{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:QIZA4IJPV2UERF74HASXZIQSJL","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":"19ce98d1b51f32ca96b43aede5e26eed0ad736e48a9329e150d829ad9d324af8","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2015-11-02T19:37:03Z","title_canon_sha256":"9a05321bfda562280bc71dcf69f3cd8db95be82ddfad3690697e16323af8d228"},"schema_version":"1.0","source":{"id":"1511.00648","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1511.00648","created_at":"2026-05-18T01:01:44Z"},{"alias_kind":"arxiv_version","alias_value":"1511.00648v2","created_at":"2026-05-18T01:01:44Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1511.00648","created_at":"2026-05-18T01:01:44Z"},{"alias_kind":"pith_short_12","alias_value":"QIZA4IJPV2UE","created_at":"2026-05-18T12:29:37Z"},{"alias_kind":"pith_short_16","alias_value":"QIZA4IJPV2UERF74","created_at":"2026-05-18T12:29:37Z"},{"alias_kind":"pith_short_8","alias_value":"QIZA4IJP","created_at":"2026-05-18T12:29:37Z"}],"graph_snapshots":[{"event_id":"sha256:3d1474cfac30ff6fdc85bc1d385e8859c3d5364b74f0f2b365d37d6db19f253f","target":"graph","created_at":"2026-05-18T01:01:44Z","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":"Given a constraint satisfaction problem (CSP) on $n$ variables, $x_1, x_2, \\dots, x_n \\in \\{\\pm 1\\}$, and $m$ constraints, a global cardinality constraint has the form of $\\sum_{i = 1}^{n} x_i = (1-2p)n$, where $p \\in (\\Omega(1), 1 - \\Omega(1))$ and $pn$ is an integer. Let $AVG$ be the expected number of constraints satisfied by randomly choosing an assignment to $x_1, x_2, \\dots, x_n$, complying with the global cardinality constraint. The CSP above average with the global cardinality constraint problem asks whether there is an assignment (complying with the cardinality constraint) that satisf","authors_text":"Xue Chen, Yuan Zhou","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2015-11-02T19:37:03Z","title":"Parameterized Algorithms for Constraint Satisfaction Problems Above Average with Global Cardinality Constraints"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1511.00648","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:ca05f12b19364adca558339c624912e02e91a2273760d27acdd6ace87d65d7fc","target":"record","created_at":"2026-05-18T01:01:44Z","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":"19ce98d1b51f32ca96b43aede5e26eed0ad736e48a9329e150d829ad9d324af8","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2015-11-02T19:37:03Z","title_canon_sha256":"9a05321bfda562280bc71dcf69f3cd8db95be82ddfad3690697e16323af8d228"},"schema_version":"1.0","source":{"id":"1511.00648","kind":"arxiv","version":2}},"canonical_sha256":"82320e212faea84897fc38257ca2124addc19905199eba2b0b87fdc89fa4e0e8","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"82320e212faea84897fc38257ca2124addc19905199eba2b0b87fdc89fa4e0e8","first_computed_at":"2026-05-18T01:01:44.903169Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:01:44.903169Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"G2m0EHy3dhelCNXbyY3flTan0ppGhhg8KaXlaQpns9axcWjokicxAW4w/LYAtu5LQE6+ixf+94DibJm4khQEBQ==","signature_status":"signed_v1","signed_at":"2026-05-18T01:01:44.903829Z","signed_message":"canonical_sha256_bytes"},"source_id":"1511.00648","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:ca05f12b19364adca558339c624912e02e91a2273760d27acdd6ace87d65d7fc","sha256:3d1474cfac30ff6fdc85bc1d385e8859c3d5364b74f0f2b365d37d6db19f253f"],"state_sha256":"31922d336f147af62bb8dcdbacab198b510ca2f2a4c17a121a3212ca22e2a405"}