Imagine two identical networks, one above the other, with links joining corresponding points. When links are randomly available, should a destination on your own layer always be easier to reach than its twin on the other layer? This was the bunkbed conjecture. Earlier researchers showed that the answer can be no. This candidate studies a broader model, where a cluster weight changes how disconnected components are favoured. Its central finding is a window with one exceptional point. Between roughly zero point seven eight seven four and two point seven six four, the weight two is the only value for which the inequality holds for every finite simple graph. Every other weight in that window admits a counterexample at any prescribed common edge probability strictly between zero and one. The graph can change with both parameters. The important advance is the mechanism. A negative value of a graph polynomial is converted into a counterexample using uniform fans and pendant vertices. Separate arguments handle different parameter regimes, including the singular value one. The positive result at two was already known. And the lower endpoint is not a numerical record: earlier work reports counterexamples farther below one. The package contains the scientific paper, exact certificates, graph recipes and executable checks, including deliberately corrupted inputs that must be rejected. This remains an unrefereed candidate, not a formally verified theorem or a complete classification of all cluster weights. This is Evidence Press, Flow-polynomial bunkbed obstructions, dated the thirtieth of September twenty twenty-six. The paper and evidence package are linked on the release page. This synthetic AI voice explains the research; it is not additional scientific evidence.