{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:B5JQLL26DFLHKDMFBRWRLAVMDI","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":"973a568a95fec5b14b2f61299199a32a798a6aa94f0182bd3f48e4206e7f2aa0","cross_cats_sorted":["cs.DS"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DM","submitted_at":"2012-03-16T15:01:40Z","title_canon_sha256":"bbb8f723d101cbb6161a686327b7aaa5ba39b35061605f9a048aea4b868d2011"},"schema_version":"1.0","source":{"id":"1203.3727","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1203.3727","created_at":"2026-05-18T03:42:23Z"},{"alias_kind":"arxiv_version","alias_value":"1203.3727v3","created_at":"2026-05-18T03:42:23Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1203.3727","created_at":"2026-05-18T03:42:23Z"},{"alias_kind":"pith_short_12","alias_value":"B5JQLL26DFLH","created_at":"2026-05-18T12:26:58Z"},{"alias_kind":"pith_short_16","alias_value":"B5JQLL26DFLHKDMF","created_at":"2026-05-18T12:26:58Z"},{"alias_kind":"pith_short_8","alias_value":"B5JQLL26","created_at":"2026-05-18T12:26:58Z"}],"graph_snapshots":[{"event_id":"sha256:b0dabc061fb02f535d1be1fa7131c21c9227969a7076687043293e4996f4edf1","target":"graph","created_at":"2026-05-18T03:42:23Z","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 Ranking r-Constraint Satisfaction Problem (ranking r-CSP) consists of a ground set of vertices V, an arity r >= 2, a parameter k and a constraint system c, where c is a function which maps rankings of r-sized subsets of V to {0,1}. The objective is to decide if there exists a ranking of the vertices satisfying all but at most k constraints. Famous ranking r-CSP include the Feedback Arc Set in Tournaments and Betweenness in Tournaments problems. We consider these problems from the kernelization viewpoint. We prove that so-called l_r-simply characterized ranking r-CSPs admit linear vertex-kern","authors_text":"Anthony Perez","cross_cats":["cs.DS"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DM","submitted_at":"2012-03-16T15:01:40Z","title":"Linear vertex-kernels for several dense ranking r-CSPs"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1203.3727","kind":"arxiv","version":3},"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":"sha256:8474e40f2e4a6a3e92991c255a7ae07e582b3d8c136843df04415403009bab66","target":"record","created_at":"2026-05-18T03:42:23Z","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":"973a568a95fec5b14b2f61299199a32a798a6aa94f0182bd3f48e4206e7f2aa0","cross_cats_sorted":["cs.DS"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DM","submitted_at":"2012-03-16T15:01:40Z","title_canon_sha256":"bbb8f723d101cbb6161a686327b7aaa5ba39b35061605f9a048aea4b868d2011"},"schema_version":"1.0","source":{"id":"1203.3727","kind":"arxiv","version":3}},"canonical_sha256":"0f5305af5e1956750d850c6d1582ac1a0750c2d23f1617ea2255d0f2ffc30e4f","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"0f5305af5e1956750d850c6d1582ac1a0750c2d23f1617ea2255d0f2ffc30e4f","first_computed_at":"2026-05-18T03:42:23.902380Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:42:23.902380Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Pwc2A28yiUevo2pTiDDZCuNxnktOb/dK020DsHn9LAqKe559k4N3xEdjm0XdyBLwxZiMz4LFkS/GDR4N0pVHDQ==","signature_status":"signed_v1","signed_at":"2026-05-18T03:42:23.903037Z","signed_message":"canonical_sha256_bytes"},"source_id":"1203.3727","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:8474e40f2e4a6a3e92991c255a7ae07e582b3d8c136843df04415403009bab66","sha256:b0dabc061fb02f535d1be1fa7131c21c9227969a7076687043293e4996f4edf1"],"state_sha256":"f7d2b4e8af145b5b05b79daeee6afc1fadbb35abf076b74ef8c7a5ca2ad4ad6f"}