{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:AU2AVEY6UCDPGV5GVD35TDJUS2","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":"7492a417dfe5d39989ac75434503fa73d9a47ed555c65bc661799f280065c97c","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DM","submitted_at":"2017-06-21T10:49:31Z","title_canon_sha256":"36d749523ae22734441dcd12ca7bd2e4bdfebf8a811f1fc3377b195a2d753412"},"schema_version":"1.0","source":{"id":"1706.06822","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1706.06822","created_at":"2026-05-18T00:37:57Z"},{"alias_kind":"arxiv_version","alias_value":"1706.06822v2","created_at":"2026-05-18T00:37:57Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1706.06822","created_at":"2026-05-18T00:37:57Z"},{"alias_kind":"pith_short_12","alias_value":"AU2AVEY6UCDP","created_at":"2026-05-18T12:31:08Z"},{"alias_kind":"pith_short_16","alias_value":"AU2AVEY6UCDPGV5G","created_at":"2026-05-18T12:31:08Z"},{"alias_kind":"pith_short_8","alias_value":"AU2AVEY6","created_at":"2026-05-18T12:31:08Z"}],"graph_snapshots":[{"event_id":"sha256:bc0a7a462bbb664f9917f499767c3997c8665c3cb39aa789c4b7ee6f329db3eb","target":"graph","created_at":"2026-05-18T00:37:57Z","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"},"paper":{"abstract_excerpt":"We study the problem of decomposing (clustering) a tree with respect to costs attributed to pairs of nodes, so as to minimize the sum of costs for those pairs of nodes that are in the same component (cluster). For the general case and for the special case of the tree being a star, we show that the problem is NP-hard. For the special case of the tree being a path, this problem is known to be polynomial time solvable. We characterize several classes of facets of the combinatorial polytope associated with a formulation of this clustering problem in terms of lifted multicuts. In particular, our re","authors_text":"Bjoern Andres, Jan-Hendrik Lange","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DM","submitted_at":"2017-06-21T10:49:31Z","title":"Decomposition of Trees and Paths via Correlation"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1706.06822","kind":"arxiv","version":2},"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:c56017f5df863c1f49afebd7ba5b5c95d660b62dfb3ce63e9ba74c7c4f62b000","target":"record","created_at":"2026-05-18T00:37:57Z","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":"7492a417dfe5d39989ac75434503fa73d9a47ed555c65bc661799f280065c97c","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DM","submitted_at":"2017-06-21T10:49:31Z","title_canon_sha256":"36d749523ae22734441dcd12ca7bd2e4bdfebf8a811f1fc3377b195a2d753412"},"schema_version":"1.0","source":{"id":"1706.06822","kind":"arxiv","version":2}},"canonical_sha256":"05340a931ea086f357a6a8f7d98d3496a8fca539b3afa184379bc64ffbb67055","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"05340a931ea086f357a6a8f7d98d3496a8fca539b3afa184379bc64ffbb67055","first_computed_at":"2026-05-18T00:37:57.423698Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:37:57.423698Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"KuCjoDS7M/7Uanhql58wESWf907rqwpa5z/XoMnzTx8uPLlvpU22x47N8/krN9nqAU5szvtnsCB8ocvKqDuWAA==","signature_status":"signed_v1","signed_at":"2026-05-18T00:37:57.424331Z","signed_message":"canonical_sha256_bytes"},"source_id":"1706.06822","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:c56017f5df863c1f49afebd7ba5b5c95d660b62dfb3ce63e9ba74c7c4f62b000","sha256:bc0a7a462bbb664f9917f499767c3997c8665c3cb39aa789c4b7ee6f329db3eb"],"state_sha256":"db1871e4d1930efdc96a57eff9a29e161cf1910c4ac0bb1ec51527cb8dc614e1"}