b9ec124b747eeaf3bcf773c01ba",
      "disposition": "Complete retained and checked current proof under the stated exact hypotheses",
      "source_locator": "Lemma23.2.8",
      "historical_pdf_ranges_superseded_by_exact_approved_edition": true,
      "human_review_complete": false
    },
    {
      "id": "AN04-HO-G08-03",
      "obligation": "Exact residual sign for first-order correction",
      "current_proof_nodes": [
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      ],
      "current_source_sha256": "b1b8dad95d3f7f5d90811d7f482585028efd3b9ec124b747eeaf3bcf773c01ba",
      "disposition": "Complete retained and checked current proof under the stated exact hypotheses",
      "source_locator": "Lemma23.2.8",
      "historical_pdf_ranges_superseded_by_exact_approved_edition": true,
      "human_review_complete": false
    },
    {
      "id": "AN04-HO-G08-04",
      "obligation": "Correction order1-mu",
      "current_proof_nodes": [
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      ],
      "current_source_sha256": "b1b8dad95d3f7f5d90811d7f482585028efd3b9ec124b747eeaf3bcf773c01ba",
      "disposition": "Complete retained and checked current proof under the stated exact hypotheses",
      "source_locator": "Lemma23.2.8",
      "historical_pdf_ranges_superseded_by_exact_approved_edition": true,
      "human_review_complete": false
    },
    {
      "id": "AN04-HO-G08-05",
      "obligation": "Every lower quotient correction order",
      "current_proof_nodes": [
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      ],
      "current_source_sha256": "b1b8dad95d3f7f5d90811d7f482585028efd3b9ec124b747eeaf3bcf773c01ba",
      "disposition": "Complete retained and checked current proof under the stated exact hypotheses",
      "source_locator": "Lemma23.2.8",
      "historical_pdf_ranges_superseded_by_exact_approved_edition": true,
      "human_review_complete": false
    },
    {
      "id": "AN04-HO-G08-06",
      "obligation": "Eliminate all nonconstant normal residual powers",
      "current_proof_nodes": [
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      ],
      "current_source_sha256": "b1b8dad95d3f7f5d90811d7f482585028efd3b9ec124b747eeaf3bcf773c01ba",
      "disposition": "Complete retained and checked current proof under the stated exact hypotheses",
      "source_locator": "Lemma23.2.8",
      "historical_pdf_ranges_superseded_by_exact_approved_edition": true,
      "human_review_complete": false
    },
    {
      "id": "AN04-HO-G08-07",
      "obligation": "Improve the tangential residual by one order",
      "current_proof_nodes": [
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      ],
      "current_source_sha256": "b1b8dad95d3f7f5d90811d7f482585028efd3b9ec124b747eeaf3bcf773c01ba",
      "disposition": "Complete retained and checked current proof under the stated exact hypotheses",
      "source_locator": "Lemma23.2.8",
      "historical_pdf_ranges_superseded_by_exact_approved_edition": true,
      "human_review_complete": false
    },
    {
      "id": "AN04-HO-G08-08",
      "obligation": "Parameter-aware support-preserving asymptotic sums",
      "current_proof_nodes": [
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      ],
      "current_source_sha256": "b1b8dad95d3f7f5d90811d7f482585028efd3b9ec124b747eeaf3bcf773c01ba",
      "disposition": "Complete retained and checked current proof under the stated exact hypotheses",
      "source_locator": "Lemma23.2.8",
      "historical_pdf_ranges_superseded_by_exact_approved_edition": true,
      "human_review_complete": false
    },
    {
      "id": "AN04-HO-G08-09",
      "obligation": "Final first-order correction is order zero",
      "current_proof_nodes": [
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      ],
      "current_source_sha256": "b1b8dad95d3f7f5d90811d7f482585028efd3b9ec124b747eeaf3bcf773c01ba",
      "disposition": "Complete retained and checked current proof under the stated exact hypotheses",
      "source_locator": "Lemma23.2.8",
      "historical_pdf_ranges_superseded_by_exact_approved_edition": true,
      "human_review_complete": false
    },
    {
      "id": "AN04-HO-G08-10",
      "obligation": "Final quotient corrections are order m-2-k",
      "current_proof_nodes": [
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      ],
      "current_source_sha256": "b1b8dad95d3f7f5d90811d7f482585028efd3b9ec124b747eeaf3bcf773c01ba",
      "disposition": "Complete retained and checked current proof under the stated exact hypotheses",
      "source_locator": "Lemma23.2.8",
      "historical_pdf_ranges_superseded_by_exact_approved_edition": true,
      "human_review_complete": false
    },
    {
      "id": "AN04-HO-G08-11",
      "obligation": "Retain the full smoothing remainder",
      "current_proof_nodes": [
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      ],
      "current_source_sha256": "b1b8dad95d3f7f5d90811d7f482585028efd3b9ec124b747eeaf3bcf773c01ba",
      "disposition": "Complete retained and checked current proof under the stated exact hypotheses",
      "source_locator": "Lemma23.2.8",
      "historical_pdf_ranges_superseded_by_exact_approved_edition": true,
      "human_review_complete": false
    },
    {
      "id": "AN04-HO-G08-12",
      "obligation": "Spatial smoothing does not automatically smooth a pure temporal direction",
      "current_proof_nodes": [
        "HC:F1"
      ],
      "current_source_sha256": "b1b8dad95d3f7f5d90811d7f482585028efd3b9ec124b747eeaf3bcf773c01ba",
      "disposition": "Complete retained and checked current proof under the stated exact hypotheses",
      "source_locator": "Lemma23.2.8",
      "historical_pdf_ranges_superseded_by_exact_approved_edition": true,
      "human_review_complete": false
    },
    {
      "id": "AN04-HO-G09-01",
      "obligation": "Microlocal elliptic removal of noncharacteristic covectors",
      "current_proof_nodes": [
        "HC:P1",
        "HC:P2",
        "HC:P3",
        "HC:P4",
        "HC:P5"
      ],
      "current_source_sha256": "b1b8dad95d3f7f5d90811d7f482585028efd3b9ec124b747eeaf3bcf773c01ba",
      "disposition": "Complete retained and checked current proof under the stated exact hypotheses",
      "source_locator": "Theorem23.2.9",
      "historical_pdf_ranges_superseded_by_exact_approved_edition": true,
      "human_review_complete": false
    },
    {
      "id": "AN04-HO-G09-02",
      "obligation": "No pure normal characteristic direction",
      "current_proof_nodes": [
        "HC:P1",
        "HC:P2",
        "HC:P3",
        "HC:P4",
        "HC:P5"
      ],
      "current_source_sha256": "b1b8dad95d3f7f5d90811d7f482585028efd3b9ec124b747eeaf3bcf773c01ba",
      "disposition": "Complete retained and checked current proof under the stated exact hypotheses",
      "source_locator": "Theorem23.2.9",
      "historical_pdf_ranges_superseded_by_exact_approved_edition": true,
      "human_review_complete": false
    },
    {
      "id": "AN04-HO-G09-03",
      "obligation": "Compact base/cone localization",
      "current_proof_nodes": [
        "HC:P1",
        "HC:P2",
        "HC:P3",
        "HC:P4",
        "HC:P5"
      ],
      "current_source_sha256": "b1b8dad95d3f7f5d90811d7f482585028efd3b9ec124b747eeaf3bcf773c01ba",
      "disposition": "Complete retained and checked current proof under the stated exact hypotheses",
      "source_locator": "Theorem23.2.9",
      "historical_pdf_ranges_superseded_by_exact_approved_edition": true,
      "human_review_complete": false
    },
    {
      "id": "AN04-HO-G09-04",
      "obligation": "Localized forcing retains its smaller regular cone",
      "current_proof_nodes": [
        "HC:P1",
        "HC:P2",
        "HC:P3",
        "HC:P4",
        "HC:P5"
      ],
      "current_source_sha256": "b1b8dad95d3f7f5d90811d7f482585028efd3b9ec124b747eeaf3bcf773c01ba",
      "disposition": "Complete retained and checked current proof under the stated exact hypotheses",
      "source_locator": "Theorem23.2.9",
      "historical_pdf_ranges_superseded_by_exact_approved_edition": true,
      "human_review_complete": false
    },
    {
      "id": "AN04-HO-G09-05",
      "obligation": "Tangential smoothing becomes ordinary smoothing after the normal cone cutoff",
      "current_proof_nodes": [
        "HC:P1",
        "HC:P2",
        "HC:P3",
        "HC:P4",
        "HC:P5"
      ],
      "current_source_sha256": "b1b8dad95d3f7f5d90811d7f482585028efd3b9ec124b747eeaf3bcf773c01ba",
      "disposition": "Complete retained and checked current proof under the stated exact hypotheses",
      "source_locator": "Theorem23.2.9",
      "historical_pdf_ranges_superseded_by_exact_approved_edition": true,
      "human_review_complete": false
    },
    {
      "id": "AN04-HO-G09-06",
      "obligation": "Refined branch quotient elliptic at the characteristic point",
      "current_proof_nodes": [
        "HC:P1",
        "HC:P2",
        "HC:P3",
        "HC:P4",
        "HC:P5"
      ],
      "current_source_sha256": "b1b8dad95d3f7f5d90811d7f482585028efd3b9ec124b747eeaf3bcf773c01ba",
      "disposition": "Complete retained and checked current proof under the stated exact hypotheses",
      "source_locator": "Theorem23.2.9",
      "historical_pdf_ranges_superseded_by_exact_approved_edition": true,
      "human_review_complete": false
    },
    {
      "id": "AN04-HO-G09-07",
      "obligation": "Scalar first-order equation for the quotient",
      "current_proof_nodes": [
        "HC:P1",
        "HC:P2",
        "HC:P3",
        "HC:P4",
        "HC:P5"
      ],
      "current_source_sha256": "b1b8dad95d3f7f5d90811d7f482585028efd3b9ec124b747eeaf3bcf773c01ba",
      "disposition": "Complete retained and checked current proof under the stated exact hypotheses",
      "source_locator": "Theorem23.2.9",
      "historical_pdf_ranges_superseded_by_exact_approved_edition": true,
      "human_review_complete": false
    },
    {
      "id": "AN04-HO-G09-08",
      "obligation": "Forced commuting-test argument on a short regular-forcing arc",
      "current_proof_nodes": [
        "HC:P1",
        "HC:P2",
        "HC:P3",
        "HC:P4",
        "HC:P5"
      ],
      "current_source_sha256": "b1b8dad95d3f7f5d90811d7f482585028efd3b9ec124b747eeaf3bcf773c01ba",
      "disposition": "Complete retained and checked current proof under the stated exact hypotheses",
      "source_locator": "Theorem23.2.9",
      "historical_pdf_ranges_superseded_by_exact_approved_edition": true,
      "human_review_complete": false
    },
    {
      "id": "AN04-HO-G09-09",
      "obligation": "Both directions along the branch",
      "current_proof_nodes": [
        "HC:P1",
        "HC:P2",
        "HC:P3",
        "HC:P4",
        "HC:P5"
      ],
      "current_source_sha256": "b1b8dad95d3f7f5d90811d7f482585028efd3b9ec124b747eeaf3bcf773c01ba",
      "disposition": "Complete retained and checked current proof under the stated exact hypotheses",
      "source_locator": "Theorem23.2.9",
      "historical_pdf_ranges_superseded_by_exact_approved_edition": true,
      "human_review_complete": false
    },
    {
      "id": "AN04-HO-G09-10",
      "obligation": "Exact full spacetime Hamilton vector comparison",
      "current_proof_nodes": [
        "HC:P1",
        "HC:P2",
        "HC:P3",
        "HC:P4",
        "HC:P5"
      ],
      "current_source_sha256": "b1b8dad95d3f7f5d90811d7f482585028efd3b9ec124b747eeaf3bcf773c01ba",
      "disposition": "Complete retained and checked current proof under the stated exact hypotheses",
      "source_locator": "Theorem23.2.9",
      "historical_pdf_ranges_superseded_by_exact_approved_edition": true,
      "human_review_complete": false
    },
    {
      "id": "AN04-HO-G09-11",
      "obligation": "Nonzero real quotient changes parameter orientation but not arcs",
      "current_proof_nodes": [
        "HC:P1",
        "HC:P2",
        "HC:P3",
        "HC:P4",
        "HC:P5"
      ],
      "current_source_sha256": "b1b8dad95d3f7f5d90811d7f482585028efd3b9ec124b747eeaf3bcf773c01ba",
      "disposition": "Complete retained and checked current proof under the stated exact hypotheses",
      "source_locator": "Theorem23.2.9",
      "historical_pdf_ranges_superseded_by_exact_approved_edition": true,
      "human_review_complete": false
    },
    {
      "id": "AN04-HO-G09-12",
      "obligation": "Transfer through the elliptic quotient",
      "current_proof_nodes": [
        "HC:P1",
        "HC:P2",
        "HC:P3",
        "HC:P4",
        "HC:P5"
      ],
      "current_source_sha256": "b1b8dad95d3f7f5d90811d7f482585028efd3b9ec124b747eeaf3bcf773c01ba",
      "disposition": "Complete retained and checked current proof under the stated exact hypotheses",
      "source_locator": "Theorem23.2.9",
      "historical_pdf_ranges_superseded_by_exact_approved_edition": true,
      "human_review_complete": false
    },
    {
      "id": "AN04-HO-G09-13",
      "obligation": "Transfer through the original ordinary cutoff",
      "current_proof_nodes": [
        "HC:P1",
        "HC:P2",
        "HC:P3",
        "HC:P4",
        "HC:P5"
      ],
      "current_source_sha256": "b1b8dad95d3f7f5d90811d7f482585028efd3b9ec124b747eeaf3bcf773c01ba",
      "disposition": "Complete retained and checked current proof under the stated exact hypotheses",
      "source_locator": "Theorem23.2.9",
      "historical_pdf_ranges_superseded_by_exact_approved_edition": true,
      "human_review_complete": false
    },
    {
      "id": "AN04-HO-G09-14",
      "obligation": "Closedness and relative openness of singular arcs",
      "current_proof_nodes": [
        "HC:P1",
        "HC:P2",
        "HC:P3",
        "HC:P4",
        "HC:P5"
      ],
      "current_source_sha256": "b1b8dad95d3f7f5d90811d7f482585028efd3b9ec124b747eeaf3bcf773c01ba",
      "disposition": "Complete retained and checked current proof under the stated exact hypotheses",
      "source_locator": "Theorem23.2.9",
      "historical_pdf_ranges_superseded_by_exact_approved_edition": true,
      "human_review_complete": false
    },
    {
      "id": "AN04-HO-G09-15",
      "obligation": "Strict hyperbolic conclusion does not close general Chapter26 propagation",
      "current_proof_nodes": [
        "HC:P1",
        "HC:P2",
        "HC:P3",
        "HC:P4",
        "HC:P5"
      ],
      "current_source_sha256": "b1b8dad95d3f7f5d90811d7f482585028efd3b9ec124b747eeaf3bcf773c01ba",
      "disposition": "Complete retained and checked current proof under the stated exact hypotheses",
      "source_locator": "Theorem23.2.9",
      "historical_pdf_ranges_superseded_by_exact_approved_edition": true,
      "human_review_complete": false
    },
    {
      "id": "AN04-HO-G10-01",
      "obligation": "Source has a barred extendible distribution hypothesis",
      "current_proof_nodes": [
        "HC:B1",
        "HC:B2",
        "HC:B3",
        "HC:B4",
        "HC:B5",
        "HC:B6",
        "HC:B7",
        "HC:B8",
        "HC:B9",
        "HC:B10",
        "HC:B11",
        "HC:B12"
      ],
      "current_source_sha256": "b1b8dad95d3f7f5d90811d7f482585028efd3b9ec124b747eeaf3bcf773c01ba",
      "disposition": "Complete retained and checked current proof under the stated exact hypotheses",
      "source_locator": "Theorem23.2.10 and23.2.9boundary",
      "historical_pdf_ranges_superseded_by_exact_approved_edition": true,
      "human_review_complete": false
    },
    {
      "id": "AN04-HO-G10-02",
      "obligation": "Forcing belongs to the exact noncharacteristic boundary class",
      "current_proof_nodes": [
        "HC:B1",
        "HC:B2",
        "HC:B3",
        "HC:B4",
        "HC:B5",
        "HC:B6",
        "HC:B7",
        "HC:B8",
        "HC:B9",
        "HC:B10",
        "HC:B11",
        "HC:B12"
      ],
      "current_source_sha256": "b1b8dad95d3f7f5d90811d7f482585028efd3b9ec124b747eeaf3bcf773c01ba",
      "disposition": "Complete retained and checked current proof under the stated exact hypotheses",
      "source_locator": "Theorem23.2.10 and23.2.9boundary",
      "historical_pdf_ranges_superseded_by_exact_approved_edition": true,
      "human_review_complete": false
    },
    {
      "id": "AN04-HO-G10-03",
      "obligation": "Unique N extension and all normal derivatives",
      "current_proof_nodes": [
        "HC:B1",
        "HC:B2",
        "HC:B3",
        "HC:B4",
        "HC:B5",
        "HC:B6",
        "HC:B7",
        "HC:B8",
        "HC:B9",
        "HC:B10",
        "HC:B11",
        "HC:B12"
      ],
      "current_source_sha256": "b1b8dad95d3f7f5d90811d7f482585028efd3b9ec124b747eeaf3bcf773c01ba",
      "disposition": "Complete retained and checked current proof under the stated exact hypotheses",
      "source_locator": "Theorem23.2.10 and23.2.9boundary",
      "historical_pdf_ranges_superseded_by_exact_approved_edition": true,
      "human_review_complete": false
    },
    {
      "id": "AN04-HO-G10-04",
      "obligation": "Intrinsic Cauchy traces for that dual topology",
      "current_proof_nodes": [
        "HC:B1",
        "HC:B2",
        "HC:B3",
        "HC:B4",
        "HC:B5",
        "HC:B6",
        "HC:B7",
        "HC:B8",
        "HC:B9",
        "HC:B10",
        "HC:B11",
        "HC:B12"
      ],
      "current_source_sha256": "b1b8dad95d3f7f5d90811d7f482585028efd3b9ec124b747eeaf3bcf773c01ba",
      "disposition": "Complete retained and checked current proof under the stated exact hypotheses",
      "source_locator": "Theorem23.2.10 and23.2.9boundary",
      "historical_pdf_ranges_superseded_by_exact_approved_edition": true,
      "human_review_complete": false
    },
    {
      "id": "AN04-HO-G10-05",
      "obligation": "Compressed boundary covectors and embedded tangential bundle",
      "current_proof_nodes": [
        "HC:B1",
        "HC:B2",
        "HC:B3",
        "HC:B4",
        "HC:B5",
        "HC:B6",
        "HC:B7",
        "HC:B8",
        "HC:B9",
        "HC:B10",
        "HC:B11",
        "HC:B12"
      ],
      "current_source_sha256": "b1b8dad95d3f7f5d90811d7f482585028efd3b9ec124b747eeaf3bcf773c01ba",
      "disposition": "Complete retained and checked current proof under the stated exact hypotheses",
      "source_locator": "Theorem23.2.10 and23.2.9boundary",
      "historical_pdf_ranges_superseded_by_exact_approved_edition": true,
      "human_review_complete": false
    },
    {
      "id": "AN04-HO-G10-06",
      "obligation": "Forward action includes forcing singularities",
      "current_proof_nodes": [
        "HC:B1",
        "HC:B2",
        "HC:B3",
        "HC:B4",
        "HC:B5",
        "HC:B6",
        "HC:B7",
        "HC:B8",
        "HC:B9",
        "HC:B10",
        "HC:B11",
        "HC:B12"
      ],
      "current_source_sha256": "b1b8dad95d3f7f5d90811d7f482585028efd3b9ec124b747eeaf3bcf773c01ba",
      "disposition": "Complete retained and checked current proof under the stated exact hypotheses",
      "source_locator": "Theorem23.2.10 and23.2.9boundary",
      "historical_pdf_ranges_superseded_by_exact_approved_edition": true,
      "human_review_complete": false
    },
    {
      "id": "AN04-HO-G10-07",
      "obligation": "Trace inclusion for every normal jet",
      "current_proof_nodes": [
        "HC:B1",
        "HC:B2",
        "HC:B3",
        "HC:B4",
        "HC:B5",
        "HC:B6",
        "HC:B7",
        "HC:B8",
        "HC:B9",
        "HC:B10",
        "HC:B11",
        "HC:B12"
      ],
      "current_source_sha256": "b1b8dad95d3f7f5d90811d7f482585028efd3b9ec124b747eeaf3bcf773c01ba",
      "disposition": "Complete retained and checked current proof under the stated exact hypotheses",
      "source_locator": "Theorem23.2.10 and23.2.9boundary",
      "historical_pdf_ranges_superseded_by_exact_approved_edition": true,
      "human_review_complete": false
    },
    {
      "id": "AN04-HO-G10-08",
      "obligation": "Separate candidate outside forcing and all jet wavefronts",
      "current_proof_nodes": [
        "HC:B1",
        "HC:B2",
        "HC:B3",
        "HC:B4",
        "HC:B5",
        "HC:B6",
        "HC:B7",
        "HC:B8",
        "HC:B9",
        "HC:B10",
        "HC:B11",
        "HC:B12"
      ],
      "current_source_sha256": "b1b8dad95d3f7f5d90811d7f482585028efd3b9ec124b747eeaf3bcf773c01ba",
      "disposition": "Complete retained and checked current proof under the stated exact hypotheses",
      "source_locator": "Theorem23.2.10 and23.2.9boundary",
      "historical_pdf_ranges_superseded_by_exact_approved_edition": true,
      "human_review_complete": false
    },
    {
      "id": "AN04-HO-G10-09",
      "obligation": "Branchwise transported tests retain supports",
      "current_proof_nodes": [
        "HC:B1",
        "HC:B2",
        "HC:B3",
        "HC:B4",
        "HC:B5",
        "HC:B6",
        "HC:B7",
        "HC:B8",
        "HC:B9",
        "HC:B10",
        "HC:B11",
        "HC:B12"
      ],
      "current_source_sha256": "b1b8dad95d3f7f5d90811d7f482585028efd3b9ec124b747eeaf3bcf773c01ba",
      "disposition": "Complete retained and checked current proof under the stated exact hypotheses",
      "source_locator": "Theorem23.2.10 and23.2.9boundary",
      "historical_pdf_ranges_superseded_by_exact_approved_edition": true,
      "human_review_complete": false
    },
    {
      "id": "AN04-HO-G10-10",
      "obligation": "All tangential smoothing actions use the original N topology",
      "current_proof_nodes": [
        "HC:B1",
        "HC:B2",
        "HC:B3",
        "HC:B4",
        "HC:B5",
        "HC:B6",
        "HC:B7",
        "HC:B8",
        "HC:B9",
        "HC:B10",
        "HC:B11",
        "HC:B12"
      ],
      "current_source_sha256": "b1b8dad95d3f7f5d90811d7f482585028efd3b9ec124b747eeaf3bcf773c01ba",
      "disposition": "Complete retained and checked current proof under the stated exact hypotheses",
      "source_locator": "Theorem23.2.10 and23.2.9boundary",
      "historical_pdf_ranges_superseded_by_exact_approved_edition": true,
      "human_review_complete": false
    },
    {
      "id": "AN04-HO-G10-11",
      "obligation": "Justify collar smoothness by the actual compact cone argument",
      "current_proof_nodes": [
        "HC:B1",
        "HC:B2",
        "HC:B3",
        "HC:B4",
        "HC:B5",
        "HC:B6",
        "HC:B7",
        "HC:B8",
        "HC:B9",
        "HC:B10",
        "HC:B11",
        "HC:B12"
      ],
      "current_source_sha256": "b1b8dad95d3f7f5d90811d7f482585028efd3b9ec124b747eeaf3bcf773c01ba",
      "disposition": "Complete retained and checked current proof under the stated exact hypotheses",
      "source_locator": "Theorem23.2.10 and23.2.9boundary",
      "historical_pdf_ranges_superseded_by_exact_approved_edition": true,
      "human_review_complete": false
    },
    {
      "id": "AN04-HO-G10-12",
      "obligation": "All trace coefficient terms act on the prescribed jets",
      "current_proof_nodes": [
        "HC:B1",
        "HC:B2",
        "HC:B3",
        "HC:B4",
        "HC:B5",
        "HC:B6",
        "HC:B7",
        "HC:B8",
        "HC:B9",
        "HC:B10",
        "HC:B11",
        "HC:B12"
      ],
      "current_source_sha256": "b1b8dad95d3f7f5d90811d7f482585028efd3b9ec124b747eeaf3bcf773c01ba",
      "disposition": "Complete retained and checked current proof under the stated exact hypotheses",
      "source_locator": "Theorem23.2.10 and23.2.9boundary",
      "historical_pdf_ranges_superseded_by_exact_approved_edition": true,
      "human_review_complete": false
    },
    {
      "id": "AN04-HO-G10-13",
      "obligation": "Scalar regularity with smooth localized source and trace",
      "current_proof_nodes": [
        "HC:B1",
        "HC:B2",
        "HC:B3",
        "HC:B4",
        "HC:B5",
        "HC:B6",
        "HC:B7",
        "HC:B8",
        "HC:B9",
        "HC:B10",
        "HC:B11",
        "HC:B12"
      ],
      "current_source_sha256": "b1b8dad95d3f7f5d90811d7f482585028efd3b9ec124b747eeaf3bcf773c01ba",
      "disposition": "Complete retained and checked current proof under the stated exact hypotheses",
      "source_locator": "Theorem23.2.10 and23.2.9boundary",
      "historical_pdf_ranges_superseded_by_exact_approved_edition": true,
      "human_review_complete": false
    },
    {
      "id": "AN04-HO-G10-14",
      "obligation": "Weighted ellipticity of the complete quotient system",
      "current_proof_nodes": [
        "HC:B1",
        "HC:B2",
        "HC:B3",
        "HC:B4",
        "HC:B5",
        "HC:B6",
        "HC:B7",
        "HC:B8",
        "HC:B9",
        "HC:B10",
        "HC:B11",
        "HC:B12"
      ],
      "current_source_sha256": "b1b8dad95d3f7f5d90811d7f482585028efd3b9ec124b747eeaf3bcf773c01ba",
      "disposition": "Complete retained and checked current proof under the stated exact hypotheses",
      "source_locator": "Theorem23.2.10 and23.2.9boundary",
      "historical_pdf_ranges_superseded_by_exact_approved_edition": true,
      "human_review_complete": false
    },
    {
      "id": "AN04-HO-G10-15",
      "obligation": "Ordered matrix parametrix with row and column orders",
      "current_proof_nodes": [
        "HC:B1",
        "HC:B2",
        "HC:B3",
        "HC:B4",
        "HC:B5",
        "HC:B6",
        "HC:B7",
        "HC:B8",
        "HC:B9",
        "HC:B10",
        "HC:B11",
        "HC:B12"
      ],
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    },
    {
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        "HC:B1",
        "HC:B2",
        "HC:B3",
        "HC:B4",
        "HC:B5",
        "HC:B6",
        "HC:B7",
        "HC:B8",
        "HC:B9",
        "HC:B10",
        "HC:B11",
        "HC:B12"
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    },
    {
      "id": "AN04-HO-G10-17",
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        "HC:B1",
        "HC:B2",
        "HC:B3",
        "HC:B4",
        "HC:B5",
        "HC:B6",
        "HC:B7",
        "HC:B8",
        "HC:B9",
        "HC:B10",
        "HC:B11",
        "HC:B12"
      ],
      "current_source_sha256": "b1b8dad95d3f7f5d90811d7f482585028efd3b9ec124b747eeaf3bcf773c01ba",
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    },
    {
      "id": "AN04-HO-G10-18",
      "obligation": "Both inclusions in the compressed boundary equality",
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        "HC:B2",
        "HC:B3",
        "HC:B4",
        "HC:B5",
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    },
    {
      "id": "AN04-HO-G10-19",
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        "HC:B1",
        "HC:B2",
        "HC:B3",
        "HC:B4",
        "HC:B5",
        "HC:B6",
        "HC:B7",
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    },
    {
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        "HC:B1",
        "HC:B2",
        "HC:B3",
        "HC:B4",
        "HC:B5",
        "HC:B6",
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    },
    {
      "id": "AN04-HO-G11-01",
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        "HC:X1",
        "HC:X2",
        "HC:X3",
        "HC:X4",
        "HC:X5",
        "HC:X6",
        "HC:X7",
        "HC:X8",
        "HC:X9",
        "HC:X10",
        "HC:X11",
        "HC:X12",
        "HC:X13",
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    },
    {
      "id": "AN04-HO-G11-02",
      "obligation": "Forced wave zero-frequency continuation",
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        "HC:X1",
        "HC:X2",
        "HC:X3",
        "HC:X4",
        "HC:X5",
        "HC:X6",
        "HC:X7",
        "HC:X8",
        "HC:X9",
        "HC:X10",
        "HC:X11",
        "HC:X12",
        "HC:X13",
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    },
    {
      "id": "AN04-HO-G11-03",
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        "HC:X1",
        "HC:X2",
        "HC:X3",
        "HC:X4",
        "HC:X5",
        "HC:X6",
        "HC:X7",
        "HC:X8",
        "HC:X9",
        "HC:X10",
        "HC:X11",
        "HC:X12",
        "HC:X13",
        "HC:X14",
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    },
    {
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        "HC:X1",
        "HC:X2",
        "HC:X3",
        "HC:X4",
        "HC:X5",
        "HC:X6",
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        "HC:X8",
        "HC:X9",
        "HC:X10",
        "HC:X11",
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        "HC:X14",
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    },
    {
      "id": "AN04-HO-G11-05",
      "obligation": "Repeated-root high-frequency jet loss",
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        "HC:X1",
        "HC:X2",
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        "HC:X4",
        "HC:X5",
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        "HC:X7",
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        "HC:X11",
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    },
    {
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        "HC:X1",
        "HC:X2",
        "HC:X3",
        "HC:X4",
        "HC:X5",
        "HC:X6",
        "HC:X7",
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    },
    {
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        "HC:X1",
        "HC:X2",
        "HC:X3",
        "HC:X4",
        "HC:X5",
        "HC:X6",
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        "HC:X11",
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    },
    {
      "id": "AN04-HO-G11-08",
      "obligation": "Extendible versus arbitrary interior distributions",
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        "HC:X1",
        "HC:X2",
        "HC:X3",
        "HC:X4",
        "HC:X5",
        "HC:X6",
        "HC:X7",
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        "HC:X10",
        "HC:X11",
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    },
    {
      "id": "AN04-HO-G11-09",
      "obligation": "Forcing boundary singularities versus initial jets",
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        "HC:X1",
        "HC:X2",
        "HC:X3",
        "HC:X4",
        "HC:X5",
        "HC:X6",
        "HC:X7",
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    },
    {
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    },
    {
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    {
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    },
    {
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    {
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    {
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    {
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    {
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