FA-40455 / Heap invariants / Member archive

Interval insertion crosses the upper heap only above the parent upper bound · case 05

The bounded interval insert certificate reports an incorrect upper.

Member previewVariant 5 · 3 implementations · 7 checks per implementation

Case contract

Insert key x into an interval-heap last-node decision. For a singleton last interval s, complete it as sorted(s,x). For a new singleton with parent [lo,hi], x below lo routes to the lower heap, above hi to the upper heap, otherwise stays. Return pair completion, lower route, upper route, contained route, parent endpoint displaced on crossing, and logical-size increment.

Why this case matters

This isolates an internal heap representation or priority-structure invariant using deterministic finite records.

One recorded failure

Sample boundary fixture

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

Boundary fixture	Actual	Expected	Outcome
regression certificate 5	`{"completed": [1, 8], "contained": true, "displaced": null, "lower": false, "new_size": 12, "upper": true}`	`{"completed": [1, 8], "contained": true, "displaced": null, "lower": false, "new_size": 12, "upper": false}`	Failed

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

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