{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:G6DR43B3547RBJVWW5HUYLOPUP","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":"1f3d88fb7fd543c63989fc5ba7cdb281801c71cbca0cbb9e883aede603b40d24","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2016-09-17T00:01:12Z","title_canon_sha256":"d1ded873282166c5b9bbb8d8c88aad8a4764dc81f2f025a6bfd758b5e50503f0"},"schema_version":"1.0","source":{"id":"1609.05255","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1609.05255","created_at":"2026-05-18T00:41:07Z"},{"alias_kind":"arxiv_version","alias_value":"1609.05255v2","created_at":"2026-05-18T00:41:07Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1609.05255","created_at":"2026-05-18T00:41:07Z"},{"alias_kind":"pith_short_12","alias_value":"G6DR43B3547R","created_at":"2026-05-18T12:30:15Z"},{"alias_kind":"pith_short_16","alias_value":"G6DR43B3547RBJVW","created_at":"2026-05-18T12:30:15Z"},{"alias_kind":"pith_short_8","alias_value":"G6DR43B3","created_at":"2026-05-18T12:30:15Z"}],"graph_snapshots":[{"event_id":"sha256:533938f087f74bc8dbe0163cf72ffb07047c86df925eb20fb73b454b5105ce2e","target":"graph","created_at":"2026-05-18T00:41:07Z","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 introduce the concept of linked systems of symmetric group divisible designs. The connection with association schemes is established, and as a consequence we obtain an upper bound on the number of symmetric group divisible designs which are linked. Several examples of linked systems of symmetric group divisible designs are provided.","authors_text":"Hadi Kharaghani, Sho Suda","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2016-09-17T00:01:12Z","title":"Linked systems of symmetric group divisible designs"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1609.05255","kind":"arxiv","version":2},"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":"sha256:283688a73d50cd123a0edb7b82ee3888869f7fa340ebb604580c5e63e9635968","target":"record","created_at":"2026-05-18T00:41:07Z","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":"1f3d88fb7fd543c63989fc5ba7cdb281801c71cbca0cbb9e883aede603b40d24","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2016-09-17T00:01:12Z","title_canon_sha256":"d1ded873282166c5b9bbb8d8c88aad8a4764dc81f2f025a6bfd758b5e50503f0"},"schema_version":"1.0","source":{"id":"1609.05255","kind":"arxiv","version":2}},"canonical_sha256":"37871e6c3bef3f10a6b6b74f4c2dcfa3cd782fd058bf960c08df268132655bdb","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"37871e6c3bef3f10a6b6b74f4c2dcfa3cd782fd058bf960c08df268132655bdb","first_computed_at":"2026-05-18T00:41:07.871593Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:41:07.871593Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"3uv5Gzxi5Ucm2NafERlLFu4Yv6NyFYOQm+6oQ3veBQ8MgwK/p/85MYv3Gf7lvz/+3QahOIr4kYwtOTnAzCy1Bw==","signature_status":"signed_v1","signed_at":"2026-05-18T00:41:07.872148Z","signed_message":"canonical_sha256_bytes"},"source_id":"1609.05255","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:283688a73d50cd123a0edb7b82ee3888869f7fa340ebb604580c5e63e9635968","sha256:533938f087f74bc8dbe0163cf72ffb07047c86df925eb20fb73b454b5105ce2e"],"state_sha256":"a9f0485665e8205a37fa3a79ee25db490635b94a48adc7a0ac8dd95ba565110b"}