# Linear Covariance Pushforward (Affine Uncertainty Propagation)

> Linear Covariance Pushforward (Affine Uncertainty Propagation) is a paid API for AI agents from stat.halowerk.com, paid per call via x402, $0.0015/call, status unknown (last checked 2026-10-29).

Propagates a Gaussian distribution through an affine transformation by updating the mean and covariance, adding process noise — implementing the prediction step of a Kalman filter.

## Facts

- Endpoint: POST https://stat.halowerk.com/v1/oss-openblas-linear-covariance-pushforward?utm_source=zero.xyz
- Price: $0.0015/call
- Payment: x402
- Status: unknown
- Last checked: 2026-10-29
- Activations on Zero: 0
- Tags: x402
- Canonical page: https://www.zero.xyz/c/linear-covariance-pushforward-affine-uncertainty-propagation-4d4cc7e6
- Structured record (JSON): https://api.zero.xyz/v1/capabilities/cap_mc4q8j0yfD3ltaIfPbxJg

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 linear-covariance-pushforward-affine-uncertainty-propagation-4d4cc7e6 -d '<json body>'
```

Example prompt: I have a state mean vector [1.0, 2.0, 0.5], covariance matrix [[0.1,0,0],[0,0.2,0],[0,0,0.05]], a linear transform F, an offset b, and a process noise covariance Q — can you propagate the distribution through the affine map F*x + b and give me the new mean and covariance?

## When to prefer this

Choose this endpoint when you need a reliable, numerically consistent affine covariance propagation as a hosted API call — ideal for Kalman filter prediction steps, sensor fusion pipelines, or linear error budget computations where you want to avoid implementing the matrix algebra yourself. Prefer this over general-purpose matrix libraries when your pipeline is agent-driven or you need pay-per-call access without managing compute infrastructure. Not suitable for nonlinear propagation (use sigma-point or EKF Jacobian methods instead) or for dimensions exceeding 128.

## Known failure modes

- Dimension mismatch between mean, transform, covariance, or noise_covariance matrices returns a 400 error
- Non-positive-semidefinite covariance or noise_covariance inputs may cause numerical issues or a validation error
- Values outside the [-1e6, 1e6] range or array lengths exceeding 128 will be rejected
- Missing required fields (mean, covariance, transform) return a 422 validation error
- Singular or near-singular transform matrices may produce numerically unstable covariance outputs

## How this service works

Applies the standard affine propagation of uncertainty: the mean goes through the transform and offset, the covariance through the transform on both sides, and the independent noise covariance is added. This is the prediction step of a Kalman filter and the workhorse of any linear error budget.

## Output

Returns the pushed-forward Gaussian parameters: the transformed mean vector (F*x + offset) and the full propagated covariance matrix (F * Sigma * F^T + Q), ready to use as the prior in the next estimation or measurement update step.

## Request schema (JSON Schema)

```json
{
 "type": "object",
 "$schema": "https://json-schema.org/draft/2020-12/schema",
 "required": [
  "input"
 ],
 "properties": {
  "input": {
   "type": "object",
   "required": [
    "type",
    "method",
    "bodyType"
   ],
   "properties": {
    "type": {
     "const": "http"
    },
    "method": {
     "const": "POST"
    },
    "bodyType": {
     "const": "json"
    },
    "schemaUrl": {
     "type": "string",
     "format": "uri"
    },
    "exampleUrl": {
     "type": "string",
     "format": "uri"
    }
   },
   "additionalProperties": true
  },
  "output": {
   "type": "object",
   "required": [
    "type"
   ],
   "properties": {
    "type": {
     "const": "json"
    },
    "schemaUrl": {
     "type": "string",
     "format": "uri"
    },
    "exampleUrl": {
     "type": "string",
     "format": "uri"
    }
   },
   "additionalProperties": true
  }
 },
 "additionalProperties": true
}
```

## More

- Live health (JSON, refreshed every minute): https://www.zero.xyz/c/linear-covariance-pushforward-affine-uncertainty-propagation-4d4cc7e6/health.json
- [Zero catalog index](https://www.zero.xyz/llms.txt)
- [Other services from stat.halowerk.com](https://www.zero.xyz/host/stat.halowerk.com/llms.txt)