{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:QZHKCOVQZDYD4Q4EM2RFSRHA5X","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":"4ffaec53c7b91ee465ee34757ef03b0f0724c8fea1d3387ace17c906cfd475f4","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2013-03-14T12:06:13Z","title_canon_sha256":"4f839ee40651d343c2b235f0b62b95fdb0bc2294d31be412c98e9dbb861e9267"},"schema_version":"1.0","source":{"id":"1303.3421","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1303.3421","created_at":"2026-05-18T03:30:53Z"},{"alias_kind":"arxiv_version","alias_value":"1303.3421v2","created_at":"2026-05-18T03:30:53Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1303.3421","created_at":"2026-05-18T03:30:53Z"},{"alias_kind":"pith_short_12","alias_value":"QZHKCOVQZDYD","created_at":"2026-05-18T12:27:57Z"},{"alias_kind":"pith_short_16","alias_value":"QZHKCOVQZDYD4Q4E","created_at":"2026-05-18T12:27:57Z"},{"alias_kind":"pith_short_8","alias_value":"QZHKCOVQ","created_at":"2026-05-18T12:27:57Z"}],"graph_snapshots":[{"event_id":"sha256:e2f2588d6129757ea0532a5048dabfd71576695748ff428161a1fdb7dce3afd4","target":"graph","created_at":"2026-05-18T03:30:53Z","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":"A Skolem sequence of order n is a sequence S_n=(s_{1},s_{2},...,s_{2n}) of 2n integers containing each of the integers 1,2,...,n exactly twice, such that two occurrences of the integer j in {1,2,...,n} are separated by exactly j-1 integers. We prove that the necessary conditions are sufficient for existence of two Skolem sequences of order n with 0,1,2,...,n-3 and n pairs in same positions. Further, we apply this result to the fine structure of cyclic two, three and four-fold triple systems, and also to the fine structure of lambda-fold directed triple systems and lambda-fold Mendelsohn triple","authors_text":"Daniela Silvesan, Nabil Shalaby","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2013-03-14T12:06:13Z","title":"The intersection spectrum of Skolem sequences and its applications to lambda fold cyclic triple systems, together with the Supplement"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1303.3421","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":"sha256:0c9f559e30cd5829c17e30f43ad8ce2de5a0d5003cf52c9847ae745412c0fa36","target":"record","created_at":"2026-05-18T03:30:53Z","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":"4ffaec53c7b91ee465ee34757ef03b0f0724c8fea1d3387ace17c906cfd475f4","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2013-03-14T12:06:13Z","title_canon_sha256":"4f839ee40651d343c2b235f0b62b95fdb0bc2294d31be412c98e9dbb861e9267"},"schema_version":"1.0","source":{"id":"1303.3421","kind":"arxiv","version":2}},"canonical_sha256":"864ea13ab0c8f03e438466a25944e0edd582796fa341e2efab9034eee884296b","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"864ea13ab0c8f03e438466a25944e0edd582796fa341e2efab9034eee884296b","first_computed_at":"2026-05-18T03:30:53.115829Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:30:53.115829Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"4r7eRc6Fzuvpua455uf8kpTopfRLHpJS8cnSBlBlv9EiAA/TdVDLixrLbLM3PsaQ6WE1+dSxt7yxfx0iL/EUBQ==","signature_status":"signed_v1","signed_at":"2026-05-18T03:30:53.118392Z","signed_message":"canonical_sha256_bytes"},"source_id":"1303.3421","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:0c9f559e30cd5829c17e30f43ad8ce2de5a0d5003cf52c9847ae745412c0fa36","sha256:e2f2588d6129757ea0532a5048dabfd71576695748ff428161a1fdb7dce3afd4"],"state_sha256":"14626d3774a9bbc8b4c716a6a7cb178a9acf3eabc9c4e79742d9dfe6de820d6c"}