{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:LTIMXAS4FXSAQMDJLAXAZ2X6OG","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":"f61bce6532128ca378874ad77ff7731296b4a9f29509fdea4dfa62ccedbb1387","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2017-06-18T21:17:40Z","title_canon_sha256":"268eaacaf5a14b83e8e127af68d51c746b4d102bddfa5cbc0569cb9c10167ff6"},"schema_version":"1.0","source":{"id":"1706.05727","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1706.05727","created_at":"2026-05-18T00:42:09Z"},{"alias_kind":"arxiv_version","alias_value":"1706.05727v1","created_at":"2026-05-18T00:42:09Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1706.05727","created_at":"2026-05-18T00:42:09Z"},{"alias_kind":"pith_short_12","alias_value":"LTIMXAS4FXSA","created_at":"2026-05-18T12:31:28Z"},{"alias_kind":"pith_short_16","alias_value":"LTIMXAS4FXSAQMDJ","created_at":"2026-05-18T12:31:28Z"},{"alias_kind":"pith_short_8","alias_value":"LTIMXAS4","created_at":"2026-05-18T12:31:28Z"}],"graph_snapshots":[{"event_id":"sha256:8807cc163fb3fcf1a89b74e34723f44156efcba456249d88ddf6d57ba4cc100b","target":"graph","created_at":"2026-05-18T00:42:09Z","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":"In this paper we construct structures from Mathieu group $M_{11}$. We classify transitive $t$-designs with 11, 12 and 22 points admitting a transitive action of Mathieu group $M_{11}$. Thereby we proved the existence of designs with parameters 3-(22,7,18) and found first simple designs with parameters 4-(11,5,6) and 5-(12,6,6). Additionally, we proved the existence of $2$-designs with certain parameters having 55 and 66 points. Furthermore, we classified strongly regular graphs on at most 450 vertices admitting a transitive action of the Mathieu group $M_{11}$.","authors_text":"Andrea Svob, Dean Crnkovic","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2017-06-18T21:17:40Z","title":"On transitive designs and strongly regular graphs constructed from Mathieu group $M_{11}$"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1706.05727","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":"sha256:29a4448024c51be5a4161247fe7f17caf4f411ccd29fcf73f62c480a5b75c455","target":"record","created_at":"2026-05-18T00:42:09Z","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":"f61bce6532128ca378874ad77ff7731296b4a9f29509fdea4dfa62ccedbb1387","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2017-06-18T21:17:40Z","title_canon_sha256":"268eaacaf5a14b83e8e127af68d51c746b4d102bddfa5cbc0569cb9c10167ff6"},"schema_version":"1.0","source":{"id":"1706.05727","kind":"arxiv","version":1}},"canonical_sha256":"5cd0cb825c2de4083069582e0ceafe71892a7b509ec321e7f6b8323f210e0b38","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"5cd0cb825c2de4083069582e0ceafe71892a7b509ec321e7f6b8323f210e0b38","first_computed_at":"2026-05-18T00:42:09.080148Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:42:09.080148Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"8zcRiJ8T/8ov8Ff5aHuBYKgvh9sHizwVj92IHSrGuHnc0gVcl5Wa0o9m9UIQ4D6ZAN4X5SVkSkZj+88rCkYsDw==","signature_status":"signed_v1","signed_at":"2026-05-18T00:42:09.080545Z","signed_message":"canonical_sha256_bytes"},"source_id":"1706.05727","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:29a4448024c51be5a4161247fe7f17caf4f411ccd29fcf73f62c480a5b75c455","sha256:8807cc163fb3fcf1a89b74e34723f44156efcba456249d88ddf6d57ba4cc100b"],"state_sha256":"5b3e7b48eea6bb8180f8fe50d9ba490b61ba2a7ba9da679a455cf943277d5574"}