{"paper":{"title":"The Holographic Multi-Entropy Cone","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"hep-th","authors_text":"Xin-Xiang Ju, Yang Zhao","submitted_at":"2026-06-13T07:42:33Z","abstract_excerpt":"We generalize the holographic entropy cone (HEC) to the holographic multi-entropy cone (HMEC) by adjoining multi-entropy coordinates to the standard bipartition entropy coordinates. We show that holographic states, through their multi-entropy vectors, form a rational polyhedral cone in multi-entropy space, and multicontraction maps provide exact certificates for holographic multi-entropy inequalities (HMEIs). We determine all facets of the $n=3,4$ HMECs, where $n$ includes the purifier, and obtain seven fundamental HMEI orbits: two for $n=3$ and five for $n=4$. We further propose two structura"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2606.15173","kind":"arxiv","version":2},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2606.15173/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}