{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2026:M7LA5S5JSXSTFMDHVFYGCZOLYP","short_pith_number":"pith:M7LA5S5J","schema_version":"1.0","canonical_sha256":"67d60ecba995e532b067a9706165cbc3d80e39214ac0b15551f0b37e84d86053","source":{"kind":"arxiv","id":"2602.04984","version":2},"attestation_state":"computed","paper":{"title":"Branch-and-price strikes back for the k-vertex cut problem","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"math.OC","authors_text":"Christopher Hojny, Fabio Ciccarelli, Fabio Furini, Marco L\\\"ubbecke","submitted_at":"2026-02-04T19:16:08Z","abstract_excerpt":"Given an undirected graph, the k-vertex cut problem (k-VCP) asks for a minimum-cost set of vertices whose removal yields at least k connected components in the resulting graph. The k-VCP is an important problem in network optimization, with applications in infrastructure protection and epidemic containment. We present a new extended integer linear programming (ILP) formulation that unifies and strengthens existing models and serves as the foundation for a new branch-and-price algorithm for the k-VCP. An in-depth theoretical study enables us to devise algorithmic components such as tailored bra"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"2602.04984","kind":"arxiv","version":2},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.OC","submitted_at":"2026-02-04T19:16:08Z","cross_cats_sorted":[],"title_canon_sha256":"315bc6abd58d86d73841baf15262054343e63cf32d242858667ea6bb5d2389fd","abstract_canon_sha256":"83a97c1cfdcfafab1f83a72ea6e2f41cdb6f23b4c0d1ebbaa23ff8b3b94578e5"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-06-08T01:05:06.970566Z","signature_b64":"yLNLsj95Z0AvXSt7KW+7EmcppUgooB0HEG9uRP/xQ/f4wZbVXN1+RfOEm6SDkGfzBv3I8UBueZLf7VkhCnEQAA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"67d60ecba995e532b067a9706165cbc3d80e39214ac0b15551f0b37e84d86053","last_reissued_at":"2026-06-08T01:05:06.969580Z","signature_status":"signed_v1","first_computed_at":"2026-06-08T01:05:06.969580Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Branch-and-price strikes back for the k-vertex cut problem","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"math.OC","authors_text":"Christopher Hojny, Fabio Ciccarelli, Fabio Furini, Marco L\\\"ubbecke","submitted_at":"2026-02-04T19:16:08Z","abstract_excerpt":"Given an undirected graph, the k-vertex cut problem (k-VCP) asks for a minimum-cost set of vertices whose removal yields at least k connected components in the resulting graph. The k-VCP is an important problem in network optimization, with applications in infrastructure protection and epidemic containment. We present a new extended integer linear programming (ILP) formulation that unifies and strengthens existing models and serves as the foundation for a new branch-and-price algorithm for the k-VCP. An in-depth theoretical study enables us to devise algorithmic components such as tailored bra"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2602.04984","kind":"arxiv","version":2},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2602.04984/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"},"aliases":[{"alias_kind":"arxiv","alias_value":"2602.04984","created_at":"2026-06-08T01:05:06.969718+00:00"},{"alias_kind":"arxiv_version","alias_value":"2602.04984v2","created_at":"2026-06-08T01:05:06.969718+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2602.04984","created_at":"2026-06-08T01:05:06.969718+00:00"},{"alias_kind":"pith_short_12","alias_value":"M7LA5S5JSXST","created_at":"2026-06-08T01:05:06.969718+00:00"},{"alias_kind":"pith_short_16","alias_value":"M7LA5S5JSXSTFMDH","created_at":"2026-06-08T01:05:06.969718+00:00"},{"alias_kind":"pith_short_8","alias_value":"M7LA5S5J","created_at":"2026-06-08T01:05:06.969718+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/M7LA5S5JSXSTFMDHVFYGCZOLYP","json":"https://pith.science/pith/M7LA5S5JSXSTFMDHVFYGCZOLYP.json","graph_json":"https://pith.science/api/pith-number/M7LA5S5JSXSTFMDHVFYGCZOLYP/graph.json","events_json":"https://pith.science/api/pith-number/M7LA5S5JSXSTFMDHVFYGCZOLYP/events.json","paper":"https://pith.science/paper/M7LA5S5J"},"agent_actions":{"view_html":"https://pith.science/pith/M7LA5S5JSXSTFMDHVFYGCZOLYP","download_json":"https://pith.science/pith/M7LA5S5JSXSTFMDHVFYGCZOLYP.json","view_paper":"https://pith.science/paper/M7LA5S5J","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2602.04984&json=true","fetch_graph":"https://pith.science/api/pith-number/M7LA5S5JSXSTFMDHVFYGCZOLYP/graph.json","fetch_events":"https://pith.science/api/pith-number/M7LA5S5JSXSTFMDHVFYGCZOLYP/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/M7LA5S5JSXSTFMDHVFYGCZOLYP/action/timestamp_anchor","attest_storage":"https://pith.science/pith/M7LA5S5JSXSTFMDHVFYGCZOLYP/action/storage_attestation","attest_author":"https://pith.science/pith/M7LA5S5JSXSTFMDHVFYGCZOLYP/action/author_attestation","sign_citation":"https://pith.science/pith/M7LA5S5JSXSTFMDHVFYGCZOLYP/action/citation_signature","submit_replication":"https://pith.science/pith/M7LA5S5JSXSTFMDHVFYGCZOLYP/action/replication_record"}},"created_at":"2026-06-08T01:05:06.969718+00:00","updated_at":"2026-06-08T01:05:06.969718+00:00"}