lp range model derived

{
  "input": {
    "type": "http",
    "method": "GET",
    "queryParams": {
      "pool": "v3 pool address 0x…",
      "horizon_days": "14, max 90",
      "lookback_hours": "168, max 720"
    }
  },
  "output": {
    "type": "json",
    "errors": {
      "400": {
        "example": {
          "error": "invalid request"
        },
        "description": "Invalid or missing parameter(s). Returned before the payment gate on paid requests, so a malformed call is never charged. JSON body: { error: <what is wrong and how to fix it> } plus usage hints."
      },
      "402": {
        "description": "Payment required — x402 v2 challenge; the accepts array lists scheme, network, and amount. Retry the same request with a PAYMENT-SIGNATURE (v2) or X-PAYMENT (v1) header. Verification is free."
      },
      "500": {
        "example": {
          "error": "upstream_failed"
        },
        "description": "Unexpected server error. If a payment settled without a usable result, contact info@theaslangroupllc.com with the settlement tx hash for a re-run or credit."
      }
    },
    "example": {
      "pair": "WETH/PONS",
      "pool": "0x50e4…",
      "method": "zero-drift GBM on trailing realized vol; fee estimate = pool fee APR × efficiency × time-in-range share",
      "scenarios": [
        {
          "width_pct": 15,
          "tick_lower": 104960,
          "tick_upper": 110400,
          "est_fee_apr_pct": 61.2,
          "capital_efficiency_x": 13.7,
          "prob_in_range_at_horizon": 0.55,
          "expected_time_in_range_share": 0.71
        }
      ],
      "disclaimer": "Educational analytics… not investment advice.",
      "current_tick": 107697,
      "horizon_days": 14,
      "current_price": 0.0000451,
      "realized_vol_per_day_pct": 9.8
    }
  }
}