Scoped semantic answer cache.

A semantic cache embeds the question, finds the nearest past question, and returns its stored answer if it's similar enough, skipping the model entirely. Day 5 (section 3.2) lists how that goes wrong: "opened" and "unopened" earphones sit close in embedding space but flip the answer; a personal answer leaks to the next customer; a policy change leaves the cache citing the old rule. This lab builds the cache with the lesson's four rules:

1. Scope the key by tenant, language and prompt version, through one key-building function that refuses to run without them (section 9.5's prevention).
2. Cache only non-personal answers.
3. Invalidate from the sources: every answer built from a changed page is purged.
4. Measure: count hits and misses, and set the threshold from data (the tests use the lesson's flip).

Implement:

Rules the tests check:

• An entry expires when clock.now() - stored_at >= ttl_s; expired entries never hit.
• Similarity is cosine(a, b) (given). Compare with >=: the threshold is the lowest similarity you accept.
• lookup returns only the answer string, and every call counts as a hit or a miss.

In JavaScript and TypeScript the names are makeScope(tenant, language, promptVersion), which returns the array [tenant, language, promptVersion], and new SemanticCache(threshold, ttlSeconds, clock) with store(scope, question, vector, answer, sources, personal = false), lookup(scope, vector) (null on a miss), invalidateSource(sourceId) and hitRate(). A ValueError is a TypeError in JavaScript (Node's convention for an invalid argument): throw it for a missing or empty part and for a scope that isn't a 3-element array. Arrays compare by reference, so compare scopes part by part, or turn them into one string with JSON.stringify. The given code has the same FakeClock, cosine, unit and toy vectors V.