data/learning.json

{
  "categories": [
    {
      "id": "core",
      "name": "Core Concepts"
    },
    {
      "id": "calculus",
      "name": "Calculus Topics"
    }
  ],
  "symbols": [
    {
      "id": "lim",
      "symbol": "lim",
      "name": "Limit operator",
      "meaning": "Describes the value a function approaches."
    },
    {
      "id": "integral",
      "symbol": "∫",
      "name": "Integral operator",
      "meaning": "Represents accumulation and area."
    }
  ],
  "formulas": [
    {
      "id": "power_rule",
      "name": "Power Rule",
      "plain": "d/dx (x^n) = n*x^(n-1)",
      "latex": "\\frac{d}{dx}x^n = nx^{n-1}",
      "tags": [
        "derivatives"
      ]
    }
  ],
  "topics": [
    {
      "id": "topic-template-derivative",
      "category": "calculus",
      "title": "Derivative Workflow Template",
      "summary": "Template entry showing how a concept page is structured.",
      "narrative": "Use this section for the plain-language teaching narrative. Explain what a derivative means, when to use it, and why the rule works.",
      "symbols": [
        "lim"
      ],
      "formulas": [
        "power_rule"
      ],
      "examples": [
        {
          "id": "example-template-1",
          "title": "Example Template",
          "problem": "d/dx (x^3)",
          "steps": [
            {
              "title": "Identify rule",
              "explanation": "Use the power rule because the function is x raised to a power.",
              "math": "d/dx (x^3)"
            },
            {
              "title": "Apply rule",
              "explanation": "Bring exponent down and subtract one from exponent.",
              "math": "3x^2"
            }
          ]
        }
      ],
      "related": [
        "topic-template-limit"
      ]
    },
    {
      "id": "topic-template-limit",
      "category": "core",
      "title": "Limit Workflow Template",
      "summary": "Template entry for linked-topic navigation.",
      "narrative": "Use this section to explain limit intuition, one-sided limits, and infinity behavior in plain language.",
      "symbols": [
        "lim"
      ],
      "formulas": [],
      "examples": [],
      "related": [
        "topic-template-derivative"
      ]
    }
  ]
}