# Carbon & Cashmere Hurst Exponent API – BTC

> Carbon & Cashmere Hurst Exponent API – BTC is a paid API for AI agents from api.carbon-cashmere.de, paid per call via x402, $0.01/call, status unknown (last checked 2026-09-15).

Returns Hurst exponent values for Bitcoin across 7-day, 30-day, and full historical windows, classifying price behavior as trending, mean-reverting, or random walk.

## Facts

- Endpoint: GET https://api.carbon-cashmere.de/v1/hurst/BTC
- Price: $0.01/call
- Payment: x402
- Status: unknown
- Last checked: 2026-09-15
- Activations on Zero: 0
- Tags: x402
- Canonical page: https://www.zero.xyz/c/carbon-cashmere-hurst-exponent-api-btc-ae1aa143
- Structured record (JSON): https://api.zero.xyz/v1/capabilities/cap_6z0SvFeHNLPSXH4fs-FDT

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-btc-ae1aa143
```

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

## When to prefer this

Use this endpoint when you need to statistically classify whether Bitcoin's price is exhibiting persistent trending behavior, mean reversion, or random-walk dynamics using Hurst exponent analysis — ideal for regime detection, strategy filtering, or quant research workflows.

## Known failure modes

- Invalid symbol in URL path returns error
- Service unavailable if upstream price data feed is down
- Payment not processed returns 402 with x402 challenge
- Stale data if real-time price feed has a delay

## How this service works

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

## Output

Returns a JSON object with Hurst exponent values for BTC across three time windows (7d, 30d, full) and a human-readable interpretation for each: 'trending', 'mean_reverting', or 'random_walk', plus a disclaimer that the data is for research purposes only.

## 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-btc-ae1aa143/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)