{
  "title": "Mathematical Gauge Theory Dependency Map",
  "question": "Which configuration, stabilizer, elliptic, topological, Fredholm-family, and probabilistic inputs license the successive conclusions of mathematical gauge theory?",
  "takeaway": "A declared bundle and gauge group define the action groupoid; stabilizers control local slices and elliptic deformation theory, while bundle and gauge-group topology and Fredholm-family holonomy create independent global obstructions, and none alone constructs a continuum gauge measure.",
  "figure_type": "dependency",
  "schematic": true,
  "scale": "not to scale",
  "nodes": [
    {
      "id": "n0",
      "label": "fixed $P\\to M$, regularity, boundary group\\\\action groupoid $[\\mathcal A/\\mathcal G]$"
    },
    {
      "id": "n1",
      "label": "stabilizers and orbit types\\\\slice $\\mathcal S_A/\\mathcal G_A$"
    },
    {
      "id": "n2",
      "label": "Faddeev--Popov and elliptic complex\\\\$H_A^0,H_A^1,H_A^2$"
    },
    {
      "id": "n3",
      "label": "bundle and gauge-group topology\\\\sectors and Gribov--Singer obstruction"
    },
    {
      "id": "n4",
      "label": "derived moduli and Fredholm families\\\\determinant or Pfaffian line"
    },
    {
      "id": "n5",
      "label": "separately proved regulator limit\\\\positive continuum state or measure"
    },
    {
      "id": "branch",
      "label": "bundle sectors and based gauge topology\\\\large transformations and no global section"
    }
  ],
  "edges": [
    {
      "from": "n0",
      "to": "n1",
      "label": "stratify",
      "logical_status": "licensed implication"
    },
    {
      "from": "n1",
      "to": "n2",
      "label": "linearize",
      "logical_status": "licensed implication"
    },
    {
      "from": "n2",
      "to": "n3",
      "label": "globalize",
      "logical_status": "licensed implication"
    },
    {
      "from": "n3",
      "to": "n4",
      "label": "family index",
      "logical_status": "licensed implication"
    },
    {
      "from": "n4",
      "to": "n5",
      "label": "take limit",
      "logical_status": "licensed implication"
    },
    {
      "from": "n2",
      "to": "branch",
      "label": "independent global path",
      "logical_status": "licensed implication"
    }
  ]
}