{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2025:ALB2ZBGCXTHITTQU6L6HBER3XK","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":"9b71bb7357d6d39edc6bd47bac972c278f10f21d9d3af3f01bb558694f32cd94","cross_cats_sorted":["cs.DM"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.DS","submitted_at":"2025-06-26T13:11:12Z","title_canon_sha256":"5d0c364fb3a153c54014edd957d14190a13a7481a6c5b35770b14bb14ab25a15"},"schema_version":"1.0","source":{"id":"2506.21216","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2506.21216","created_at":"2026-07-05T11:27:41Z"},{"alias_kind":"arxiv_version","alias_value":"2506.21216v1","created_at":"2026-07-05T11:27:41Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2506.21216","created_at":"2026-07-05T11:27:41Z"},{"alias_kind":"pith_short_12","alias_value":"ALB2ZBGCXTHI","created_at":"2026-07-05T11:27:41Z"},{"alias_kind":"pith_short_16","alias_value":"ALB2ZBGCXTHITTQU","created_at":"2026-07-05T11:27:41Z"},{"alias_kind":"pith_short_8","alias_value":"ALB2ZBGC","created_at":"2026-07-05T11:27:41Z"}],"graph_snapshots":[{"event_id":"sha256:0eb96c74e0c41fe33bbf59d49f9040eb53074063183d0264fabac8a65c57243f","target":"graph","created_at":"2026-07-05T11:27:41Z","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/2506.21216/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Covering and partitioning the edges of a graph into cliques are classical problems at the intersection of combinatorial optimization and graph theory, having been studied through a range of algorithmic and complexity-theoretic lenses. Despite the well-known fixed-parameter tractability of these problems when parameterized by the total number of cliques, such a parameterization often fails to be meaningful for sparse graphs. In many real-world instances, on the other hand, the minimum number of cliques in an edge cover or partition can be very close to the size of a maximum independent set \\alp","authors_text":"Danil Sagunov, Fedor V. Fomin, Kirill Simonov, Petr A. Golovach","cross_cats":["cs.DM"],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.DS","submitted_at":"2025-06-26T13:11:12Z","title":"Edge Clique Partition and Cover Beyond Independence"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2506.21216","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":"sha256:4eee4bbc9aa47dc5c3d8d5e5c3dc8ffe29add3800da297d48a911be4d2c432a8","target":"record","created_at":"2026-07-05T11:27:41Z","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":"9b71bb7357d6d39edc6bd47bac972c278f10f21d9d3af3f01bb558694f32cd94","cross_cats_sorted":["cs.DM"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.DS","submitted_at":"2025-06-26T13:11:12Z","title_canon_sha256":"5d0c364fb3a153c54014edd957d14190a13a7481a6c5b35770b14bb14ab25a15"},"schema_version":"1.0","source":{"id":"2506.21216","kind":"arxiv","version":1}},"canonical_sha256":"02c3ac84c2bcce89ce14f2fc70923bba989c2e28b293348c1c61a56c47398a8e","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"02c3ac84c2bcce89ce14f2fc70923bba989c2e28b293348c1c61a56c47398a8e","first_computed_at":"2026-07-05T11:27:41.577701Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T11:27:41.577701Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"BlivXTdeZ13Wxru8YYiXIykvsbmgXiF//uXr3Bwpe4c+IQkbYBUZeoo6T4+Y0vyrme9ZAz3qwDtBSyRzPD/1Dg==","signature_status":"signed_v1","signed_at":"2026-07-05T11:27:41.578303Z","signed_message":"canonical_sha256_bytes"},"source_id":"2506.21216","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:4eee4bbc9aa47dc5c3d8d5e5c3dc8ffe29add3800da297d48a911be4d2c432a8","sha256:0eb96c74e0c41fe33bbf59d49f9040eb53074063183d0264fabac8a65c57243f"],"state_sha256":"d641a21fe97f73efc3d2fa626f4c82aa2653b535138a40c6c36fb40ad38bbc3c"}