{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2023:FS527B7E3E2AP5OIIM6KNQASIJ","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":"63152d72d7672dd0988d07729bcb3644ea069d734c02ba3b9cad45eaed0a4ac9","cross_cats_sorted":["math.CO","math.IT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2023-06-15T02:35:27Z","title_canon_sha256":"167cdf2602dc2dac774bcfc22c0956a0f4653612af810289f53bec76edebfa59"},"schema_version":"1.0","source":{"id":"2306.08824","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2306.08824","created_at":"2026-07-05T06:20:56Z"},{"alias_kind":"arxiv_version","alias_value":"2306.08824v1","created_at":"2026-07-05T06:20:56Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2306.08824","created_at":"2026-07-05T06:20:56Z"},{"alias_kind":"pith_short_12","alias_value":"FS527B7E3E2A","created_at":"2026-07-05T06:20:56Z"},{"alias_kind":"pith_short_16","alias_value":"FS527B7E3E2AP5OI","created_at":"2026-07-05T06:20:56Z"},{"alias_kind":"pith_short_8","alias_value":"FS527B7E","created_at":"2026-07-05T06:20:56Z"}],"graph_snapshots":[{"event_id":"sha256:a8b462f4d8c2e8fffdb3fa798a199701862ce30101fa4083acf82c1dbf4a3f14","target":"graph","created_at":"2026-07-05T06:20:56Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2306.08824/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Recently, Gilmer proved the first constant lower bound for the union-closed sets conjecture via an information-theoretic argument. The heart of the argument is an entropic inequality involving the OR function of two i.i.d.\\ binary vectors, and the best constant obtainable through the i.i.d.\\ coupling is $\\frac{3-\\sqrt{5}}{2}\\approx0.38197$. Sawin demonstrated that the bound can be strictly improved by considering a convex combination of the i.i.d.\\ coupling and the max-entropy coupling, and the best constant obtainable through this approach is around 0.38234, as evaluated by Yu and Cambie. In ","authors_text":"Jingbo Liu","cross_cats":["math.CO","math.IT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2023-06-15T02:35:27Z","title":"Improving the Lower Bound for the Union-closed Sets Conjecture via Conditionally IID Coupling"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2306.08824","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:a94be2733bfd1049391ee24b280b1fed94a4fadb4b7de6c171bfc66e4a947d3c","target":"record","created_at":"2026-07-05T06:20:56Z","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":"63152d72d7672dd0988d07729bcb3644ea069d734c02ba3b9cad45eaed0a4ac9","cross_cats_sorted":["math.CO","math.IT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2023-06-15T02:35:27Z","title_canon_sha256":"167cdf2602dc2dac774bcfc22c0956a0f4653612af810289f53bec76edebfa59"},"schema_version":"1.0","source":{"id":"2306.08824","kind":"arxiv","version":1}},"canonical_sha256":"2cbbaf87e4d93407f5c8433ca6c0124270087406c1b23b6e33bb8a28069aab83","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"2cbbaf87e4d93407f5c8433ca6c0124270087406c1b23b6e33bb8a28069aab83","first_computed_at":"2026-07-05T06:20:56.716484Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T06:20:56.716484Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"1O5NWovP0nlkpZtku7g1zfhTj7wr3H0C8AuCMqgz7RGVmm8u82SfgF8+DOAt4906+l5u5DW1bE17Ou6NksXzAg==","signature_status":"signed_v1","signed_at":"2026-07-05T06:20:56.716869Z","signed_message":"canonical_sha256_bytes"},"source_id":"2306.08824","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:a94be2733bfd1049391ee24b280b1fed94a4fadb4b7de6c171bfc66e4a947d3c","sha256:a8b462f4d8c2e8fffdb3fa798a199701862ce30101fa4083acf82c1dbf4a3f14"],"state_sha256":"c7b879d3455575864a229933c71d0ff1ee527376d4910fdb378597de2482493b"}