feat: 14 research ideas with flip cards, fix action persistence

- IdeaBoard: replace 6 placeholder items with 14 full research problems;
  front shows title + TLDR + category chip; back shows two-paragraph
  description + formatted references list; remove upvote buttons;
  4-column grid (responsive: 3→2→1); per-category colour coding
- InteractiveDemo: selected action now persists when switching the
  boundary type — endpoint and ring recompute for the new boundary
  without clearing the selection

Co-Authored-By: Claude Sonnet 4.6 <noreply@anthropic.com>

Author: amirhk