feat: Add Sentence Space Visualizer with Live Semantic Search

[scheuclu]

Description

Upgrade the landing page concept from static individual words to a 2D sentence coordinate space, letting users search/type full sentences and see them plot in real-time next to existing topic clusters.

Implementation Checklist

• Precompute Sentence Corpus:
  • Embed a dataset of 5,000–10,000 sentences (e.g., from news headlines, quotes, or commonsense questions) using sentence-transformers/all-MiniLM-L6-v2.
  • Project them to 2D coordinates using UMAP and write them to a lightweight binary vector sheet.
• FastAPI Search Engine:
  • Create a /api/embed-query endpoint to encode a user's typed sentence on-the-fly.
  • Perform cosine similarity against the precomputed sentence coordinates.
• Frontend t-SNE Canvas:
  • Render the sentence space.
  • When the user searches a phrase, plot a glowing beacon indicating where their phrase landed, showing the nearest sentence matches with connections.