Add embedding similarity calculations

[dkotter]

What?

Partially closes #962

Adds a Vector_Math class with various public methods that can be used to run similarity calculations against two vector embeddings. Also adds a Vector_Ranker class to score vectors against one another.

Why?

#892 and #975 brought in embedding code from the PHP AI Client. #976 brought in the data layer to store embeddings. This PR is one of the next steps in the overall embedding goal, allowing us to run comparisons from one vector to another.

How?

• Adds a Vector_Math class with various public methods that can be used to run similarity calculations against two vector embeddings
• Adds a Vector_Ranker class to score vectors against one another
• Adds another command to our temporary embeddings WP-CLI command to test things

Use of AI Tools

AI assistance: Yes
Tool(s): Claude Code
Model(s): Fable 5.1, Opus 5
Used for: Planning approach and executing on that. Review of approach and final review and testing by me

Testing Instructions

Easiest way to test is the custom WP-CLI command added as part of this PR:

1. Open a terminal window
2. Ensure you have embeddings generated for at least two posts

wp ai embeddings generate --post-id=1 --dry-run=false --chunk --provider=ollama --model=nomic-embed-text:latest
wp ai embeddings generate --post-id=2 --dry-run=false --chunk --provider=ollama --model=nomic-embed-text:latest

3. Compare the same post against itself:

wp ai embeddings compare 1 1

4. You should see a cosine similarity of 1 and euclidean distance of 0
5. Compare the posts against each other:

wp ai embeddings compare 1 2

6. You should see similarity numbers for each chunk as well as a single number for the overall comparison

Changelog Entry

Added - New Vector_Math and Vector_Ranker classes, allowing users to run similarity and ranking queries against vectors.

[github-actions]

The following accounts have interacted with this PR and/or linked issues. I will continue to update these lists as activity occurs. You can also manually ask me to refresh this list by adding the props-bot label.

If you're merging code through a pull request on GitHub, copy and paste the following into the bottom of the merge commit message.

Co-authored-by: dkotter <dkotter@git.wordpress.org>
Co-authored-by: ColinM-sys <colinmcdonough@git.wordpress.org>
Co-authored-by: jeffpaul <jeffpaul@git.wordpress.org>

To understand the WordPress project's expectations around crediting contributors, please review the Contributor Attribution page in the Core Handbook.

[codecov]

Codecov Report

❌ Patch coverage is 32.17391% with 234 lines in your changes missing coverage. Please review.
✅ Project coverage is 74.24%. Comparing base (813c81d) to head (d9990d5).

Files with missing lines	Patch %	Lines
includes/CLI/Embeddings_Command.php	0.00%	230 Missing ⚠️
includes/Embeddings/Vector_Ranker.php	90.32%	3 Missing ⚠️
includes/Embeddings/Vector_Math.php	98.79%	1 Missing ⚠️

Additional details and impacted files

@@              Coverage Diff              @@
##             develop     #993      +/-   ##
=============================================
- Coverage      75.37%   74.24%   -1.14%     
- Complexity      3357     3447      +90     
=============================================
  Files            138      140       +2     
  Lines          12976    13315     +339     
=============================================
+ Hits            9781     9886     +105     
- Misses          3195     3429     +234     

Flag	Coverage Δ
unit	74.24% <32.17%> (-1.14%)	⬇️

Flags with carried forward coverage won't be shown. Click here to find out more.

☔ View full report in Codecov by Harness.
📢 Have feedback on the report? Share it here.

🚀 New features to boost your workflow:

• ❄️ Test Analytics: Detect flaky tests, report on failures, and find test suite problems.
• 📦 JS Bundle Analysis: Save yourself from yourself by tracking and limiting bundle sizes in JS merges.