# Numora Calculus Gradient Endpoint

> Numora Calculus Gradient Endpoint is a paid API for AI agents from numorapoi.orbonomy.xyz, paid per call via x402, $0.04/call, status unknown (last checked 2026-09-14).

Computes the numerical gradient (vector of partial derivatives) of a multivariable function at a given point

## Facts

- Endpoint: POST https://numorapoi.orbonomy.xyz/api/calculus/gradient
- Price: $0.04/call
- Payment: x402
- Status: unknown
- Last checked: 2026-09-14
- Activations on Zero: 0
- Tags: x402
- Canonical page: https://www.zero.xyz/c/numora-calculus-gradient-api-8be1f6a8
- Structured record (JSON): https://api.zero.xyz/v1/capabilities/cap_XTyG-aHrBLrU3mPHWRrGe

Status and success rate cover calls made through Zero and Zero's own probes. Third-party monitors may report differently.

## How to call it through Zero

Zero handles the 402 payment challenge and records the run. With the Zero CLI installed (`npm i -g @zeroxyz/cli`):

```sh
zero fetch --capability numora-calculus-gradient-api-8be1f6a8 -d '<json body>'
```

Example prompt: Can you compute the gradient of f(x, y) = x^2 + 3*x*y + y^3 at the point [1.0, 2.0]?

## When to prefer this

Choose this endpoint when you need a pure serverless numerical gradient computation with no external library dependencies, billed per-call via x402 micropayments. Ideal for AI agents needing on-demand calculus without spinning up a compute environment. Best for single-point gradient queries rather than batch or symbolic differentiation.

## Known failure modes

- Malformed function string causes parse error — returns error response
- Point array dimension mismatch with number of variables in fn — may return NaN or error
- Division by zero or singularity in function at evaluation point — undefined result
- Non-numeric values in point array — validation error
- Unsupported mathematical syntax in fn string — parse or evaluation error

## How this service works

100 pure math computation endpoints for AI agents. Statistics, financial math, linear algebra, equation solving, calculus, number theory, sequence generation, and unit conversions. Zero external dependencies. x402 micropayments on Base.

## Output

Returns a JSON object with a 'result' containing the gradient vector (array of partial derivative values), a 'success' boolean, and a 'computation' string describing what was computed in human-readable form.

## Request schema (JSON Schema)

```json
{
 "type": "object",
 "required": [
  "fn",
  "point"
 ],
 "properties": {
  "fn": {
   "type": "string"
  },
  "point": {
   "type": "array"
  }
 }
}
```

## Response schema (JSON Schema)

```json
{
 "type": "object",
 "required": [
  "success",
  "result",
  "computation"
 ],
 "properties": {
  "result": {
   "type": "object",
   "description": "Computation result varies by endpoint"
  },
  "success": {
   "type": "boolean",
   "description": "Always true on success"
  },
  "computation": {
   "type": "string",
   "description": "Human-readable description of what was computed"
  }
 }
}
```

## More

- Live health (JSON, refreshed every minute): https://www.zero.xyz/c/numora-calculus-gradient-api-8be1f6a8/health.json
- [Zero catalog index](https://www.zero.xyz/llms.txt)
- [Other services from numorapoi.orbonomy.xyz](https://www.zero.xyz/host/numorapoi.orbonomy.xyz/llms.txt)