# protective-depth

`station__tov-proofs__protective-depth` · external (needs EXECUTION_BACKEND_URL configured) · domain `tov-proofs` · pv-relevance `pv-core`

Compute minimum protective depth H such that ℙ(H) < target_probability. Formula: H ≥ 1 + log(1/ε)/α. Answers: 'how many safety layers do I need?'

> **Note:** This tool routes through an external execution backend. If `EXECUTION_BACKEND_URL` is unset on the server, calls return JSON-RPC error `-32603 "Tool execution backend not configured"`. Tools with `backend: native` execute in-process and are always callable.

## Agent metadata

- `idempotent`: unknown
- `read_only`: unknown
- `expected_latency_ms`: unknown (not yet contract-tested)
- `cost_tokens_estimate`: unknown

## Input schema

- `target_probability` *number* (required) — Target probability threshold ε, in (0, 1). Example: 0.05 for 5% residual risk
- `attenuation_rate` *number* (required) — Attenuation rate α (must be positive)

## Example call

```json
POST /api/mcp
Content-Type: application/json

{
  "jsonrpc": "2.0",
  "id": 1,
  "method": "tools/call",
  "params": {
    "name": "station__tov-proofs__protective-depth",
    "arguments": {
      "target_probability": 0,
      "attenuation_rate": 0
    }
  }
}
```

## Related

- [/tools](/tools) — all 3062 tools
- [/tools/tov-proofs__protective-depth](/tools/tov-proofs__protective-depth) — HTML page
- [/tools/tov-proofs__protective-depth/json](/tools/tov-proofs__protective-depth/json) — JSON form (agent-friendly)
- [/api/mcp](/api/mcp) — endpoint
- [/AGENTS.md](/AGENTS.md) — agent guide