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  "body": "\n## Statement\n\nA tame [[knot|QYEAZTYGPT]] $K \\subset S^3$ is a *ribbon knot* if it bounds an immersed disk $D$ in $S^3$ whose only self-intersections are ribbon singularities.\nA ribbon singularity is an arc of double points with two preimages in $D$.\nOne preimage is an arc interior to $D$, and the other is an arc meeting $\\partial D$ in its two endpoints.\nThe conjecture states that every smoothly [[slice knot|P68G28E4AD]] is a ribbon knot.\n\n## Remarks\n\nThe converse holds: pushing the interior of a ribbon disk into $B^4$ removes the singularities, so every ribbon knot is slice.\nEquivalently, $K$ is ribbon if and only if it bounds a smoothly embedded disk in $B^4$ on which the radial distance function has no local maxima.\nLisca proved the conjecture for two-bridge knots.\nThe conjecture is open in general.\n\n## Explanations\n\n### L1 human\n\nA ribbon knot bounds a disk in ordinary space that passes through itself only in a mild way.\nThe disk looks like a ribbon threaded through a slit in itself.\nSuch a disk can be pushed into four dimensions so that it no longer meets itself, so ribbon knots are slice.\nThe conjecture says that this is the only way a knot can be slice.\nIt would turn a four-dimensional question into a three-dimensional one.\n",
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    "about": [
      "P68G28E4AD"
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    "history": {
      "first_stated": "1962",
      "posed_by": "Ralph Fox"
    },
    "kind": "conjecture",
    "msc": [
      "57K10",
      "57K40"
    ],
    "name": "Slice-ribbon conjecture",
    "sources": [
      {
        "url": "https://en.wikipedia.org/wiki/Slice_knot"
      }
    ],
    "tag": "EQB39X4HGB",
    "uses": [
      "QYEAZTYGPT",
      "P68G28E4AD"
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  "kind": "conjecture",
  "link": "https://math2.tamnd.com/node/EQB39X4HGB/",
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      "target": "P68G28E4AD"
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      "target": "P68G28E4AD"
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  "markdown": "https://math2.tamnd.com/node/EQB39X4HGB.md",
  "msc": [
    "57K10",
    "57K40"
  ],
  "name": "Slice-ribbon conjecture",
  "prov": null,
  "role": "",
  "source": "https://github.com/tamnd/math2/blob/main/nodes/EQB/EQB39X4HGB.md",
  "status": null,
  "tag": "EQB39X4HGB",
  "uri": "m2://EQB39X4HGB",
  "url": "https://math2.tamnd.com/wiki/slice-ribbon-conjecture/",
  "writing": {
    "tag": "EQB39X4HGB",
    "kind": "conjecture",
    "level": "W0",
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