{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:B2FIFYY3POR5RWSTCNEBTTAXPU","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":"7ffa3efb1469c1f5b1dffa8f238531b0ebadbed5f5736537b34521c92f4aa27e","cross_cats_sorted":["math-ph","math.IT","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2015-05-26T16:29:50Z","title_canon_sha256":"080629cba45522341d9f6c4c6f369f7b650283113b373ba78e619285c72d98d9"},"schema_version":"1.0","source":{"id":"1505.07038","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1505.07038","created_at":"2026-05-18T00:47:29Z"},{"alias_kind":"arxiv_version","alias_value":"1505.07038v3","created_at":"2026-05-18T00:47:29Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1505.07038","created_at":"2026-05-18T00:47:29Z"},{"alias_kind":"pith_short_12","alias_value":"B2FIFYY3POR5","created_at":"2026-05-18T12:29:14Z"},{"alias_kind":"pith_short_16","alias_value":"B2FIFYY3POR5RWST","created_at":"2026-05-18T12:29:14Z"},{"alias_kind":"pith_short_8","alias_value":"B2FIFYY3","created_at":"2026-05-18T12:29:14Z"}],"graph_snapshots":[{"event_id":"sha256:537a4c7aa0245105125e4a58bfbb0695ba54974640759467b222686d06fd46c1","target":"graph","created_at":"2026-05-18T00:47:29Z","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":"A new method is proposed to derive rigorous bounds on {\\eta}, the growth rate of the logarithm of the number of independent sets on a hexagonal lattice. Specifically, we prove that 1.546440708536001 <= {\\eta} <= 1.5513, which improves upon the best known 1.5463 <= {\\eta} <= 1.5527 due to Nagy and Zeger. Our lower bound matches the numerical estimate of Baxter up to 9 digits after the decimal point.","authors_text":"Jie Ding, Mohammad Noshad, Vahid Tarokh, Zhun Deng","cross_cats":["math-ph","math.IT","math.MP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2015-05-26T16:29:50Z","title":"The Number of Independent Sets in Hexagonal Graphs"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1505.07038","kind":"arxiv","version":3},"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":"sha256:74cc3bf3e7a7393bb4b5b5648cb1bb03a0542f64f1c15eea867c44f3449f8203","target":"record","created_at":"2026-05-18T00:47:29Z","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":"7ffa3efb1469c1f5b1dffa8f238531b0ebadbed5f5736537b34521c92f4aa27e","cross_cats_sorted":["math-ph","math.IT","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2015-05-26T16:29:50Z","title_canon_sha256":"080629cba45522341d9f6c4c6f369f7b650283113b373ba78e619285c72d98d9"},"schema_version":"1.0","source":{"id":"1505.07038","kind":"arxiv","version":3}},"canonical_sha256":"0e8a82e31b7ba3d8da53134819cc177d31e97c295a8f3eaeb50db48c049177da","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"0e8a82e31b7ba3d8da53134819cc177d31e97c295a8f3eaeb50db48c049177da","first_computed_at":"2026-05-18T00:47:29.598990Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:47:29.598990Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"XydD04aiauHt0a26MkedOeiK4HtOUDD/6gsORpiWssI1gYRazWFFIGIzc1MPkQXh6ZAXcYEwz0EmZaBLC/KzDg==","signature_status":"signed_v1","signed_at":"2026-05-18T00:47:29.599543Z","signed_message":"canonical_sha256_bytes"},"source_id":"1505.07038","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:74cc3bf3e7a7393bb4b5b5648cb1bb03a0542f64f1c15eea867c44f3449f8203","sha256:537a4c7aa0245105125e4a58bfbb0695ba54974640759467b222686d06fd46c1"],"state_sha256":"777c2e96374d567b417380219c7ad276118800060a236278724c39d4756130cb"}