Add a safe live API example

[JAORMX]

Summary

• Add a small reusable live sample using an explicit API-key file, fixed official endpoint, pinned model, bounded timeout, and disabled retries.
• Send one synthetic request containing Noul, Choice, and Score questions; print typed answers, model, and usage only.
• Keep ordinary tests offline and document the authorized live smoke check without recording credentials or the operator-specific key path.

Verification

• Offline tests, race tests, and vet passed with Go 1.26.6.
• Credential-boundary review completed before execution. Model metadata is intentionally retained to verify the resolved version; it contains no credential.
• One authorized live request succeeded: jev-1.13.0, 445 input tokens and 70 output tokens, duplicate-charge probability 0.98, billing selection, urgency 0.95.
• No live OAuth gateway or exhaustive service-boundary conformance claim.