FA-40717 / Heap invariants / Member archive

Pairing cut replaces the parent first-child pointer only when necessary · case 02

The bounded pairing cut splice certificate reports an incorrect first.

Member previewVariant 2 · 3 implementations · 7 checks per implementation

Case contract

A pairing-heap cut input contains parent id, ordered child ids, selected child, and preexisting roots. Remove the child while preserving sibling order. Return remaining children, new first child, successor previous pointer (parent if selected was first), predecessor next pointer, promoted root list, and detached child links [parent,previous,next] all None.

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 2	`{"children": [2], "detached": [null, null, null], "first": 1, "predecessor_next": null, "roots": [9, 8, 1], "successor_previous": [2, 9]}`	`{"children": [2], "detached": [null, null, null], "first": 2, "predecessor_next": null, "roots": [9, 8, 1], "successor_previous": [2, 9]}`	Failed

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

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