{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2019:LKCSMQXDPUVEUJPVMKQNAS52QB","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":"27f6c210107db15c83d60cb03ac1e2b7728840416367d0cf05a4227eadd483a4","cross_cats_sorted":["cs.LO"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2019-02-09T15:03:37Z","title_canon_sha256":"524ce6654aed0fda96d408d2c56e2ff199da51b0a580da3b856932bcac1b8717"},"schema_version":"1.0","source":{"id":"1902.03431","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1902.03431","created_at":"2026-05-17T23:54:20Z"},{"alias_kind":"arxiv_version","alias_value":"1902.03431v1","created_at":"2026-05-17T23:54:20Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1902.03431","created_at":"2026-05-17T23:54:20Z"},{"alias_kind":"pith_short_12","alias_value":"LKCSMQXDPUVE","created_at":"2026-05-18T12:33:21Z"},{"alias_kind":"pith_short_16","alias_value":"LKCSMQXDPUVEUJPV","created_at":"2026-05-18T12:33:21Z"},{"alias_kind":"pith_short_8","alias_value":"LKCSMQXD","created_at":"2026-05-18T12:33:21Z"}],"graph_snapshots":[{"event_id":"sha256:23869a43b0217fdd2b70d5827f215dbfe077949632882be9525165fe1d0fe0bd","target":"graph","created_at":"2026-05-17T23:54:20Z","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":"Inspired by a recent article by Anthony Zaleski and Doron Zeilberger, we investigate the question of determining the largest k for which there exists boolean formulas in disjunctive normal form (DNF) with n variables, none of whose conjunctions are `parallel', and such that all of them have at least k literals. Using a SAT solver, we answer some of the questions they left open. We also determine the corresponding numbers for DNFs obeying certain symmetries.","authors_text":"Doron Zeilberger, Manuel Kauers, Martina Seidl","cross_cats":["cs.LO"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2019-02-09T15:03:37Z","title":"On the maximal minimal cube lengths in distinct DNF tautologies"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1902.03431","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":"sha256:88d355d24a3bbba416844bab66d3cd77c91b4ba78e8bcdfcea3bcf5dcfc73f16","target":"record","created_at":"2026-05-17T23:54:20Z","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":"27f6c210107db15c83d60cb03ac1e2b7728840416367d0cf05a4227eadd483a4","cross_cats_sorted":["cs.LO"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2019-02-09T15:03:37Z","title_canon_sha256":"524ce6654aed0fda96d408d2c56e2ff199da51b0a580da3b856932bcac1b8717"},"schema_version":"1.0","source":{"id":"1902.03431","kind":"arxiv","version":1}},"canonical_sha256":"5a852642e37d2a4a25f562a0d04bba804c0dd5e1dded6bafadc159259162107c","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"5a852642e37d2a4a25f562a0d04bba804c0dd5e1dded6bafadc159259162107c","first_computed_at":"2026-05-17T23:54:20.842548Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:54:20.842548Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"wpEclePDlBxSZbKOYOk4fggdZCou7RLBWQYnm6hXdyUu9pmqY4P11hXMlZwYhopCcsjMUwAmJHH3QDqtZwooCQ==","signature_status":"signed_v1","signed_at":"2026-05-17T23:54:20.843024Z","signed_message":"canonical_sha256_bytes"},"source_id":"1902.03431","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:88d355d24a3bbba416844bab66d3cd77c91b4ba78e8bcdfcea3bcf5dcfc73f16","sha256:23869a43b0217fdd2b70d5827f215dbfe077949632882be9525165fe1d0fe0bd"],"state_sha256":"3c421c7072ada6e2dd7c468336f88f1509f8fa103b1adf37fdba0f01a73619b0"}