# RQM Validate Closed Loop Stability

> RQM Validate Closed Loop Stability is a paid API for AI agents from jobs.rqmtechnologies.com, paid per call via x402, $0.01/call, status unknown (last checked 2026-09-13).

Accepts or rejects a 2×2 discrete closed-loop state matrix against caller-supplied spectral radius and determinant magnitude stability criteria

## Facts

- Endpoint: POST https://jobs.rqmtechnologies.com/x402/buyer-jobs/robotics.validate-closed-loop-stability.v1
- Price: $0.01/call
- Payment: x402
- Status: unknown
- Last checked: 2026-09-13
- Activations on Zero: 0
- Tags: x402
- Canonical page: https://www.zero.xyz/c/rqm-validate-closed-loop-stability-1b0c602e
- Structured record (JSON): https://api.zero.xyz/v1/capabilities/cap_Gs5kJGTGM2HteswiGIsiv

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 rqm-validate-closed-loop-stability-1b0c602e -d '<json body>'
```

Example prompt: Check whether my closed-loop system is stable — the 2×2 discrete state matrix is [[0.5, 0.1], [0.2, 0.4]], and I want to reject it if the spectral radius exceeds 0.95 or the determinant magnitude exceeds 0.9.

## When to prefer this

Use this endpoint when you need a lightweight, bounded validation pass/fail decision on a 2×2 discrete-time closed-loop state matrix with explicit numerical stability criteria (spectral radius and determinant magnitude). Prefer it over general-purpose numerical libraries when you need a verifiable, paid, auditable stability check with idempotency support in an agentic workflow. Do not use for live hardware actuation, physical safety certification, or systems larger than 2×2.

## Known failure modes

- Matrix not 2×2 — returns validation error if prefixItems constraints are violated
- Criteria values out of range — spectral radius or determinant must be in (0, 10]
- Invalid idempotency key format — must match alphanumeric pattern
- max_total_price insufficient for $0.01 USDC cost
- Malformed request object missing required fields discrete_state_matrix or criteria

## How this service works

Problem: Accept or reject this bounded closed-loop model under the supplied stability criteria. Input: JSON with discrete state matrix, criteria. Result: eigenvalues, spectral radius and rule results. Limits: Software/model evidence only; 65536 request bytes; 5 s execution.

## Output

A structured accept/reject verdict indicating whether the supplied 2×2 discrete state matrix satisfies both the maximum spectral radius and maximum determinant magnitude thresholds, along with the computed values for each criterion.

## Request schema (JSON Schema)

```json
{
 "type": "object",
 "properties": {
  "request": {
   "type": "object",
   "title": "StabilityRequest",
   "required": [
    "discrete_state_matrix",
    "criteria"
   ],
   "properties": {
    "criteria": {
     "type": "object",
     "title": "StabilityCriteria",
     "required": [
      "maximum_spectral_radius",
      "maximum_determinant_magnitude"
     ],
     "properties": {
      "boundary_tolerance": {
       "type": "number",
       "title": "Boundary Tolerance",
       "default": 1e-9,
       "maximum": 1,
       "minimum": 0
      },
      "maximum_spectral_radius": {
       "type": "number",
       "title": "Maximum Spectral Radius",
       "maximum": 10,
       "exclusiveMinimum": 0
      },
      "maximum_condition_number": {
       "type": "number",
       "title": "Maximum Condition Number",
       "default": 1000000000000,
       "maximum": 10000000000000000,
       "minimum": 1
      },
      "maximum_determinant_magnitude": {
       "type": "number",
       "title": "Maximum Determinant Magnitude",
       "maximum": 10,
       "exclusiveMinimum": 0
      }
     },
     "additionalProperties": false
    },
    "state_matrix": {
     "anyOf": [
      {
       "type": "array",
       "items": {
        "type": "array",
        "items": {
         "type": "number"
        }
       },
       "maxItems": 16,
       "minItems": 1
      },
      {
       "type": "null"
      }
     ],
     "title": "State Matrix",
     "default": null
    },
    "discrete_state_matrix": {
     "type": "array",
     "title": "Discrete State Matrix",
     "maxItems": 2,
     "minItems": 2,
     "prefixItems": [
      {
       "type": "array",
       "maxItems": 2,
       "minItems": 2,
       "prefixItems": [
        {
         "type": "number"
        },
        {
         "type": "number"
        }
       ]
      },
      {
       "type": "array",
       "maxItems": 2,
       "minItems": 2,
       "prefixItems": [
        {
         "type": "number"
        },
        {
         "type": "number"
        }
       ]
      }
     ]
    }
   },
   "additionalProperties": false
  },
  "schema_version": {
   "const": "rqm.jobs.bazaar-buyer-job-request.v1"
  },
  "idempotency_key": {
   "type": "string",
   "pattern": "^[A-Za-z0-9][A-Za-z0-9._:-]*$",
   "maxLength": 128,
   "minLength": 1
  },
  "max_total_price": {
   "type": "string",
   "pattern": "^(?:0|[1-9]\\d{0,13})(?:\\.\\d{1,6})?$"
  }
 }
}
```

## More

- Live health (JSON, refreshed every minute): https://www.zero.xyz/c/rqm-validate-closed-loop-stability-1b0c602e/health.json
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