{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:3VCW45JP4C5G7ETH4OR6X2OOJ4","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":"fd724e9d44a9dbda02fd7e83c2e663062d27a90c23b02254e71331ad3f1d9201","cross_cats_sorted":["cs.AI"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CC","submitted_at":"2013-09-12T08:42:11Z","title_canon_sha256":"726e023b5aca209c1d018d2373fb0c3387cb64a81f7a454e35098d9da5fc310e"},"schema_version":"1.0","source":{"id":"1309.3060","kind":"arxiv","version":4}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1309.3060","created_at":"2026-05-18T02:49:12Z"},{"alias_kind":"arxiv_version","alias_value":"1309.3060v4","created_at":"2026-05-18T02:49:12Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1309.3060","created_at":"2026-05-18T02:49:12Z"},{"alias_kind":"pith_short_12","alias_value":"3VCW45JP4C5G","created_at":"2026-05-18T12:27:32Z"},{"alias_kind":"pith_short_16","alias_value":"3VCW45JP4C5G7ETH","created_at":"2026-05-18T12:27:32Z"},{"alias_kind":"pith_short_8","alias_value":"3VCW45JP","created_at":"2026-05-18T12:27:32Z"}],"graph_snapshots":[{"event_id":"sha256:3741e8d53c42512a9d8300523f48e9d495ef937a2a1cebda4849ccf471490ef5","target":"graph","created_at":"2026-05-18T02:49:12Z","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 representation of systems S of linear equations over the two-element field (aka xor- or parity-constraints) via conjunctive normal forms F (boolean clause-sets). First we consider the problem of finding an \"arc-consistent\" representation (\"AC\"), meaning that unit-clause propagation will fix all forced assignments for all possible instantiations of the xor-variables. Our main negative result is that there is no polysize AC-representation in general. On the positive side we show that finding such an AC-representation is fixed-parameter tractable (fpt) in the number of equations. The","authors_text":"Matthew Gwynne, Oliver Kullmann","cross_cats":["cs.AI"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CC","submitted_at":"2013-09-12T08:42:11Z","title":"On SAT representations of XOR constraints"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1309.3060","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":"sha256:1699048b1eb28daced93fd34531b4d49becfa17b57e37828cde6aba5a9f6c7fd","target":"record","created_at":"2026-05-18T02:49:12Z","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":"fd724e9d44a9dbda02fd7e83c2e663062d27a90c23b02254e71331ad3f1d9201","cross_cats_sorted":["cs.AI"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CC","submitted_at":"2013-09-12T08:42:11Z","title_canon_sha256":"726e023b5aca209c1d018d2373fb0c3387cb64a81f7a454e35098d9da5fc310e"},"schema_version":"1.0","source":{"id":"1309.3060","kind":"arxiv","version":4}},"canonical_sha256":"dd456e752fe0ba6f9267e3a3ebe9ce4f139863015d068bbfa82abe6bc6bdc298","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"dd456e752fe0ba6f9267e3a3ebe9ce4f139863015d068bbfa82abe6bc6bdc298","first_computed_at":"2026-05-18T02:49:12.198446Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:49:12.198446Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"5ZpCqS6ooemNYbSXvcfzU5kOXhED/DDVV+sgRtHKEG2DArbZtbD41TUWvzBidI+m8hKASCImNt9TS6/aqXgHCQ==","signature_status":"signed_v1","signed_at":"2026-05-18T02:49:12.198972Z","signed_message":"canonical_sha256_bytes"},"source_id":"1309.3060","source_kind":"arxiv","source_version":4}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:1699048b1eb28daced93fd34531b4d49becfa17b57e37828cde6aba5a9f6c7fd","sha256:3741e8d53c42512a9d8300523f48e9d495ef937a2a1cebda4849ccf471490ef5"],"state_sha256":"03cc77d581a852bf3bed4e35d6265614dfbedcb6dd6c5d71f80a408a5209a590"}