Tom's April 1 fix of logic of composite matching lecture

[mmcky]

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Pull request overview

This PR corrects the algebra/logic used in the “second case of intersecting pairs” argument in match_transport.md, ensuring the strict concavity step is applied to the right convex combinations in the uncrossing proof.

Changes:

• Replaces the prior (incorrect) definition of (\alpha) with one consistent with the ordering (x < x' < y' < y).
• Rewrites the convex-combination equalities for (|x-y'|) and (|x'-y|) in terms of (|x-y|) and (|x'-y'|).
• Expands the strict concavity argument into two inequalities and then adds them to obtain the desired strict improvement.

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[mmcky]

I've reviewed the mathematical fix in this PR and confirm it is correct.

The original proof had two bugs:

1. Wrong alpha formula: The original alpha = (|x-y| + |x'-y|) / (|x-y'| - |x'-y|) is not generally in (0,1). A quick check with x=0, x'=2, y'=5, y=6 gives alpha = 10, and the denominator can even be zero.

2. Reversed convex decomposition: The original wrote |x-y| and |x'-y'| as combinations of |x-y'| and |x'-y|, but the proof needs the opposite direction -- expressing the crossed distances as combinations of the uncrossed ones -- so that strict concavity of h yields the desired inequality.

The fix is sound:

• The new alpha = (|x-y'| - |x'-y'|) / (|x-y| - |x'-y'|) simplifies to (x'-x) / ((y-y') + (x'-x)), which is always in (0,1).
• The convex combination identities hold and are verified algebraically.
• Applying strict concavity of h and adding the two resulting inequalities correctly yields h(|x-y'|) + h(|x'-y|) > h(|x-y|) + h(|x'-y'|), proving uncrossing strictly reduces cost.

The presentation is also improved by breaking the final inequality chain into clear, individually justified steps.

[mmcky]

thanks @thomassargent30 - I will let @HumphreyYang make the final approval and then we will merge.

[HumphreyYang]

Closing in favor of #319.