{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2006:6LKVNARKYPDV2OBRIFQV42HODO","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":"5e6d22cf6428ef928080f3a3fb96cf2cdd612543109937c285fe1ec891cf9094","cross_cats_sorted":["cs.LO"],"license":"","primary_cat":"cs.CC","submitted_at":"2006-09-19T15:12:46Z","title_canon_sha256":"84247258062a55752ea9bd23c615e6ce4d3c99feb32f2a7b0e6636d00d8a4624"},"schema_version":"1.0","source":{"id":"cs/0609108","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"cs/0609108","created_at":"2026-05-18T00:53:03Z"},{"alias_kind":"arxiv_version","alias_value":"cs/0609108v2","created_at":"2026-05-18T00:53:03Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.cs/0609108","created_at":"2026-05-18T00:53:03Z"},{"alias_kind":"pith_short_12","alias_value":"6LKVNARKYPDV","created_at":"2026-05-18T12:25:53Z"},{"alias_kind":"pith_short_16","alias_value":"6LKVNARKYPDV2OBR","created_at":"2026-05-18T12:25:53Z"},{"alias_kind":"pith_short_8","alias_value":"6LKVNARK","created_at":"2026-05-18T12:25:53Z"}],"graph_snapshots":[{"event_id":"sha256:d11ae7dd961452cbf97c266bfbcf4ae7620e6c41da0f07ab4e97e73cf79b9440","target":"graph","created_at":"2026-05-18T00:53:03Z","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":"Generalized majority-minority (GMM) operations are introduced as a common generalization of near unanimity operations and Mal'tsev operations on finite sets. We show that every instance of the constraint satisfaction problem (CSP), where all constraint relations are invariant under a (fixed) GMM operation, is solvable in polynomial time. This constitutes one of the largest tractable cases of the CSP.","authors_text":"Victor Dalmau","cross_cats":["cs.LO"],"headline":"","license":"","primary_cat":"cs.CC","submitted_at":"2006-09-19T15:12:46Z","title":"Generalized Majority-Minority Operations are Tractable"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"cs/0609108","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:d76fff7775fc94277f467b6a57ab2288fda169b084d85857dbedbc011abf7840","target":"record","created_at":"2026-05-18T00:53:03Z","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":"5e6d22cf6428ef928080f3a3fb96cf2cdd612543109937c285fe1ec891cf9094","cross_cats_sorted":["cs.LO"],"license":"","primary_cat":"cs.CC","submitted_at":"2006-09-19T15:12:46Z","title_canon_sha256":"84247258062a55752ea9bd23c615e6ce4d3c99feb32f2a7b0e6636d00d8a4624"},"schema_version":"1.0","source":{"id":"cs/0609108","kind":"arxiv","version":2}},"canonical_sha256":"f2d556822ac3c75d383141615e68ee1b84801dda9b92462186cdca06cfe34c3f","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"f2d556822ac3c75d383141615e68ee1b84801dda9b92462186cdca06cfe34c3f","first_computed_at":"2026-05-18T00:53:03.320268Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:53:03.320268Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"b4csK89U7G6k7xNnswp1sYyhbLTQtZS21ifSU0jN+s/5Ez1n0bUl3xb+mDviNFLL1EDW65by21ueMhGufyxrDA==","signature_status":"signed_v1","signed_at":"2026-05-18T00:53:03.320835Z","signed_message":"canonical_sha256_bytes"},"source_id":"cs/0609108","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:d76fff7775fc94277f467b6a57ab2288fda169b084d85857dbedbc011abf7840","sha256:d11ae7dd961452cbf97c266bfbcf4ae7620e6c41da0f07ab4e97e73cf79b9440"],"state_sha256":"a2b79e52f35ef979d869898c497b2271988b83c13e8aa5930c958330e57ecf01"}