# Numora Calculus Series Computation

> Numora Calculus Series 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 sum or convergence of a mathematical series given a term expression in index n, with configurable maximum terms and tolerance.

## Facts

- Endpoint: POST https://numorapoi.orbonomy.xyz/api/calculus/series
- 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-series-computation-747a2eff
- Structured record (JSON): https://api.zero.xyz/v1/capabilities/cap_V8-5_8w1WkrBzNwYd26Rs

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-series-computation-747a2eff -d '<json body>'
```

Example prompt: Can you compute the sum of the series defined by the term 1/n^2, stopping after 100 terms or when the result converges within a tolerance of 0.0001?

## When to prefer this

Use this endpoint when you need server-side, dependency-free computation of a mathematical series given a symbolic term formula in index n. Prefer this over client-side JavaScript math or general-purpose LLM arithmetic when you need reliable numerical convergence with configurable precision and term limits, especially in agentic pipelines that can handle x402 micropayments on Base.

## Known failure modes

- Invalid or unparseable term expression fn returns a computation error
- Missing required fn parameter returns a 400-level validation error
- Series diverges and no tolerance stopping condition is met, potentially hitting maxTerms limit
- Payment not included or insufficient USDC micropayment returns a 402 Payment Required response
- Malformed JSON body returns a parse 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 success flag, a result object containing the computed series sum and convergence details, and a human-readable computation string describing what was evaluated.

## Request schema (JSON Schema)

```json
{
 "type": "object",
 "required": [
  "fn"
 ],
 "properties": {
  "fn": {
   "type": "string",
   "description": "Term expression with index n"
  },
  "maxTerms": {
   "type": "integer"
  },
  "tolerance": {
   "type": "number"
  }
 }
}
```

## 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-series-computation-747a2eff/health.json
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