{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2025:FCZGSBSKN422T6HLUJPDUXHXVC","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":"9bb0e8c2ff50468d29a48aa5e2474d27aaade6d2ceda982145e5cd4d8b74b16f","cross_cats_sorted":["cs.CC"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.DS","submitted_at":"2025-09-16T22:59:51Z","title_canon_sha256":"92799fd37016e0791068b3307e74e0535cff7ec797c77079d02d675a9f7ca5d5"},"schema_version":"1.0","source":{"id":"2509.13584","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2509.13584","created_at":"2026-06-25T00:18:11Z"},{"alias_kind":"arxiv_version","alias_value":"2509.13584v2","created_at":"2026-06-25T00:18:11Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2509.13584","created_at":"2026-06-25T00:18:11Z"},{"alias_kind":"pith_short_12","alias_value":"FCZGSBSKN422","created_at":"2026-06-25T00:18:11Z"},{"alias_kind":"pith_short_16","alias_value":"FCZGSBSKN422T6HL","created_at":"2026-06-25T00:18:11Z"},{"alias_kind":"pith_short_8","alias_value":"FCZGSBSK","created_at":"2026-06-25T00:18:11Z"}],"graph_snapshots":[{"event_id":"sha256:6871a7d4df8f45a77872600f5375cd35124b430efe60a44c720e269ae0d86ac1","target":"graph","created_at":"2026-06-25T00:18:11Z","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/2509.13584/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"The k-core of a graph is its maximal subgraph with minimum degree at least k, and the core value of a vertex u is the largest k for which u is contained in the k-core of the graph. Among cohesive subgraphs, k-core and its variants have received a lot of attention recently, particularly on dynamic graphs, as reported by Hanauer, Henzinger, and Schulz in their recent survey on dynamic graph algorithms. We answer questions on k-core stated in the survey, proving that there is no efficient dynamic algorithm for k-core or to find (2 - {\\epsilon})-approximations for the core values, unless we can im","authors_text":"Cristina G. Fernandes, Yan S. Couto","cross_cats":["cs.CC"],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.DS","submitted_at":"2025-09-16T22:59:51Z","title":"Hardness of Dynamic Core and Truss Decompositions"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2509.13584","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":"sha256:5d9ad49968085492f53ef19e794eace26ede9349c2de27360a2c1507234c8078","target":"record","created_at":"2026-06-25T00:18:11Z","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":"9bb0e8c2ff50468d29a48aa5e2474d27aaade6d2ceda982145e5cd4d8b74b16f","cross_cats_sorted":["cs.CC"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.DS","submitted_at":"2025-09-16T22:59:51Z","title_canon_sha256":"92799fd37016e0791068b3307e74e0535cff7ec797c77079d02d675a9f7ca5d5"},"schema_version":"1.0","source":{"id":"2509.13584","kind":"arxiv","version":2}},"canonical_sha256":"28b269064a6f35a9f8eba25e3a5cf7a88a7f847b8ff64afcce69dd661cfb7182","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"28b269064a6f35a9f8eba25e3a5cf7a88a7f847b8ff64afcce69dd661cfb7182","first_computed_at":"2026-06-25T00:18:11.619454Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-06-25T00:18:11.619454Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"estpJK4XVo8yl6WBEVGi8fYRVCuim8Yzw39BDofqfq9yVvZ3cPzkEjFAB0+4121sYfxrLpFswAi34hvQyVBSAQ==","signature_status":"signed_v1","signed_at":"2026-06-25T00:18:11.619940Z","signed_message":"canonical_sha256_bytes"},"source_id":"2509.13584","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:5d9ad49968085492f53ef19e794eace26ede9349c2de27360a2c1507234c8078","sha256:6871a7d4df8f45a77872600f5375cd35124b430efe60a44c720e269ae0d86ac1"],"state_sha256":"6ca99f22220619589041528b448518b01aeab3beec5fc2255cd40dbfa79297ea"}