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Rational nullspace basis: basis free coordinate order · case 04

The exact rational nullspace basis result violates the stated contract at basis free coordinate order.

Member previewVariant 4 · 3 implementations · 8 checks per implementation

Case contract

Input nonempty rectangular integer matrix; return canonical nullspace basis, one vector per free column increasing, with that free coordinate one and other free coordinates zero.

Why this case matters

Exact discrete arithmetic with observable algorithmic state; no floating point approximation is used.

One recorded failure

Sample boundary fixture

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

Boundary fixture	Actual	Expected	Outcome
explicit oracle 0	`[[[0, 1], [1, 1]], [[1, 1], [0, 1]]]`	`[[[1, 1], [0, 1]], [[0, 1], [1, 1]]]`	Failed

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This record includes three runnable implementations, regression fixtures, execution results, and source hashes.

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