{
  "schema": "AN04-restored-oscillatory-proof-map/v1",
  "proofs": [
    {
      "id": "OSC:O1",
      "source": "oscillatory-distributions-and-order.md",
      "source_sha256": "4986c817394f51267692cc1a800bef8f73cdfa0f557997873f6b02f7f5159aef",
      "proof_locator": "## 1. Frequency cutoffs define a distribution",
      "dependencies": [
        "U001:U001-A4",
        "U001:P8-smooth",
        "P3:M3",
        "P3:M4",
        "P3:M8"
      ]
    },
    {
      "id": "OSC:O2",
      "source": "oscillatory-distributions-and-order.md",
      "source_sha256": "4986c817394f51267692cc1a800bef8f73cdfa0f557997873f6b02f7f5159aef",
      "proof_locator": "## 2. The directions where singularities can occur",
      "dependencies": [
        "OSC:O1",
        "U001:U001-A4",
        "U001:F0-COMP"
      ]
    },
    {
      "id": "OSC:O3",
      "source": "oscillatory-distributions-and-order.md",
      "source_sha256": "4986c817394f51267692cc1a800bef8f73cdfa0f557997873f6b02f7f5159aef",
      "proof_locator": "## 3. Order is fixed by the dimension balance",
      "dependencies": [
        "PH:F1",
        "U001:U001-A5"
      ]
    },
    {
      "id": "OSC:O4",
      "source": "oscillatory-distributions-and-order.md",
      "source_sha256": "4986c817394f51267692cc1a800bef8f73cdfa0f557997873f6b02f7f5159aef",
      "proof_locator": "## 4. Fourier reduction near a frequency graph",
      "dependencies": [
        "OSC:O1",
        "OSC:O3",
        "GEO:C4",
        "PH:F1",
        "U001:U001-6.1",
        "U001:U001-7.2",
        "U001:U001-A5"
      ]
    },
    {
      "id": "OSC:O5",
      "source": "oscillatory-distributions-and-order.md",
      "source_sha256": "4986c817394f51267692cc1a800bef8f73cdfa0f557997873f6b02f7f5159aef",
      "proof_locator": "## 5. Changing phase variables and adding a quadratic block",
      "dependencies": [
        "OSC:O1",
        "OSC:O4",
        "U001:U001-3.2",
        "U001:U001-6.1",
        "U001:U001-A4",
        "U001:P21.6"
      ]
    },
    {
      "id": "OSC:O6",
      "source": "oscillatory-distributions-and-order.md",
      "source_sha256": "4986c817394f51267692cc1a800bef8f73cdfa0f557997873f6b02f7f5159aef",
      "proof_locator": "## 6. Examples and the endpoint regularity",
      "dependencies": [
        "OSC:O1",
        "OSC:O2",
        "OSC:O3",
        "U001:U001-A1",
        "U001:U001-A2",
        "U001:U001-A4"
      ]
    },
    {
      "id": "OSC:EX1",
      "source": "oscillatory-distributions-and-order.md",
      "source_sha256": "4986c817394f51267692cc1a800bef8f73cdfa0f557997873f6b02f7f5159aef",
      "proof_locator": "**Exercise 7.1 ",
      "dependencies": [
        "OSC:O2",
        "OSC:O3",
        "OSC:O6"
      ]
    },
    {
      "id": "OSC:EX2",
      "source": "oscillatory-distributions-and-order.md",
      "source_sha256": "4986c817394f51267692cc1a800bef8f73cdfa0f557997873f6b02f7f5159aef",
      "proof_locator": "**Exercise 7.2 ",
      "dependencies": [
        "OSC:O6",
        "U001:U001-A2"
      ]
    },
    {
      "id": "OSC:EX3",
      "source": "oscillatory-distributions-and-order.md",
      "source_sha256": "4986c817394f51267692cc1a800bef8f73cdfa0f557997873f6b02f7f5159aef",
      "proof_locator": "**Exercise 7.3 ",
      "dependencies": [
        "OSC:O5"
      ]
    },
    {
      "id": "OSC:EX4",
      "source": "oscillatory-distributions-and-order.md",
      "source_sha256": "4986c817394f51267692cc1a800bef8f73cdfa0f557997873f6b02f7f5159aef",
      "proof_locator": "**Exercise 7.4 ",
      "dependencies": [
        "OSC:O4"
      ]
    },
    {
      "id": "OSC:EX5",
      "source": "oscillatory-distributions-and-order.md",
      "source_sha256": "4986c817394f51267692cc1a800bef8f73cdfa0f557997873f6b02f7f5159aef",
      "proof_locator": "**Exercise 7.5 ",
      "dependencies": [
        "OSC:O1",
        "P3:M3"
      ]
    }
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    "P12.6",
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    "P14.2-inverse",
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    "P14.3",
    "P15.1",
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    "P16.2",
    "P16.3",
    "P17.1",
    "P17.2",
    "P17.3",
    "P17.4",
    "P17.4-grid",
    "P17.5-order",
    "P17.5-upper",
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    "notice": "The elementary proof providers have exact earlier-programme routes in C10/C20, with public PDF destinations and editable TeX passages. The author English edition remains available. Human source text and figures stay external to this CC0 export and retain their own terms."
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}