{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:W3UGVP5QAPHWLBNTY6H2SYQ5E7","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":"d90efb741688054a29d8c402aafda1bcf0c24ddae86c221b8bbea60d3850bcbb","cross_cats_sorted":["math.CO"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2018-01-04T18:33:55Z","title_canon_sha256":"73df59986ff709bd51f5b387c7a8d874ffcedd2b884ada2aeee2c435dfe42ccb"},"schema_version":"1.0","source":{"id":"1801.01482","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1801.01482","created_at":"2026-05-18T00:26:42Z"},{"alias_kind":"arxiv_version","alias_value":"1801.01482v1","created_at":"2026-05-18T00:26:42Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1801.01482","created_at":"2026-05-18T00:26:42Z"},{"alias_kind":"pith_short_12","alias_value":"W3UGVP5QAPHW","created_at":"2026-05-18T12:32:59Z"},{"alias_kind":"pith_short_16","alias_value":"W3UGVP5QAPHWLBNT","created_at":"2026-05-18T12:32:59Z"},{"alias_kind":"pith_short_8","alias_value":"W3UGVP5Q","created_at":"2026-05-18T12:32:59Z"}],"graph_snapshots":[{"event_id":"sha256:3e33f17d9bfa11bd2297094902220ab9d95d0f309d82c145d0db91af8686b8ef","target":"graph","created_at":"2026-05-18T00:26:42Z","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":"For an integer $n\\geq 2$, let NCSL$(n)$ denote the set of sizes of congruence lattices of $n$-element semilattices. We find the four largest numbers belonging to NCSL$(n)$, provided that $n$ is large enough to ensure that $|$NCSL$(n)|\\geq 4$. Furthermore, we describe the $n$-element semilattices witnessing these numbers.","authors_text":"G\\'abor Cz\\'edli","cross_cats":["math.CO"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2018-01-04T18:33:55Z","title":"Finite semilattices with many congruences"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1801.01482","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:dc48fc2b3ac1da44479fc686194aee613fffd7146427bcec79f4978869eae27e","target":"record","created_at":"2026-05-18T00:26:42Z","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":"d90efb741688054a29d8c402aafda1bcf0c24ddae86c221b8bbea60d3850bcbb","cross_cats_sorted":["math.CO"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2018-01-04T18:33:55Z","title_canon_sha256":"73df59986ff709bd51f5b387c7a8d874ffcedd2b884ada2aeee2c435dfe42ccb"},"schema_version":"1.0","source":{"id":"1801.01482","kind":"arxiv","version":1}},"canonical_sha256":"b6e86abfb003cf6585b3c78fa9621d27d5477942e2b5d497eb57d2e692fb9033","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"b6e86abfb003cf6585b3c78fa9621d27d5477942e2b5d497eb57d2e692fb9033","first_computed_at":"2026-05-18T00:26:42.002480Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:26:42.002480Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"jAh0gWu9bvTsOgI6oIjp9CXk1JsuXdXB59rpnHzn1EGeW/hRxM37lQh5A7sRGgFcFFaeZaER2RYWCYCVQVkOCg==","signature_status":"signed_v1","signed_at":"2026-05-18T00:26:42.003106Z","signed_message":"canonical_sha256_bytes"},"source_id":"1801.01482","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:dc48fc2b3ac1da44479fc686194aee613fffd7146427bcec79f4978869eae27e","sha256:3e33f17d9bfa11bd2297094902220ab9d95d0f309d82c145d0db91af8686b8ef"],"state_sha256":"d7ddac20696ad55fb8c4faeafbaa57de60d42c0685231e85e8bb470b34454936"}