Understanding the Stemfard API JSON response structure

Every Stemfard API response returns a consistent JSON object regardless of which endpoint you call. The fields present in a given response depend on the api_level you request and which optional parameters you enable. Understanding this structure helps you write resilient parsing logic and lets you display only the data your application actually needs.

Top-level fields

object

required

Request metadata returned with every response. Includes the result_name used to key the answer in result, the operation name, and other contextual identifiers.

Show properties

string

The name used as the key for the computed answer in the result object. Defaults to "ans". You can override this with the result_name request parameter.

string

The mathematical operation performed (e.g., "add", "matmul", "row-mean").

object

required

Topic classification for the operation. Present in lite, standard, and detailed responses.

Show properties

string

High-level mathematical domain (e.g., "Linear Algebra").

string

Narrower classification within the topic (e.g., "Matrix Arithmetic", "Matrix Statistics").

object

required

The computed answer. The key inside this object matches the result_name from metadata (default "ans"). Present in all API levels.

object

A human-readable statement of the problem. Present only in detailed responses.

Show properties

string

Full problem statement as a string (e.g., "Find the sum of matrices A and B").

object

The normalized version of your input parameters as interpreted by the API. Returned when you set request_params: true in the request. Available in detailed mode only.

object

Intermediate calculation data generated during computation. Present in detailed responses. Useful for debugging or displaying partial results.

array

An ordered array of step-by-step solution objects. Present in standard and detailed responses. Each element describes one step in the solution process. The format of step content (HTML, LaTeX, or speech) is controlled by the steps_output_formats request parameter.

Show step object properties

integer

Step number, starting from 1.

string

Plain-text explanation of what this step does.

string

The mathematical expression at this step, in the requested output format.

Links to related Stemfard API endpoints. Only included in detailed responses when you set related: true in the request.

Show item properties

string

Human-readable label describing the related operation.

string

Full URL to the related endpoint.

array

Curated links to educational resources and pathway endpoints relevant to the operation. Only included in detailed responses when you set learning_pathways: true in the request.

Show item properties

string

Label for the learning pathway.

string

URL to the pathway resource.

object

Usage hints and syntax guidance for the called endpoint. Present in detailed responses.

Show properties

string

A short string showing the expected call signature (e.g., "derivative(expression, variable)").

object

Computed properties of the result object (e.g., degree, domain, whether the result is a polynomial). Returned when you set properties: true in the request. Available in detailed mode only.

Field availability by level

Field	`lite`	`standard`	`detailed`
`metadata`	Yes	Yes	Yes
`taxonomy`	Yes	Yes	Yes
`result`	Yes	Yes	Yes
`steps`	—	Yes	Yes
`problem`	—	—	Yes
`request_normalized`	—	—	Yes (opt-in)
`intermediate`	—	—	Yes
`related`	—	—	Yes (opt-in)
`learning_pathways`	—	—	Yes (opt-in)
`syntax`	—	—	Yes
`properties`	—	—	Yes (opt-in)

Sample detailed response

The following example shows a complete detailed response with all optional fields enabled.

detailed response

{
  "metadata": {
    "result_name": "product",
    "operation": "matmul"
  },
  "taxonomy": {
    "topic": "Linear Algebra",
    "subtopic": "Matrix Arithmetic"
  },
  "problem": {
    "statement": "Compute the matrix product of A and B"
  },
  "request_normalized": {
    "a": [[2, 7], [4, -1]],
    "b": [[1, 0], [0, 1]],
    "operation": "matmul"
  },
  "result": {
    "product": [[2, 7], [4, -1]]
  },
  "intermediate": {
    "steps_count": 4
  },
  "steps": [
    {
      "step": 1,
      "description": "Multiply row 1 of A by column 1 of B",
      "expression": "(2×1) + (7×0) = 2"
    },
    {
      "step": 2,
      "description": "Multiply row 1 of A by column 2 of B",
      "expression": "(2×0) + (7×1) = 7"
    },
    {
      "step": 3,
      "description": "Multiply row 2 of A by column 1 of B",
      "expression": "(4×1) + (-1×0) = 4"
    },
    {
      "step": 4,
      "description": "Multiply row 2 of A by column 2 of B",
      "expression": "(4×0) + (-1×1) = -1"
    }
  ],
  "related": [
    {
      "label": "Matrix addition",
      "href": "/api/v1/mathematics/linear-algebra/matrix-operations/matrix-arithmetic/add"
    },
    {
      "label": "Matrix statistics",
      "href": "/api/v1/mathematics/linear-algebra/matrix-operations/matrix-statistics"
    }
  ],
  "learning_pathways": [
    {
      "label": "Matrix determinants",
      "href": "/api/v1/mathematics/linear-algebra/matrix-determinant"
    }
  ],
  "syntax": {
    "hint": "POST /api/v1/mathematics/linear-algebra/matrix-operations/matrix-arithmetic/matmul"
  },
  "properties": {
    "dimensions": [2, 2],
    "is_square": true
  }
}

The result object uses the value of result_name as its key. If you pass result_name: "f_prime" in the request, the answer appears as result.f_prime rather than result.ans.

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Understanding the Stemfard API JSON response structure

Top-level fields

Field availability by level

Sample detailed response

​Top-level fields

​Field availability by level

​Sample detailed response

Top-level fields

Field availability by level

Sample detailed response