{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:45CDZXFKMXJYRD5YXII3ITRWTZ","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":"bd9b3bca244c7f0103a885bd58b2497cf0f73b9f9c5e2680679530ba73b356c2","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CC","submitted_at":"2011-10-03T19:58:32Z","title_canon_sha256":"39ee2277f1c218a95e93cb603d425b34991fde8a09ef02588956924831ab2d6f"},"schema_version":"1.0","source":{"id":"1110.0461","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1110.0461","created_at":"2026-05-18T03:52:54Z"},{"alias_kind":"arxiv_version","alias_value":"1110.0461v2","created_at":"2026-05-18T03:52:54Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1110.0461","created_at":"2026-05-18T03:52:54Z"},{"alias_kind":"pith_short_12","alias_value":"45CDZXFKMXJY","created_at":"2026-05-18T12:26:20Z"},{"alias_kind":"pith_short_16","alias_value":"45CDZXFKMXJYRD5Y","created_at":"2026-05-18T12:26:20Z"},{"alias_kind":"pith_short_8","alias_value":"45CDZXFK","created_at":"2026-05-18T12:26:20Z"}],"graph_snapshots":[{"event_id":"sha256:07049edfc3d2d21d3d1508706a254f65beb17874bf5a581716cd00321a092c54","target":"graph","created_at":"2026-05-18T03:52:54Z","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":"The material in this note is now superseded by arXiv:1108.5288v4.\n  Bulatov et al. [1] defined the operation of (efficient) pps_\\omega-definability in order to study the computational complexity of certain approximate counting problems. They asked whether all log-supermodular functions can be defined by binary implication and unary functions in this sense. We give a negative answer to this question.","authors_text":"Colin McQuillan","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CC","submitted_at":"2011-10-03T19:58:32Z","title":"LSM is not generated by binary functions"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1110.0461","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":"sha256:9e29563d296ae76c39d9740d589cf661c1e683a3c7d32c4ae78880248b977729","target":"record","created_at":"2026-05-18T03:52:54Z","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":"bd9b3bca244c7f0103a885bd58b2497cf0f73b9f9c5e2680679530ba73b356c2","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CC","submitted_at":"2011-10-03T19:58:32Z","title_canon_sha256":"39ee2277f1c218a95e93cb603d425b34991fde8a09ef02588956924831ab2d6f"},"schema_version":"1.0","source":{"id":"1110.0461","kind":"arxiv","version":2}},"canonical_sha256":"e7443cdcaa65d3888fb8ba11b44e369e4046a35bf7fa9036786f49a538d15480","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"e7443cdcaa65d3888fb8ba11b44e369e4046a35bf7fa9036786f49a538d15480","first_computed_at":"2026-05-18T03:52:54.816160Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:52:54.816160Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"eau04XrevKTpEwODNpvs+UsUvYYImXc/PwuqcZFGmqgFGiKkje+7LHXoq6ZarRqDOLCEaZMgj+ChTYjr+JV1Aw==","signature_status":"signed_v1","signed_at":"2026-05-18T03:52:54.816861Z","signed_message":"canonical_sha256_bytes"},"source_id":"1110.0461","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:9e29563d296ae76c39d9740d589cf661c1e683a3c7d32c4ae78880248b977729","sha256:07049edfc3d2d21d3d1508706a254f65beb17874bf5a581716cd00321a092c54"],"state_sha256":"fe9722551c6f85c6ac0aa9d38af650566892ab3821bccc98cdcc261c4ca188e5"}