{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:DLUSMSPDBT2ZZYOZHR23MLJBGV","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":"b5668785c770a3829f1d185c0c673fa1284563f25ce6d55864359c4d6939e4bf","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2018-09-20T10:17:06Z","title_canon_sha256":"79f00818c86f642dcfc25058cf975e76935832297001b421563a6505ea491b44"},"schema_version":"1.0","source":{"id":"1809.07553","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1809.07553","created_at":"2026-05-17T23:40:34Z"},{"alias_kind":"arxiv_version","alias_value":"1809.07553v2","created_at":"2026-05-17T23:40:34Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1809.07553","created_at":"2026-05-17T23:40:34Z"},{"alias_kind":"pith_short_12","alias_value":"DLUSMSPDBT2Z","created_at":"2026-05-18T12:32:19Z"},{"alias_kind":"pith_short_16","alias_value":"DLUSMSPDBT2ZZYOZ","created_at":"2026-05-18T12:32:19Z"},{"alias_kind":"pith_short_8","alias_value":"DLUSMSPD","created_at":"2026-05-18T12:32:19Z"}],"graph_snapshots":[{"event_id":"sha256:43022448ec5854fcd83ddcc76f31f6e54addacc5fe536eaf646eaf4e1c0b5096","target":"graph","created_at":"2026-05-17T23:40:34Z","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 complete the classification of tight $4$-designs in Hamming association schemes $H(n,q)$, i.e., that of tight orthogonal arrays of strength $4$, which had been open since a result by Noda (1979). To do so, we construct an association scheme attached to a tight $4$-design in $H(n,q)$ and analyze its triple intersection numbers to conclude the non-existence in all open cases.","authors_text":"Alexander Gavrilyuk, Jano\\v{s} Vidali, Sho Suda","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2018-09-20T10:17:06Z","title":"On tight $4$-designs in Hamming association schemes"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1809.07553","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":"sha256:4b8e157ff353d13abd3bd929d5b594308153b0d2b410ad7dbf042bb549289f0a","target":"record","created_at":"2026-05-17T23:40:34Z","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":"b5668785c770a3829f1d185c0c673fa1284563f25ce6d55864359c4d6939e4bf","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2018-09-20T10:17:06Z","title_canon_sha256":"79f00818c86f642dcfc25058cf975e76935832297001b421563a6505ea491b44"},"schema_version":"1.0","source":{"id":"1809.07553","kind":"arxiv","version":2}},"canonical_sha256":"1ae92649e30cf59ce1d93c75b62d21357bda69140f0383050c7939120d55eab4","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"1ae92649e30cf59ce1d93c75b62d21357bda69140f0383050c7939120d55eab4","first_computed_at":"2026-05-17T23:40:34.403978Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:40:34.403978Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"m/tMjfKMOG9Oz9LgHsTWFnPZgfuwpGYKs/uIych1hIVprkdm0ccpwxJwd/vLf5yt8deIEyOEXbBIwlxKao+5Dw==","signature_status":"signed_v1","signed_at":"2026-05-17T23:40:34.404452Z","signed_message":"canonical_sha256_bytes"},"source_id":"1809.07553","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:4b8e157ff353d13abd3bd929d5b594308153b0d2b410ad7dbf042bb549289f0a","sha256:43022448ec5854fcd83ddcc76f31f6e54addacc5fe536eaf646eaf4e1c0b5096"],"state_sha256":"934ac036c872fe93818776eaa6e1a38b95cd51d4086afe711aa4896fb3e21098"}