{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:I32L2JNDLRRY2IINR5HGD34XZS","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":"18b86154033d44de4db7912cd8870a9c614e4ef5678e02d0518e8ecba027a468","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2012-05-29T15:33:53Z","title_canon_sha256":"4beeecb61cbb8abafbacd878612fee354d3193a8bda4b2164af1d4a1c49f93e1"},"schema_version":"1.0","source":{"id":"1205.6395","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1205.6395","created_at":"2026-05-18T03:52:41Z"},{"alias_kind":"arxiv_version","alias_value":"1205.6395v2","created_at":"2026-05-18T03:52:41Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1205.6395","created_at":"2026-05-18T03:52:41Z"},{"alias_kind":"pith_short_12","alias_value":"I32L2JNDLRRY","created_at":"2026-05-18T12:27:09Z"},{"alias_kind":"pith_short_16","alias_value":"I32L2JNDLRRY2IIN","created_at":"2026-05-18T12:27:09Z"},{"alias_kind":"pith_short_8","alias_value":"I32L2JND","created_at":"2026-05-18T12:27:09Z"}],"graph_snapshots":[{"event_id":"sha256:a7e62f6ba1c411ee33880d87481aad98866225f68c7cd1f5558aa1584e6d7144","target":"graph","created_at":"2026-05-18T03:52:41Z","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 $2-(v,k,\\lambda)$ directed design (or simply a $2-(v,k,\\lambda)DD$) is super-simple if its underlying $2-(v,k,2\\lambda)BIBD$ is super-simple, that is, any two blocks of the $BIBD$ intersect in at most two points. A $2-(v,k,\\lambda)DD$ is simple if its underlying $2-(v,k,2\\lambda)BIBD$ is simple, that is, it has no repeated blocks.\n  A set of blocks which is a subset of a unique $2-(v,k,\\lambda)DD$ is said to be a defining set of the directed design. A smallest defining set, is a defining set which has smallest cardinality. In this paper simultaneously we show that the necessary and sufficien","authors_text":"Farzane Amirzade, Nasrin Soltankhah","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2012-05-29T15:33:53Z","title":"Smallest defining sets of super-simple 2 - (v, 4,1) directed designs"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1205.6395","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:a885d2f8b80c82b9b2090aa84bc513e372b33a9f9aed437f33e1850949835b8d","target":"record","created_at":"2026-05-18T03:52:41Z","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":"18b86154033d44de4db7912cd8870a9c614e4ef5678e02d0518e8ecba027a468","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2012-05-29T15:33:53Z","title_canon_sha256":"4beeecb61cbb8abafbacd878612fee354d3193a8bda4b2164af1d4a1c49f93e1"},"schema_version":"1.0","source":{"id":"1205.6395","kind":"arxiv","version":2}},"canonical_sha256":"46f4bd25a35c638d210d8f4e61ef97cc85db240b5b779678ca9e76068a2a5991","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"46f4bd25a35c638d210d8f4e61ef97cc85db240b5b779678ca9e76068a2a5991","first_computed_at":"2026-05-18T03:52:41.213299Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:52:41.213299Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"kwk0u9e9iugoq79IpXP4SA0XlLjVByyaAMWpBSR9OXInKv3yMa00sj9DkmaD07s1W0DUnafx7Wq/6TXLSHVNAw==","signature_status":"signed_v1","signed_at":"2026-05-18T03:52:41.214008Z","signed_message":"canonical_sha256_bytes"},"source_id":"1205.6395","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:a885d2f8b80c82b9b2090aa84bc513e372b33a9f9aed437f33e1850949835b8d","sha256:a7e62f6ba1c411ee33880d87481aad98866225f68c7cd1f5558aa1584e6d7144"],"state_sha256":"f7b81618976eb577d219d7f90057c6b34c1f274cd968c9c62b8e701180b70cd3"}