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Causal length set: any recorded history counts as membership · case 03

Removed elements keep appearing as members.

Member previewVariant 3 · 3 implementations · 8 checks per implementation

Case contract

Each replica maps elements to a causal length. An element is present when its length is odd. ["add", r, e] increments the length only when it is even; ["rem", r, e] increments it only when it is odd. ["merge", s, d] takes the per-element maximum. Return per replica the sorted members and the sorted [element, length] pairs.

Why this case matters

Causal-length sets encode an element's add/remove history as a single counter whose parity is its membership.

One recorded failure

Sample boundary fixture

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

Boundary fixture	Actual	Expected	Outcome
add then remove	`[[["x"], [["x", 2]]], [[], []]]`	`[[[], [["x", 2]]], [[], []]]`	Failed

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