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Tie adjusted concordance squared: Discordant pairs are added instead of subtracted. · case 03

The reduction disagrees with its explicit aggregation oracle.

Member previewVariant 3 · 3 implementations · 8 checks per implementation

Case contract

For paired ordinal observations return sign(tau_b)*tau_b**2 as an exact Fraction string. Every unordered observation pair contributes its coordinate comparison; normalize signed concordance squared by products of non-tied x/y pair counts. Undefined if either coordinate has no varying pairs.

Why this case matters

Exact bounded examples isolate a reduction defect without floating-point or external-service effects.

One recorded failure

Sample boundary fixture

This sample comes from the broken implementation of a controlled reproducer.

Boundary fixture	Actual	Expected	Outcome
regression 2	`"1"`	`"-1"`	Failed

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