# Lattice Basis Length Estimator

> Lattice Basis Length Estimator is a paid API for AI agents from quantum.halowerk.com, paid per call via x402, $0.003/call, status unknown (last checked 2026-09-14).

Estimates Gaussian-heuristic and reduced-basis vector lengths in log2 units from a lattice dimension, log2 determinant, and assumed root-Hermite factor — without executing actual lattice reduction.

## Facts

- Endpoint: POST https://quantum.halowerk.com/v1/lattice-check
- Price: $0.003/call
- Payment: x402
- Status: unknown
- Last checked: 2026-09-14
- Activations on Zero: 0
- Tags: x402
- Canonical page: https://www.zero.xyz/c/lattice-basis-length-estimator-491caa08
- Structured record (JSON): https://api.zero.xyz/v1/capabilities/cap_vTAUNoInOPcL2cl6pMSXK

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 lattice-basis-length-estimator-491caa08 -d '<json body>'
```

Example prompt: Can you estimate the Gaussian-heuristic and reduced-basis vector lengths in log2 for a lattice with dimension 512, log2 determinant 4096, and a root-Hermite factor of 1.0045?

## When to prefer this

Choose this endpoint when you need quick analytical estimates of lattice basis vector lengths from known parameters — ideal for parameter exploration, sanity-checking lattice designs, or comparing reduction quality proxies without the computational cost of running actual BKZ or LLL. Not suitable when you need a verified cryptographic security level, actual lattice reduction output, or LWE hardness estimates.

## Known failure modes

- dimension below 2 or above 100000 causes validation error
- root_hermite_factor outside [1,2] range rejected
- log2_determinant outside [-1e9, 1e9] range rejected
- missing required fields (dimension, log2_determinant) returns 400
- payment failure (x402) if USDC balance is insufficient

## How this service works

Uses lattice dimension, log2 determinant and an assumed root-Hermite factor to estimate Gaussian-heuristic and reduced-basis vector lengths in log2 units. It does not execute lattice reduction, validate an LWE instance or provide a cryptographic security level.

## Output

Returns the Gaussian-heuristic expected shortest vector length and the estimated reduced-basis vector length, both expressed in log2 units, computed analytically from the supplied dimension, log2 determinant, and root-Hermite factor — without performing actual lattice reduction.

## Request schema (JSON Schema)

```json
{
 "type": "object",
 "properties": {
  "dimension": {
   "type": "integer",
   "maximum": 100000,
   "minimum": 2
  },
  "log2_determinant": {
   "type": "number",
   "maximum": 1000000000,
   "minimum": -1000000000
  },
  "target_norm_log2": {
   "type": "number",
   "maximum": 1000000000,
   "minimum": -1000000000
  },
  "root_hermite_factor": {
   "type": "number",
   "maximum": 2,
   "minimum": 1
  }
 }
}
```

## More

- Live health (JSON, refreshed every minute): https://www.zero.xyz/c/lattice-basis-length-estimator-491caa08/health.json
- [Zero catalog index](https://www.zero.xyz/llms.txt)
- [Other services from quantum.halowerk.com](https://www.zero.xyz/host/quantum.halowerk.com/llms.txt)