{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:D5JL5DSMBIVBCYOLQZWYMRBHYU","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":"7909e21b7a4858c0e398a886dc184838cea45d3a2fd057d02b9148b87b063ee0","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2018-07-23T13:03:13Z","title_canon_sha256":"fc2dcb445a7ae375d0eae926c9f6b2dd739c7847df6993e539bbbdfad5ab6de3"},"schema_version":"1.0","source":{"id":"1807.08580","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1807.08580","created_at":"2026-05-18T00:10:05Z"},{"alias_kind":"arxiv_version","alias_value":"1807.08580v1","created_at":"2026-05-18T00:10:05Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1807.08580","created_at":"2026-05-18T00:10:05Z"},{"alias_kind":"pith_short_12","alias_value":"D5JL5DSMBIVB","created_at":"2026-05-18T12:32:19Z"},{"alias_kind":"pith_short_16","alias_value":"D5JL5DSMBIVBCYOL","created_at":"2026-05-18T12:32:19Z"},{"alias_kind":"pith_short_8","alias_value":"D5JL5DSM","created_at":"2026-05-18T12:32:19Z"}],"graph_snapshots":[{"event_id":"sha256:19f17208f2b52acaeab2986436faac44d3cdd0477635ff8daa755f73590fcfd0","target":"graph","created_at":"2026-05-18T00:10:05Z","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":"Regarding neighbor balance, we consider natural generalizations of $D$-complete Latin squares and Vatican squares from the finite to the infinite. We show that if $G$ is an infinite abelian group with $|G|$-many square elements, then it is possible to permute the rows and columns of the Cayley table to create an infinite Vatican square. We also construct a Vatican square of any given infinite order that is not obtainable by permuting the rows and columns of a Cayley table. Regarding orthogonality, we show that every infinite group $G$ has a set of $|G|$ mutually orthogonal orthomorphisms and h","authors_text":"Anthony B. Evans, Gage N. Martin, Kaethe Minden, M. A. Ollis","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2018-07-23T13:03:13Z","title":"Infinite Latin Squares: Neighbor Balance and Orthogonality"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1807.08580","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:e8d7cf0ef7a34e1a1a1411d5028e2c903070af4fd7c069035e321b45479f37c7","target":"record","created_at":"2026-05-18T00:10:05Z","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":"7909e21b7a4858c0e398a886dc184838cea45d3a2fd057d02b9148b87b063ee0","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2018-07-23T13:03:13Z","title_canon_sha256":"fc2dcb445a7ae375d0eae926c9f6b2dd739c7847df6993e539bbbdfad5ab6de3"},"schema_version":"1.0","source":{"id":"1807.08580","kind":"arxiv","version":1}},"canonical_sha256":"1f52be8e4c0a2a1161cb866d864427c51985012a639a8d0135c875b3d806e8d8","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"1f52be8e4c0a2a1161cb866d864427c51985012a639a8d0135c875b3d806e8d8","first_computed_at":"2026-05-18T00:10:05.477754Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:10:05.477754Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"fBtReblP95hLWIU/N65hNlYAT3lAgNmzRozOxPBX5cVOgz0Dan2LGDx6AgyLP0BHSScaqr3RKpM+vNJyzA1/Cg==","signature_status":"signed_v1","signed_at":"2026-05-18T00:10:05.478411Z","signed_message":"canonical_sha256_bytes"},"source_id":"1807.08580","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:e8d7cf0ef7a34e1a1a1411d5028e2c903070af4fd7c069035e321b45479f37c7","sha256:19f17208f2b52acaeab2986436faac44d3cdd0477635ff8daa755f73590fcfd0"],"state_sha256":"36d9afd6921be0233fb9ed8224d9f1ef79fe2725bc1149f314744e40e6f75adf"}