{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:OOZRC5GNFQQWS4ARRG37HGIEQF","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":"33131bc4b24461140282c8d5872d209cee4d1097b41dbba65be047a5232575d7","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2017-08-07T13:05:54Z","title_canon_sha256":"584f53b5a25c030d3e6698717877e93591fdc364006cefa3e2038eded8f08921"},"schema_version":"1.0","source":{"id":"1708.02104","kind":"arxiv","version":5}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1708.02104","created_at":"2026-05-17T23:48:53Z"},{"alias_kind":"arxiv_version","alias_value":"1708.02104v5","created_at":"2026-05-17T23:48:53Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1708.02104","created_at":"2026-05-17T23:48:53Z"},{"alias_kind":"pith_short_12","alias_value":"OOZRC5GNFQQW","created_at":"2026-05-18T12:31:34Z"},{"alias_kind":"pith_short_16","alias_value":"OOZRC5GNFQQWS4AR","created_at":"2026-05-18T12:31:34Z"},{"alias_kind":"pith_short_8","alias_value":"OOZRC5GN","created_at":"2026-05-18T12:31:34Z"}],"graph_snapshots":[{"event_id":"sha256:dbf60d9ea0cd0e07062782a8e218c10e59a80a8b283b9c0f45355dcbecf0b3bc","target":"graph","created_at":"2026-05-17T23:48:53Z","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":"We investigate the alternate order on a congruence-uniform lattice $\\mathcal{L}$ as introduced by N. Reading, which we dub the core label order of $\\mathcal{L}$. When $\\mathcal{L}$ can be realized as a poset of regions of a simplicial hyperplane arrangement, the core label order is always a lattice. For general $\\mathcal{L}$, however, this fails. We provide an equivalent characterization for the core label order to be a lattice. As a consequence we show that the property of the core label order being a lattice is inherited to lattice quotients. We use the core label order to characterize the c","authors_text":"Henri M\\\"uhle","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2017-08-07T13:05:54Z","title":"The Core Label Order of a Congruence-Uniform Lattice"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1708.02104","kind":"arxiv","version":5},"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:c86e2052572c816bda2d6add7d4eeb0f83fd1aecc84ce35dc21a7333ffcf9e53","target":"record","created_at":"2026-05-17T23:48:53Z","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":"33131bc4b24461140282c8d5872d209cee4d1097b41dbba65be047a5232575d7","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2017-08-07T13:05:54Z","title_canon_sha256":"584f53b5a25c030d3e6698717877e93591fdc364006cefa3e2038eded8f08921"},"schema_version":"1.0","source":{"id":"1708.02104","kind":"arxiv","version":5}},"canonical_sha256":"73b31174cd2c2169701189b7f39904817b02cfa8ad3bde2aa03839a17b3a55bb","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"73b31174cd2c2169701189b7f39904817b02cfa8ad3bde2aa03839a17b3a55bb","first_computed_at":"2026-05-17T23:48:53.118135Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:48:53.118135Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"jtlMrNtetEyIQHZ6w9QWMQgKEyM76hxfkvZ9c2+Ln8DaevFH+d76nBLDH3333BhO+T3mS3ZtePVqkKEQRDY3DA==","signature_status":"signed_v1","signed_at":"2026-05-17T23:48:53.118563Z","signed_message":"canonical_sha256_bytes"},"source_id":"1708.02104","source_kind":"arxiv","source_version":5}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:c86e2052572c816bda2d6add7d4eeb0f83fd1aecc84ce35dc21a7333ffcf9e53","sha256:dbf60d9ea0cd0e07062782a8e218c10e59a80a8b283b9c0f45355dcbecf0b3bc"],"state_sha256":"f02314a0e7f99ca7c63f52a33ec6841e415e97389b2de1a1408690f2452f0e10"}