{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2010:2NWVR2FNHDZHQMWBFH64NAVAUY","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":"219813ee23086a3ac8230cfd4d1b66e8b6f7be7be349cd7201d23469b073b2b5","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CC","submitted_at":"2010-12-27T20:49:07Z","title_canon_sha256":"2269d0d674eac9dac14a2b537b899ee185901cc85a75d8aef17874dcc02bd82b"},"schema_version":"1.0","source":{"id":"1012.5659","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1012.5659","created_at":"2026-05-18T04:32:22Z"},{"alias_kind":"arxiv_version","alias_value":"1012.5659v1","created_at":"2026-05-18T04:32:22Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1012.5659","created_at":"2026-05-18T04:32:22Z"},{"alias_kind":"pith_short_12","alias_value":"2NWVR2FNHDZH","created_at":"2026-05-18T12:26:03Z"},{"alias_kind":"pith_short_16","alias_value":"2NWVR2FNHDZHQMWB","created_at":"2026-05-18T12:26:03Z"},{"alias_kind":"pith_short_8","alias_value":"2NWVR2FN","created_at":"2026-05-18T12:26:03Z"}],"graph_snapshots":[{"event_id":"sha256:ebcee00ab3da8afd07fc71897ab7bccc1b5bbcd9b8b4888037188323df96ab41","target":"graph","created_at":"2026-05-18T04:32:22Z","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":"We prove a complexity dichotomy theorem for all non-negative weighted counting Constraint Satisfaction Problems (CSP). This caps a long series of important results on counting problems including unweighted and weighted graph homomorphisms and the celebrated dichotomy theorem for unweighted #CSP. Our dichotomy theorem gives a succinct criterion for tractability. If a set F of constraint functions satisfies the criterion, then the counting CSP problem defined by F is solvable in polynomial time; if it does not satisfy the criterion, then the problem is #P-hard. We furthermore show that the quest","authors_text":"Jin-Yi Cai, Pinyan Lu, Xi Chen","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CC","submitted_at":"2010-12-27T20:49:07Z","title":"Non-negative Weighted #CSPs: An Effective Complexity Dichotomy"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1012.5659","kind":"arxiv","version":1},"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:b068a2507f10ae60bed0d2f10774fdc5f7796b50bb74bc7903501f64442c3fed","target":"record","created_at":"2026-05-18T04:32:22Z","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":"219813ee23086a3ac8230cfd4d1b66e8b6f7be7be349cd7201d23469b073b2b5","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CC","submitted_at":"2010-12-27T20:49:07Z","title_canon_sha256":"2269d0d674eac9dac14a2b537b899ee185901cc85a75d8aef17874dcc02bd82b"},"schema_version":"1.0","source":{"id":"1012.5659","kind":"arxiv","version":1}},"canonical_sha256":"d36d58e8ad38f27832c129fdc682a0a620f6ad9aabd5914885ec31e853017778","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"d36d58e8ad38f27832c129fdc682a0a620f6ad9aabd5914885ec31e853017778","first_computed_at":"2026-05-18T04:32:22.655763Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:32:22.655763Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Qy+UhOeyCii/K0O8OmfU+bz9BKnDYB5YaJaM9jCvLyJoGBlzVbQIPSGvopoIENN7+mT3nkmLsS2mwNOgNkQoAg==","signature_status":"signed_v1","signed_at":"2026-05-18T04:32:22.656478Z","signed_message":"canonical_sha256_bytes"},"source_id":"1012.5659","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:b068a2507f10ae60bed0d2f10774fdc5f7796b50bb74bc7903501f64442c3fed","sha256:ebcee00ab3da8afd07fc71897ab7bccc1b5bbcd9b8b4888037188323df96ab41"],"state_sha256":"8453bcea18396082a6c841a4a771a27b0d53dcd33ab5dcfb4a7e743003e2411d"}