{
  "schemaVersion": "1.0",
  "slug": "prerequisite-order-60-skill-graph-test",
  "title": "When Does a Learning Path Become a Dependency Trap? A 60-Skill Graph Test",
  "runDate": "2026-07-28",
  "executed": true,
  "sanitized": true,
  "question": "Which graph properties make a proposed learning path impossible, overconstrained, or dependent on a single bottleneck?",
  "baseline": "A visually tidy sequence can still contain cycles, excessive prerequisites, or nodes whose removal blocks much of the path.",
  "protocol": [
    "Freeze sixty skill nodes in three tracks with required prerequisite edges.",
    "Calculate incoming and outgoing degree, self-cycles, and overconstraint flags for every node.",
    "Report structural defects without claiming that the graph predicts human learning."
  ],
  "sample": {
    "skills": 60,
    "tracks": 3
  },
  "results": {
    "selfCycles": 0,
    "overconstrainedNodes": 0,
    "zeroPrerequisiteEntries": 3,
    "maximumOutDegree": 2
  },
  "negativeFindings": [
    "No node exceeded three prerequisites, so overconstraint was not the principal defect in this frozen graph."
  ],
  "limitations": [
    "The graph represents declared dependencies only; it cannot reveal whether a learner already possesses equivalent prior knowledge."
  ],
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      "id": "analysis-1",
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      "selfCycle": false,
      "overconstrained": false
    },
    {
      "id": "analysis-2",
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      "level": 2,
      "prerequisites": [
        "analysis-1"
      ],
      "inDegree": 1,
      "outDegree": 1,
      "selfCycle": false,
      "overconstrained": false
    },
    {
      "id": "analysis-3",
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      "level": 3,
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      ],
      "inDegree": 1,
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      "overconstrained": false
    },
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    },
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    },
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}