{"paper":{"title":"Notes on the Graph-Encoded Manifolds for the (Genuine) Multi-Entropy","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"hep-th","authors_text":"Norihiro Iizuka","submitted_at":"2026-08-07T03:24:16Z","abstract_excerpt":"Genuine multi-entropy is the part of the $\\mathtt{q}$-partite multi-entropy that captures entanglement genuinely shared among all $\\mathtt{q}$ parties, rather than entanglement already present among fewer subsystems. It was recently proposed that this genuine part -- so-called a multipartite entanglement signal -- can be studied via the graph-encoded manifold (GEM) built from the underlying $\\mathtt{q}$-partite multi-entropy permutation family: reading its $\\mathtt{q}$-colored contraction graph $\\Gamma_{\\mathtt{q},n}$ as a triangulation by $(\\mathtt{q}-1)$-simplices. Focusing on $\\mathtt{q}=4$"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2608.06755","kind":"arxiv","version":1},"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/2608.06755/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"}