Next.js + Vercel AI SDK + PostHog (OpenTelemetry) repro

Minimal Next.js 16 app that sends Vercel AI SDK spans to PostHog LLM analytics, using the setup from PostHog's Vercel AI SDK installation docs.

Run

pnpm install
cp .env.example .env.local    # fill in POSTHOG_PROJECT_API_KEY and OPENAI_API_KEY
./scripts/smoke.sh

The script boots next dev, POSTs once to /api/chat, waits for the span batch to flush, then shuts the server down. A $ai_generation event should appear in PostHog → LLM analytics within ~30s.

For EU projects, set POSTHOG_HOST=https://eu.i.posthog.com in .env.local.