{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2013:6NHE5SFM4K55DAPODAFFPXRK2I","short_pith_number":"pith:6NHE5SFM","schema_version":"1.0","canonical_sha256":"f34e4ec8ace2bbd181ee180a57de2ad21884c272fbfa6e7ad5d6520804610bfe","source":{"kind":"arxiv","id":"1309.6827","version":1},"attestation_state":"computed","paper":{"title":"Optimization With Parity Constraints: From Binary Codes to Discrete Integration","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.AI","authors_text":"Ashish Sabharwal, Bart Selman, Carla P. Gomes, Stefano Ermon","submitted_at":"2013-09-26T12:37:33Z","abstract_excerpt":"Many probabilistic inference tasks involve summations over exponentially large sets. Recently, it has been shown that these problems can be reduced to solving a polynomial number of MAP inference queries for a model augmented with randomly generated parity constraints. By exploiting a connection with max-likelihood decoding of binary codes, we show that these optimizations are computationally hard. Inspired by iterative message passing decoding algorithms, we propose an Integer Linear Programming (ILP) formulation for the problem, enhanced with new sparsification techniques to improve decoding"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1309.6827","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.AI","submitted_at":"2013-09-26T12:37:33Z","cross_cats_sorted":[],"title_canon_sha256":"f921b6a33432503dc6a5fb41115f5a9dfdb9ed04e6892127970a6877264ff5ee","abstract_canon_sha256":"2ff6d944d56f5db96c771ad9a44ce5e8f3bbc9a26c6cb98c18262515aa203371"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:12:10.289281Z","signature_b64":"YJDskypii8+xYtZGr7+ANgsBMvKpDAV3LpeUHKWAvisf4IGAMQIccahRdLitYWA1XaiCpPbp0iM6Ha9JC8v0Cg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"f34e4ec8ace2bbd181ee180a57de2ad21884c272fbfa6e7ad5d6520804610bfe","last_reissued_at":"2026-05-18T03:12:10.288554Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:12:10.288554Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Optimization With Parity Constraints: From Binary Codes to Discrete Integration","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.AI","authors_text":"Ashish Sabharwal, Bart Selman, Carla P. Gomes, Stefano Ermon","submitted_at":"2013-09-26T12:37:33Z","abstract_excerpt":"Many probabilistic inference tasks involve summations over exponentially large sets. Recently, it has been shown that these problems can be reduced to solving a polynomial number of MAP inference queries for a model augmented with randomly generated parity constraints. By exploiting a connection with max-likelihood decoding of binary codes, we show that these optimizations are computationally hard. Inspired by iterative message passing decoding algorithms, we propose an Integer Linear Programming (ILP) formulation for the problem, enhanced with new sparsification techniques to improve decoding"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1309.6827","kind":"arxiv","version":1},"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"},"aliases":[{"alias_kind":"arxiv","alias_value":"1309.6827","created_at":"2026-05-18T03:12:10.288670+00:00"},{"alias_kind":"arxiv_version","alias_value":"1309.6827v1","created_at":"2026-05-18T03:12:10.288670+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1309.6827","created_at":"2026-05-18T03:12:10.288670+00:00"},{"alias_kind":"pith_short_12","alias_value":"6NHE5SFM4K55","created_at":"2026-05-18T12:27:36.564083+00:00"},{"alias_kind":"pith_short_16","alias_value":"6NHE5SFM4K55DAPO","created_at":"2026-05-18T12:27:36.564083+00:00"},{"alias_kind":"pith_short_8","alias_value":"6NHE5SFM","created_at":"2026-05-18T12:27:36.564083+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/6NHE5SFM4K55DAPODAFFPXRK2I","json":"https://pith.science/pith/6NHE5SFM4K55DAPODAFFPXRK2I.json","graph_json":"https://pith.science/api/pith-number/6NHE5SFM4K55DAPODAFFPXRK2I/graph.json","events_json":"https://pith.science/api/pith-number/6NHE5SFM4K55DAPODAFFPXRK2I/events.json","paper":"https://pith.science/paper/6NHE5SFM"},"agent_actions":{"view_html":"https://pith.science/pith/6NHE5SFM4K55DAPODAFFPXRK2I","download_json":"https://pith.science/pith/6NHE5SFM4K55DAPODAFFPXRK2I.json","view_paper":"https://pith.science/paper/6NHE5SFM","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1309.6827&json=true","fetch_graph":"https://pith.science/api/pith-number/6NHE5SFM4K55DAPODAFFPXRK2I/graph.json","fetch_events":"https://pith.science/api/pith-number/6NHE5SFM4K55DAPODAFFPXRK2I/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/6NHE5SFM4K55DAPODAFFPXRK2I/action/timestamp_anchor","attest_storage":"https://pith.science/pith/6NHE5SFM4K55DAPODAFFPXRK2I/action/storage_attestation","attest_author":"https://pith.science/pith/6NHE5SFM4K55DAPODAFFPXRK2I/action/author_attestation","sign_citation":"https://pith.science/pith/6NHE5SFM4K55DAPODAFFPXRK2I/action/citation_signature","submit_replication":"https://pith.science/pith/6NHE5SFM4K55DAPODAFFPXRK2I/action/replication_record"}},"created_at":"2026-05-18T03:12:10.288670+00:00","updated_at":"2026-05-18T03:12:10.288670+00:00"}