{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:67VSJS3QOHJHH6SGWQTHTW3MTH","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":"c0744abf91205dd39069bb5d49351d3b1e7915e91bea549f4a90d5192380b53d","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2015-07-14T09:21:57Z","title_canon_sha256":"eae8a58e5dff61b67099652bfa473d44fec5e40679bcece42ed539e670d31ee3"},"schema_version":"1.0","source":{"id":"1507.03783","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1507.03783","created_at":"2026-05-18T01:36:57Z"},{"alias_kind":"arxiv_version","alias_value":"1507.03783v1","created_at":"2026-05-18T01:36:57Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1507.03783","created_at":"2026-05-18T01:36:57Z"},{"alias_kind":"pith_short_12","alias_value":"67VSJS3QOHJH","created_at":"2026-05-18T12:29:07Z"},{"alias_kind":"pith_short_16","alias_value":"67VSJS3QOHJHH6SG","created_at":"2026-05-18T12:29:07Z"},{"alias_kind":"pith_short_8","alias_value":"67VSJS3Q","created_at":"2026-05-18T12:29:07Z"}],"graph_snapshots":[{"event_id":"sha256:ea623df4f654298c6038b314cfb36311cb5211fadb75409be5c04c74b52b146c","target":"graph","created_at":"2026-05-18T01:36:57Z","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":"Let $p$ be an odd prime. In this paper we provide a construction which gives four non-Schurian association schemes for every $p\\geq 5$ and two for $p=3$. This construction is explained using incidences between points and lines of a biaffine plane and we also provide a pure algebraic model for it with the aid of finite Heisenberg groups. The obtained results are discussed in a more wide framework.","authors_text":"Mikhail Klin, \\v{S}tefan Gy\\\"urki","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2015-07-14T09:21:57Z","title":"Construction of infinite families of non-Schurian association schemes of order $2p^2$, $p$ an odd prime, based on biaffine planes and Heisenberg groups: research report and beyond"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1507.03783","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":"sha256:132022d26f1c7eb528bb278c1368916719c5ed5e05d7b7f2f7c33c6ed4869ae6","target":"record","created_at":"2026-05-18T01:36:57Z","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":"c0744abf91205dd39069bb5d49351d3b1e7915e91bea549f4a90d5192380b53d","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2015-07-14T09:21:57Z","title_canon_sha256":"eae8a58e5dff61b67099652bfa473d44fec5e40679bcece42ed539e670d31ee3"},"schema_version":"1.0","source":{"id":"1507.03783","kind":"arxiv","version":1}},"canonical_sha256":"f7eb24cb7071d273fa46b42679db6c99dc8b32f5227b54d969cb1e460c078545","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"f7eb24cb7071d273fa46b42679db6c99dc8b32f5227b54d969cb1e460c078545","first_computed_at":"2026-05-18T01:36:57.354600Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:36:57.354600Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"6dREgkzFpKqeW3ZAc/lqQE/ENAmqrRUVLo7Kwb73lESp27E6Rs9vel2Fdx4WU9uAdVvqAYpwjw2sluKiUTltCg==","signature_status":"signed_v1","signed_at":"2026-05-18T01:36:57.355056Z","signed_message":"canonical_sha256_bytes"},"source_id":"1507.03783","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:132022d26f1c7eb528bb278c1368916719c5ed5e05d7b7f2f7c33c6ed4869ae6","sha256:ea623df4f654298c6038b314cfb36311cb5211fadb75409be5c04c74b52b146c"],"state_sha256":"0b887b4fe64f84dc834d382e025abab66982b06ba815c477dff69e53fb7d9728"}