Automate homepage footer update date

[fanyangCS]

Summary

• derive the homepage footer date at Jekyll build time from the checked-out repository HEAD commit's committer timestamp
• render that value in the existing Last updated on … wording instead of a hard-coded date
• cover timestamp extraction with a focused regression test and run it in both production and branch-preview builds

Implementation

A highest-priority Jekyll generator runs git log -1 --format=%cI HEAD in the site source and exposes the result as site.repository_last_updated_at. The homepage Liquid layout formats that timestamp as the existing human-readable month/day/year date. This makes merged changes and redeploys reflect the effective commit rather than the wall-clock build time, with no client-side JavaScript.

Verification

• ruby test/repository_last_updated_test.rb — 1 run, 1 assertion, pass
• ruby test/cache_bust_test.rb — 6 runs, 8 assertions, pass
• npx prettier . --check — pass
• JEKYLL_ENV=production bundle exec jekyll build — pass
• inspected generated _site/index.html; it rendered Last updated on July 13, 2026, matching the source HEAD commit date used by that build

This change and PR description were AI-generated under human direction and review.