{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2012:5J3SMXPNZY6G4DEEWCJ26LGQQH","short_pith_number":"pith:5J3SMXPN","canonical_record":{"source":{"id":"1210.2987","kind":"arxiv","version":4},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CC","submitted_at":"2012-10-10T17:17:43Z","cross_cats_sorted":[],"title_canon_sha256":"98d0219f0ff6975425bc5972179a9672b447be18fcdbf8c660709429503fe54f","abstract_canon_sha256":"ca16dfd448ad91d43aacb1345fcf22a0c52ad12d2ae21a0eda9ff1c686d64b5e"},"schema_version":"1.0"},"canonical_sha256":"ea77265dedce3c6e0c84b093af2cd081d845e26997c09b9baefccd1228cac49a","source":{"kind":"arxiv","id":"1210.2987","version":4},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1210.2987","created_at":"2026-05-18T01:04:09Z"},{"alias_kind":"arxiv_version","alias_value":"1210.2987v4","created_at":"2026-05-18T01:04:09Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1210.2987","created_at":"2026-05-18T01:04:09Z"},{"alias_kind":"pith_short_12","alias_value":"5J3SMXPNZY6G","created_at":"2026-05-18T12:26:53Z"},{"alias_kind":"pith_short_16","alias_value":"5J3SMXPNZY6G4DEE","created_at":"2026-05-18T12:26:53Z"},{"alias_kind":"pith_short_8","alias_value":"5J3SMXPN","created_at":"2026-05-18T12:26:53Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2012:5J3SMXPNZY6G4DEEWCJ26LGQQH","target":"record","payload":{"canonical_record":{"source":{"id":"1210.2987","kind":"arxiv","version":4},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CC","submitted_at":"2012-10-10T17:17:43Z","cross_cats_sorted":[],"title_canon_sha256":"98d0219f0ff6975425bc5972179a9672b447be18fcdbf8c660709429503fe54f","abstract_canon_sha256":"ca16dfd448ad91d43aacb1345fcf22a0c52ad12d2ae21a0eda9ff1c686d64b5e"},"schema_version":"1.0"},"canonical_sha256":"ea77265dedce3c6e0c84b093af2cd081d845e26997c09b9baefccd1228cac49a","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:04:09.705495Z","signature_b64":"MowszFbqDqja/mfAILrDXHxTSFCKix61AgyMsGplPtLNA0oWck4aSYYrtExZ4rsvz4OitqZ0F7+5mJS48v+rBw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"ea77265dedce3c6e0c84b093af2cd081d845e26997c09b9baefccd1228cac49a","last_reissued_at":"2026-05-18T01:04:09.704850Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:04:09.704850Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1210.2987","source_version":4,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T01:04:09Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"PBvVwz4B+r9pnF+vIWqMSVSo0jIsGrEM+4nyvpP0/SIHlymP3KVusY36G0+M8ROiQxxir0A9iO5TIzmikMdaAw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-05T10:28:45.460549Z"},"content_sha256":"9464dfac2d35020672f6b3a7c6bec5ae544598885b435fa85673603d17ebf1e3","schema_version":"1.0","event_id":"sha256:9464dfac2d35020672f6b3a7c6bec5ae544598885b435fa85673603d17ebf1e3"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2012:5J3SMXPNZY6G4DEEWCJ26LGQQH","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"The complexity of finite-valued CSPs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.CC","authors_text":"Johan Thapper, Stanislav Zivny","submitted_at":"2012-10-10T17:17:43Z","abstract_excerpt":"We study the computational complexity of exact minimisation of rational-valued discrete functions. Let $\\Gamma$ be a set of rational-valued functions on a fixed finite domain; such a set is called a finite-valued constraint language. The valued constraint satisfaction problem, $\\operatorname{VCSP}(\\Gamma)$, is the problem of minimising a function given as a sum of functions from $\\Gamma$. We establish a dichotomy theorem with respect to exact solvability for all finite-valued constraint languages defined on domains of arbitrary finite size.\n  We show that every constraint language $\\Gamma$ eit"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1210.2987","kind":"arxiv","version":4},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"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"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T01:04:09Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"rY5kEd+reLCa3A/lRA+l6pHn1TwcfDU3HRAOYbj5CJkcmFS8bvekdSyCSp7iKUuh/AACrTQ01PuCvP5qTGWBCw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-05T10:28:45.460894Z"},"content_sha256":"bda20cf717f82480dc29a1b678497b3c2d57650822c4b6091ef31445d1bbefd2","schema_version":"1.0","event_id":"sha256:bda20cf717f82480dc29a1b678497b3c2d57650822c4b6091ef31445d1bbefd2"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/5J3SMXPNZY6G4DEEWCJ26LGQQH/bundle.json","state_url":"https://pith.science/pith/5J3SMXPNZY6G4DEEWCJ26LGQQH/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/5J3SMXPNZY6G4DEEWCJ26LGQQH/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-06-05T10:28:45Z","links":{"resolver":"https://pith.science/pith/5J3SMXPNZY6G4DEEWCJ26LGQQH","bundle":"https://pith.science/pith/5J3SMXPNZY6G4DEEWCJ26LGQQH/bundle.json","state":"https://pith.science/pith/5J3SMXPNZY6G4DEEWCJ26LGQQH/state.json","well_known_bundle":"https://pith.science/.well-known/pith/5J3SMXPNZY6G4DEEWCJ26LGQQH/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:5J3SMXPNZY6G4DEEWCJ26LGQQH","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":"ca16dfd448ad91d43aacb1345fcf22a0c52ad12d2ae21a0eda9ff1c686d64b5e","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CC","submitted_at":"2012-10-10T17:17:43Z","title_canon_sha256":"98d0219f0ff6975425bc5972179a9672b447be18fcdbf8c660709429503fe54f"},"schema_version":"1.0","source":{"id":"1210.2987","kind":"arxiv","version":4}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1210.2987","created_at":"2026-05-18T01:04:09Z"},{"alias_kind":"arxiv_version","alias_value":"1210.2987v4","created_at":"2026-05-18T01:04:09Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1210.2987","created_at":"2026-05-18T01:04:09Z"},{"alias_kind":"pith_short_12","alias_value":"5J3SMXPNZY6G","created_at":"2026-05-18T12:26:53Z"},{"alias_kind":"pith_short_16","alias_value":"5J3SMXPNZY6G4DEE","created_at":"2026-05-18T12:26:53Z"},{"alias_kind":"pith_short_8","alias_value":"5J3SMXPN","created_at":"2026-05-18T12:26:53Z"}],"graph_snapshots":[{"event_id":"sha256:bda20cf717f82480dc29a1b678497b3c2d57650822c4b6091ef31445d1bbefd2","target":"graph","created_at":"2026-05-18T01:04:09Z","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 study the computational complexity of exact minimisation of rational-valued discrete functions. Let $\\Gamma$ be a set of rational-valued functions on a fixed finite domain; such a set is called a finite-valued constraint language. The valued constraint satisfaction problem, $\\operatorname{VCSP}(\\Gamma)$, is the problem of minimising a function given as a sum of functions from $\\Gamma$. We establish a dichotomy theorem with respect to exact solvability for all finite-valued constraint languages defined on domains of arbitrary finite size.\n  We show that every constraint language $\\Gamma$ eit","authors_text":"Johan Thapper, Stanislav Zivny","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CC","submitted_at":"2012-10-10T17:17:43Z","title":"The complexity of finite-valued CSPs"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1210.2987","kind":"arxiv","version":4},"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":"sha256:9464dfac2d35020672f6b3a7c6bec5ae544598885b435fa85673603d17ebf1e3","target":"record","created_at":"2026-05-18T01:04:09Z","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":"ca16dfd448ad91d43aacb1345fcf22a0c52ad12d2ae21a0eda9ff1c686d64b5e","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CC","submitted_at":"2012-10-10T17:17:43Z","title_canon_sha256":"98d0219f0ff6975425bc5972179a9672b447be18fcdbf8c660709429503fe54f"},"schema_version":"1.0","source":{"id":"1210.2987","kind":"arxiv","version":4}},"canonical_sha256":"ea77265dedce3c6e0c84b093af2cd081d845e26997c09b9baefccd1228cac49a","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"ea77265dedce3c6e0c84b093af2cd081d845e26997c09b9baefccd1228cac49a","first_computed_at":"2026-05-18T01:04:09.704850Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:04:09.704850Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"MowszFbqDqja/mfAILrDXHxTSFCKix61AgyMsGplPtLNA0oWck4aSYYrtExZ4rsvz4OitqZ0F7+5mJS48v+rBw==","signature_status":"signed_v1","signed_at":"2026-05-18T01:04:09.705495Z","signed_message":"canonical_sha256_bytes"},"source_id":"1210.2987","source_kind":"arxiv","source_version":4}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:9464dfac2d35020672f6b3a7c6bec5ae544598885b435fa85673603d17ebf1e3","sha256:bda20cf717f82480dc29a1b678497b3c2d57650822c4b6091ef31445d1bbefd2"],"state_sha256":"b807299bb7c85c1fd65254fa248b354f7d867d05fbca18cbc001a02a47e56a26"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"+48Cp6SIBcWiY14bF6V5qZc1fDuxaXWvKG/1/8EhimwyEn4z6fF3IovD+yzvOf4Fgn3HskWLzDrHApObG7WJCQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-05T10:28:45.462835Z","bundle_sha256":"41ced1471a789cf12568f298f0aa4abe953bf730ba0e21f6b7e34b6787bf8434"}}