Can AI replace Perplexity?

Build me a personal answer engine like Perplexity, wrapping real search and LLM APIs,
not rebuilding them. Requirements:

- A local web app on localhost:3000: Node + Express + htmx, one input box, streamed
  answers.
- Per question: query the Brave Search API (key in .env), fetch the top 6 results with
  undici, extract readable text with @mozilla/readability + jsdom, then pass the
  question plus numbered excerpts to Claude or GPT (key in .env) with instructions to
  answer only from the excerpts and cite as [1][2].
- Render citations as footnote links; show the full source list under every answer.
- Follow-up questions stay in the same thread with prior Q&A in the context window.
- Threads stored in SQLite via better-sqlite3; a sidebar lists past threads by first
  question.
- If a page fails to fetch or extract, drop it and continue. Never cite a page that was
  not fetched.
- Binds to localhost only; no accounts, no telemetry, only the search and LLM calls
  leave my machine.
- Out of scope: crawling my own web index, model routing, and mobile apps. Answer
  quality tracks the search API, that is the deal.
- README: which keys to get (Brave Search has a free tier) and rough per-query cost.