{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:7QLLCT3UQPAW5IKATLZ7RD7CYB","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":"ef69f9839cc7eeed9bfa1235498e5080cf3d56d50a2ae46cfb26617f25e14e78","cross_cats_sorted":["cs.CC","cs.SI"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2018-09-07T12:21:03Z","title_canon_sha256":"ad8d14fb812b2fa8cf9a1ad0dc24fcf80e6f0dfa16c4f2a6b2ab89f6d8e4fa1e"},"schema_version":"1.0","source":{"id":"1809.02434","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1809.02434","created_at":"2026-05-17T23:55:07Z"},{"alias_kind":"arxiv_version","alias_value":"1809.02434v2","created_at":"2026-05-17T23:55:07Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1809.02434","created_at":"2026-05-17T23:55:07Z"},{"alias_kind":"pith_short_12","alias_value":"7QLLCT3UQPAW","created_at":"2026-05-18T12:32:11Z"},{"alias_kind":"pith_short_16","alias_value":"7QLLCT3UQPAW5IKA","created_at":"2026-05-18T12:32:11Z"},{"alias_kind":"pith_short_8","alias_value":"7QLLCT3U","created_at":"2026-05-18T12:32:11Z"}],"graph_snapshots":[{"event_id":"sha256:5190213b45e6f691f32d518992b9d0bac65c05fca3fd49072b42d1c6438d036e","target":"graph","created_at":"2026-05-17T23:55:07Z","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":"A central problem in graph mining is finding dense subgraphs, with several applications in different fields, a notable example being identifying communities. While a lot of effort has been put on the problem of finding a single dense subgraph, only recently the focus has been shifted to the problem of finding a set of densest subgraphs. Some approaches aim at finding disjoint subgraphs, while in many real-world networks communities are often overlapping. An approach introduced to find possible overlapping subgraphs is the Top-k Overlapping Densest Subgraphs problem. For a given integer k >= 1,","authors_text":"Giancarlo Mauri, Italo Zoppis, Mohammad Mehdi Hosseinzadeh, Riccardo Dondi","cross_cats":["cs.CC","cs.SI"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2018-09-07T12:21:03Z","title":"Top-k Overlapping Densest Subgraphs: Approximation and Complexity"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1809.02434","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":"sha256:32ed433b1cd010b75055aab811375cf6a3567dfab6d49484afa48ba9d30c0ec0","target":"record","created_at":"2026-05-17T23:55:07Z","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":"ef69f9839cc7eeed9bfa1235498e5080cf3d56d50a2ae46cfb26617f25e14e78","cross_cats_sorted":["cs.CC","cs.SI"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2018-09-07T12:21:03Z","title_canon_sha256":"ad8d14fb812b2fa8cf9a1ad0dc24fcf80e6f0dfa16c4f2a6b2ab89f6d8e4fa1e"},"schema_version":"1.0","source":{"id":"1809.02434","kind":"arxiv","version":2}},"canonical_sha256":"fc16b14f7483c16ea1409af3f88fe2c0431cbd80c44c99520a3f9b2eb0b9ec82","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"fc16b14f7483c16ea1409af3f88fe2c0431cbd80c44c99520a3f9b2eb0b9ec82","first_computed_at":"2026-05-17T23:55:07.439056Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:55:07.439056Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"C+jIoU04AFmcO6ei/o/yJqT3h3JK4p1bVZt5kPMDr1m3iCua0e9X+S0TN/EEzz/BNBXxQZM4urqtBMJ2QP2xDg==","signature_status":"signed_v1","signed_at":"2026-05-17T23:55:07.439596Z","signed_message":"canonical_sha256_bytes"},"source_id":"1809.02434","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:32ed433b1cd010b75055aab811375cf6a3567dfab6d49484afa48ba9d30c0ec0","sha256:5190213b45e6f691f32d518992b9d0bac65c05fca3fd49072b42d1c6438d036e"],"state_sha256":"26b874d05d2098cc04089f940f41fb2d8dceb9f511acf1baae7a395f147872b4"}