{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:OTH2CUFZLLSVWBIEKDIWSI2D7S","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":"8a838c5cc618bcae5393e715b9b2b21b333b4dc69923943a125218ee601c3721","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2018-04-02T01:37:30Z","title_canon_sha256":"18e3f78d7f5c37c90963534df3e587a092379a344427727e8523ec88634eafe7"},"schema_version":"1.0","source":{"id":"1804.00369","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1804.00369","created_at":"2026-05-18T00:19:37Z"},{"alias_kind":"arxiv_version","alias_value":"1804.00369v1","created_at":"2026-05-18T00:19:37Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1804.00369","created_at":"2026-05-18T00:19:37Z"},{"alias_kind":"pith_short_12","alias_value":"OTH2CUFZLLSV","created_at":"2026-05-18T12:32:43Z"},{"alias_kind":"pith_short_16","alias_value":"OTH2CUFZLLSVWBIE","created_at":"2026-05-18T12:32:43Z"},{"alias_kind":"pith_short_8","alias_value":"OTH2CUFZ","created_at":"2026-05-18T12:32:43Z"}],"graph_snapshots":[{"event_id":"sha256:e28e7538ee8741263bee6c97a396b7c9666c1b6c1dd4942cb2116ed124bf9c64","target":"graph","created_at":"2026-05-18T00:19:37Z","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":"In this paper, we show that a connected graph with smallest eigenvalue at least -3 and large enough minimal degree is 2-integrable. This result generalizes a 1977 result of Hoffman for connected graphs with smallest eigenvalue at least -2.","authors_text":"Jack H. Koolen, Jae Young Yang, Qianqian Yang","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2018-04-02T01:37:30Z","title":"On graphs with smallest eigenvalue at least -3 and their lattices"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1804.00369","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:fad337a4e49937474ad35fd0200ef12263d9a235c140f66e6ac7e54d5d354134","target":"record","created_at":"2026-05-18T00:19:37Z","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":"8a838c5cc618bcae5393e715b9b2b21b333b4dc69923943a125218ee601c3721","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2018-04-02T01:37:30Z","title_canon_sha256":"18e3f78d7f5c37c90963534df3e587a092379a344427727e8523ec88634eafe7"},"schema_version":"1.0","source":{"id":"1804.00369","kind":"arxiv","version":1}},"canonical_sha256":"74cfa150b95ae55b050450d1692343fcb9976527f5350c3ffeec61b50d8b7779","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"74cfa150b95ae55b050450d1692343fcb9976527f5350c3ffeec61b50d8b7779","first_computed_at":"2026-05-18T00:19:37.465731Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:19:37.465731Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"qbG9vaZs/54czv2pw5pOI7D9UpZ3Z/86b8LZdZ//yjQa19WYdeXmYIM7e+EnzjbvcbBYgxvbuMlHb48GRbPoCA==","signature_status":"signed_v1","signed_at":"2026-05-18T00:19:37.466620Z","signed_message":"canonical_sha256_bytes"},"source_id":"1804.00369","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:fad337a4e49937474ad35fd0200ef12263d9a235c140f66e6ac7e54d5d354134","sha256:e28e7538ee8741263bee6c97a396b7c9666c1b6c1dd4942cb2116ed124bf9c64"],"state_sha256":"67dfcc084f7b6dd3f7598df4471ec23db99dd29fb8ccd300abce057f3f13ab68"}