{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2026:YCT2XJ2DFWFJHBJJO6MJUZ5HEN","merge_version":"pith-open-graph-merge-v1","event_count":2,"valid_event_count":2,"invalid_event_count":0,"equivocation_count":0,"current":{"canonical_record":{"metadata":{"abstract_canon_sha256":"124aade3459c4541bec8e53e557721354c13235a1fc32037e7985d53213f2abc","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.CO","submitted_at":"2026-08-05T13:05:09Z","title_canon_sha256":"1eb07277f1bbcd38c07262652425f3341fba632b365fd17917f69bd65975fa2f"},"schema_version":"1.0","source":{"id":"2608.09983","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2608.09983","created_at":"2026-08-12T00:22:32Z"},{"alias_kind":"arxiv_version","alias_value":"2608.09983v1","created_at":"2026-08-12T00:22:32Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2608.09983","created_at":"2026-08-12T00:22:32Z"},{"alias_kind":"pith_short_12","alias_value":"YCT2XJ2DFWFJ","created_at":"2026-08-12T00:22:32Z"},{"alias_kind":"pith_short_16","alias_value":"YCT2XJ2DFWFJHBJJ","created_at":"2026-08-12T00:22:32Z"},{"alias_kind":"pith_short_8","alias_value":"YCT2XJ2D","created_at":"2026-08-12T00:22:32Z"}],"graph_snapshots":[{"event_id":"sha256:be68189dc10ec7ca76310e4d7621a11797238f7632a9f886fe93f1edc7f7fd5b","target":"graph","created_at":"2026-08-12T00:22:32Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"graph_snapshot":{"author_claims":{"count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","strong_count":0},"builder_version":"pith-number-builder-2026-05-17-v1","claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2608.09983/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"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","authors_text":"Jaan Allikvere","cross_cats":[],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.CO","submitted_at":"2026-08-05T13:05:09Z","title":"The edge multiset dimension of hypercubes"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2608.09983","kind":"arxiv","version":1},"verdict":{"created_at":null,"id":null,"model_set":{},"one_line_summary":"","pipeline_version":null,"pith_extraction_headline":"","strongest_claim":"","weakest_assumption":""}},"verdict_id":null}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:c9562853d5b873e325105869cf254637bbed69db722030dd00bf1396071fdc29","target":"record","created_at":"2026-08-12T00:22:32Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"attestation_state":"computed","canonical_record":{"metadata":{"abstract_canon_sha256":"124aade3459c4541bec8e53e557721354c13235a1fc32037e7985d53213f2abc","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.CO","submitted_at":"2026-08-05T13:05:09Z","title_canon_sha256":"1eb07277f1bbcd38c07262652425f3341fba632b365fd17917f69bd65975fa2f"},"schema_version":"1.0","source":{"id":"2608.09983","kind":"arxiv","version":1}},"canonical_sha256":"c0a7aba7432d8a93852977989a67a723645f3483058a6551cc8238bde1909103","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"c0a7aba7432d8a93852977989a67a723645f3483058a6551cc8238bde1909103","first_computed_at":"2026-08-12T00:22:32.014222Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-08-12T00:22:32.014222Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"B9U06t6bCVsw7RmzKjXFumhoi8pQMnJO6Zg9O8KzmmdfpE5zuk19loE8JE8+P5EGpjzmojyAZ2658iFzO12wBQ==","signature_status":"signed_v1","signed_at":"2026-08-12T00:22:32.015838Z","signed_message":"canonical_sha256_bytes"},"source_id":"2608.09983","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:c9562853d5b873e325105869cf254637bbed69db722030dd00bf1396071fdc29","sha256:be68189dc10ec7ca76310e4d7621a11797238f7632a9f886fe93f1edc7f7fd5b"],"state_sha256":"2669a52f3e0309f6ca5be63af7573795dc256b42b3bdc758ba0043e47725a9ff"}