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Build me a product analytics service for my own app: I send events, I get funnels and retention back.

STACK
- Node with Fastify for ingest, Postgres with TimescaleDB for storage
- A server-rendered dashboard, no frontend framework
- One binary to run, one database to back up

INGEST
- POST /event taking name, distinct_id, timestamp and a JSON properties object
- Accept a batch of up to 500 in one request, and return 202 before writing
- Deduplicate on a client-supplied insert_id kept for 24 hours
- Reject an event with an unknown name unless the schema is set to open, so a typo does not become a new metric

IDENTITY
- An alias table mapping anonymous ids to a user id once they sign in
- Rewrite history on alias so a funnel started anonymously still completes
- Never store an IP address; keep a country derived from it and discard the rest

QUESTIONS IT MUST ANSWER
- Funnel: ordered steps within a window, with drop-off per step and a breakdown by one property
- Retention: cohort by first-seen week, returning in each following week, as a triangle
- Trend: any event over time, counted or unique-by-user, split by a property
- Every one of these as a single SQL query against continuous aggregates, not a loop in application code

DASHBOARD
- Saved reports with a shareable URL that carries the whole query
- Numbers that state the window they cover and the day the data ends

LIMITS TO DOCUMENT
- Cardinality: a property with millions of distinct values will not group usefully
- Late-arriving events and how far back aggregates are recomputed

Include a README with the retention policy, the cost of storage per million events, and how to add a new event schema.