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We show via explicit construction that for six or more parties, there existextreme rays of the subadditivity cone that can be realized by quantum states,but not by holographic states. This is a counterexample to a conjecture firstformulated in arXiv:2204.00075, and implies the existence of deep holographicconstraints that restrict the allowed patterns of independence among varioussubsystems beyond the universal quantum mechanical restrictions.

A gap between holographic and quantum mechanical extreme rays of the subadditivity cone