# Numora Hessian Matrix Computation

> Numora Hessian Matrix Computation 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 Hessian matrix (matrix of second-order partial derivatives) of a multivariable function at a given point

## Facts

- Endpoint: POST https://numorapoi.orbonomy.xyz/api/calculus/hessian
- 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-hessian-matrix-computation-a1874f15
- Structured record (JSON): https://api.zero.xyz/v1/capabilities/cap_2m-RFRHwQA_M9jqSu2eUH

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-hessian-matrix-computation-a1874f15 -d '<json body>'
```

Example prompt: Compute the Hessian matrix of f(x, y) = x^3 + y^3 - 3*x*y at the point [1, 1] so I can determine the nature of the critical point there.

## When to prefer this

Use this endpoint when you need pure server-side symbolic or numerical computation of the Hessian matrix with no external dependencies — ideal for optimization tasks, convexity analysis, Newton's method steps, or saddle point detection where you need the full matrix of second partial derivatives at a specific point. Prefer this over general-purpose math libraries when you need a lightweight, stateless API call paid per-use via USDC micropayment.

## Known failure modes

- Invalid or unparseable function expression returns an error
- Point array dimension mismatch with number of variables in function
- Non-differentiable function at the given point causes computation failure
- Malformed input JSON or missing required fields returns 400-level error
- Payment not completed via x402 micropayment returns 402 Payment Required

## 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 success=true, the Hessian matrix as a 2D array in 'result', and a human-readable 'computation' string describing what was computed — e.g. the n×n matrix of all second-order partial derivatives evaluated at the given point.

## 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-hessian-matrix-computation-a1874f15/health.json
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