# Bounded Dense Multi-Output Least-Squares Minimum-Norm Solver

> Bounded Dense Multi-Output Least-Squares Minimum-Norm Solver is a paid API for AI agents from stat.halowerk.com, paid per call via x402, $0.002/call, status unknown (last checked 2026-10-29).

Solves a bounded dense multi-output least-squares problem and returns the minimum-norm solution along with diagnostics including numerical rank, singular value spectrum, rank threshold, residual, and effective condition number.

## Facts

- Endpoint: POST https://stat.halowerk.com/v1/oss-openblas-dense-minimum-norm-solve?utm_source=zero.xyz
- Price: $0.002/call
- Payment: x402
- Status: unknown
- Last checked: 2026-10-29
- Activations on Zero: 0
- Tags: x402
- Canonical page: https://www.zero.xyz/c/bounded-dense-multi-output-least-squares-minimum-norm-solver-7383288b
- Structured record (JSON): https://api.zero.xyz/v1/capabilities/cap_JVX6ZP9theKW0DDBx8IB_

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 bounded-dense-multi-output-least-squares-minimum-norm-solver-7383288b -d '<json body>'
```

Example prompt: Solve this overdetermined system for me: matrix A is [[1,2],[3,4],[5,6]] and B is [[7],[8],[9]] — use an rcond of 1e-10 and give me the minimum-norm solution along with the numerical rank, full singular value spectrum, and condition number so I know whether to trust the result.

## When to prefer this

Prefer this endpoint when you need not just a least-squares solution but also trustworthiness diagnostics — especially for potentially rank-deficient or ill-conditioned systems where a silent answer would be dangerous. It is ideal for multi-output problems (multiple right-hand side columns), when you need the full singular value spectrum, or when you want the minimum-norm solution among all possible least-squares solutions. Choose it over a simple linear solver when numerical reliability assessment matters as much as the solution itself.

## Known failure modes

- Matrix A or B dimensions are mismatched (rows of A must equal rows of B)
- rcond value outside allowed range [1e-12, 0.01]
- Matrix values outside the bounded range [-1e6, 1e6]
- Matrix A exceeds 128x128 or B exceeds 128x32 dimensions
- Malformed array structure (non-rectangular or empty arrays)
- Payment failure via x402 protocol

## How this service works

Solves a bounded dense multi-output least-squares problem and returns the minimum-norm solution together with the diagnostics that say whether it can be trusted: numerical rank, the full singular value spectrum, the rank threshold actually applied, the residual, and the effective condition number. A rank-deficient system still gets an answer here, but it gets one that announces its own deficiency instead of a plausible vector with no warning attached.

## Output

Returns the minimum-norm least-squares solution matrix (X such that AX ≈ B), along with: the numerical rank of A as determined by the rcond threshold, the complete singular value spectrum of A, the rank-condition threshold actually applied, the residual norm of the solution, and the effective condition number. For rank-deficient systems, the response explicitly announces the deficiency rather than silently returning a plausible-looking answer.

## 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/bounded-dense-multi-output-least-squares-minimum-norm-solver-7383288b/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)