# Carbon & Cashmere Hurst Exponent API – ETH

> Carbon & Cashmere Hurst Exponent API – ETH is a paid API for AI agents from api.carbon-cashmere.de, paid per call via x402, $0.01/call, status unknown (last checked 2026-09-14).

Returns Hurst exponent values and trend/randomness interpretations for Ethereum (ETH) across multiple time windows (7d, 30d, full history)

## Facts

- Endpoint: GET https://api.carbon-cashmere.de/v1/hurst/ETH
- Price: $0.01/call
- Payment: x402
- Status: unknown
- Last checked: 2026-09-14
- Activations on Zero: 0
- Tags: x402
- Canonical page: https://www.zero.xyz/c/carbon-cashmere-hurst-exponent-api-eth-8a88a1b1
- Structured record (JSON): https://api.zero.xyz/v1/capabilities/cap_rGOC_mtYl7ZlrqB29-ICc

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 carbon-cashmere-hurst-exponent-api-eth-8a88a1b1
```

Example prompt: What's the Hurst exponent for ETH right now — is it trending, mean-reverting, or a random walk across the 7-day, 30-day, and full history windows?

## When to prefer this

Use this endpoint when you need to quantify whether ETH price dynamics exhibit trending (persistent) or random-walk behavior using the Hurst exponent — a rigorous statistical measure of long-range dependence. Prefer this over simple moving average or RSI-based signals when you want a fractal/statistical characterization of market regime rather than a momentum or mean-reversion indicator alone.

## Known failure modes

- Invalid or unsupported coin symbol in URL path returns an error
- Network or upstream data unavailability causes a 5xx response
- Malformed request headers (e.g. missing x402 payment) result in 402 Payment Required
- Rate limiting may occur under heavy usage

## How this service works

Professional crypto market intelligence. Real-time prices, signals, and market scoring.

## Output

A JSON object containing Hurst exponent scores for ETH across three time horizons (7d, 30d, full), each accompanied by an interpretation label ('random_walk' or 'trending'), plus a disclaimer noting the data is for informational research only and not investment advice.

## Request schema (JSON Schema)

```json
{
 "type": "object",
 "properties": {
  "properties": {
   "type": "string"
  }
 }
}
```

## Response schema (JSON Schema)

```json
{
 "type": "json",
 "example": {
  "_meta": {
   "disclaimer": "Informational research data only — not investment advice."
  },
  "symbol": "BTC",
  "hurst_7d": 0.48,
  "hurst_30d": 0.55,
  "hurst_full": 0.52,
  "interpretation_7d": "random_walk",
  "interpretation_30d": "trending",
  "interpretation_full": "random_walk"
 }
}
```

## More

- Live health (JSON, refreshed every minute): https://www.zero.xyz/c/carbon-cashmere-hurst-exponent-api-eth-8a88a1b1/health.json
- [Zero catalog index](https://www.zero.xyz/llms.txt)
- [Other services from api.carbon-cashmere.de](https://www.zero.xyz/host/api.carbon-cashmere.de/llms.txt)