{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2023:5HM2ZCAKENXFSOIAWWFUULW5BR","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":"de164dc173c0c788bc6cf2f7d97aa35ec7bbe4ee4d37585120531a37280130c0","cross_cats_sorted":["cs.DM"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.CO","submitted_at":"2023-04-13T12:46:36Z","title_canon_sha256":"5180989f5bd73b7d20e6edd934b12f17ca5eb17d52562c1841e85a8403af885d"},"schema_version":"1.0","source":{"id":"2304.06453","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2304.06453","created_at":"2026-07-05T06:00:43Z"},{"alias_kind":"arxiv_version","alias_value":"2304.06453v1","created_at":"2026-07-05T06:00:43Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2304.06453","created_at":"2026-07-05T06:00:43Z"},{"alias_kind":"pith_short_12","alias_value":"5HM2ZCAKENXF","created_at":"2026-07-05T06:00:43Z"},{"alias_kind":"pith_short_16","alias_value":"5HM2ZCAKENXFSOIA","created_at":"2026-07-05T06:00:43Z"},{"alias_kind":"pith_short_8","alias_value":"5HM2ZCAK","created_at":"2026-07-05T06:00:43Z"}],"graph_snapshots":[{"event_id":"sha256:c2567a4888a8e8d58224f7b944147980fe6d19388dba8172f614f5a3b5b0d385","target":"graph","created_at":"2026-07-05T06:00:43Z","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/2304.06453/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Median graphs are connected graphs in which for all three vertices there is a unique vertex that belongs to shortest paths between each pair of these three vertices. To be more formal, a graph $G$ is a median graph if, for all $\\mu, u,v\\in V(G)$, it holds that $|I(\\mu,u)\\cap I(\\mu,v)\\cap I(u,v)|=1$ where $I(x,y)$ denotes the set of all vertices that lie on shortest paths connecting $x$ and $y$. In this paper we are interested in a natural generalization of median graphs, called $k$-median graphs. A graph $G$ is a $k$-median graph, if there are $k$ vertices $\\mu_1,\\dots,\\mu_k\\in V(G)$ such that","authors_text":"Marc Hellmuth, Sandhya Thekkumpadan Puthiyaveedu","cross_cats":["cs.DM"],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.CO","submitted_at":"2023-04-13T12:46:36Z","title":"On a generalization of median graphs: $k$-median graphs"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2304.06453","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:b29fade8f1fef99d425291131f19c00d002149ee971cd21e7cf1fe098bab3180","target":"record","created_at":"2026-07-05T06:00:43Z","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":"de164dc173c0c788bc6cf2f7d97aa35ec7bbe4ee4d37585120531a37280130c0","cross_cats_sorted":["cs.DM"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.CO","submitted_at":"2023-04-13T12:46:36Z","title_canon_sha256":"5180989f5bd73b7d20e6edd934b12f17ca5eb17d52562c1841e85a8403af885d"},"schema_version":"1.0","source":{"id":"2304.06453","kind":"arxiv","version":1}},"canonical_sha256":"e9d9ac880a236e593900b58b4a2edd0c780d4110dcfda7aa156eb3ff58ce5c6c","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"e9d9ac880a236e593900b58b4a2edd0c780d4110dcfda7aa156eb3ff58ce5c6c","first_computed_at":"2026-07-05T06:00:43.544791Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T06:00:43.544791Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"0wknNrPSmhbosk6smpluPtLXKzXU6F4gWJFb2ZDSQGwz874Vakxw3gZsRYlULU2qr25Tf1ueEaiIx7pEYPpyAQ==","signature_status":"signed_v1","signed_at":"2026-07-05T06:00:43.545199Z","signed_message":"canonical_sha256_bytes"},"source_id":"2304.06453","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:b29fade8f1fef99d425291131f19c00d002149ee971cd21e7cf1fe098bab3180","sha256:c2567a4888a8e8d58224f7b944147980fe6d19388dba8172f614f5a3b5b0d385"],"state_sha256":"734d178ea0f1f5e16aa01d77d58350e2b3bbff28c112a9bd5c14f2a92049f542"}