{"paper":{"title":"The edge multiset dimension of hypercubes","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Jaan Allikvere","submitted_at":"2026-08-05T13:05:09Z","abstract_excerpt":"For a graph G and a nonempty set S of vertices, the edge multiset representation of an edge e is the multiset of distances from e to the elements of S, where d(uv,s)=min{d(u,s),d(v,s)}. The edge multiset dimension edim_m(G) is the minimum cardinality of a set whose edge representations are pairwise distinct, and is infinite if no such set exists. A recent survey asked whether edim_m(Q_d) is infinite for every d >= 3. We answer this question negatively and determine the finite-infinite transition completely: edim_m(Q_d) is infinite if and only if 2 <= d <= 5. An exhaustive computation proves ed"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2608.09983","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/2608.09983/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"}