Mathematical walkthrough

Teaching notes contain the complete derivation sequence, literal equation readings, intuition, proof assumptions, numerical examples, and source links. Equation readings link directly to the new reveal stages. Slide-to-code map connects implementations to their native slides. Exercises provide small extensions and answers.

For a compact starting point, run python lecture_7/numerical_examples.py --output lecture_7/outputs/numerical, then python -m unittest discover -s lecture_7/tests -v. The LP dual certificate, Sinkhorn marginals, finite bridge probabilities, CTMC master equation, and score-to-drift factor are checked independently of the neural training reports.