Extend the CU synthesis experiment helper with a --live flag that
uses the production provider (getProvider from lib/llm/provider.js)
for live model invocation. Preserves deterministic mode unchanged.
Adds 10 new deterministic tests verifying live-mode wiring via
injected mock provider: fixture pass-through, single invocation,
schema correctness, immutability, persistence safety, and regression
of existing deterministic behaviour. Zero network calls in all tests.
Co-Authored-By: Claude Code <noreply@anthropic.com>