{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2015:67VSJS3QOHJHH6SGWQTHTW3MTH","short_pith_number":"pith:67VSJS3Q","canonical_record":{"source":{"id":"1507.03783","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2015-07-14T09:21:57Z","cross_cats_sorted":[],"title_canon_sha256":"eae8a58e5dff61b67099652bfa473d44fec5e40679bcece42ed539e670d31ee3","abstract_canon_sha256":"c0744abf91205dd39069bb5d49351d3b1e7915e91bea549f4a90d5192380b53d"},"schema_version":"1.0"},"canonical_sha256":"f7eb24cb7071d273fa46b42679db6c99dc8b32f5227b54d969cb1e460c078545","source":{"kind":"arxiv","id":"1507.03783","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"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2015:67VSJS3QOHJHH6SGWQTHTW3MTH","target":"record","payload":{"canonical_record":{"source":{"id":"1507.03783","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2015-07-14T09:21:57Z","cross_cats_sorted":[],"title_canon_sha256":"eae8a58e5dff61b67099652bfa473d44fec5e40679bcece42ed539e670d31ee3","abstract_canon_sha256":"c0744abf91205dd39069bb5d49351d3b1e7915e91bea549f4a90d5192380b53d"},"schema_version":"1.0"},"canonical_sha256":"f7eb24cb7071d273fa46b42679db6c99dc8b32f5227b54d969cb1e460c078545","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:36:57.355056Z","signature_b64":"6dREgkzFpKqeW3ZAc/lqQE/ENAmqrRUVLo7Kwb73lESp27E6Rs9vel2Fdx4WU9uAdVvqAYpwjw2sluKiUTltCg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"f7eb24cb7071d273fa46b42679db6c99dc8b32f5227b54d969cb1e460c078545","last_reissued_at":"2026-05-18T01:36:57.354600Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:36:57.354600Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1507.03783","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T01:36:57Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"8gVGiaLfbz6+/1bxi+PbLwU7vfBSvylOafkE9bKUSwBKdKUd5/9+2kF61H7wXyetXPh/0PvwQOppcfi6H0gbAA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-29T13:14:07.459122Z"},"content_sha256":"132022d26f1c7eb528bb278c1368916719c5ed5e05d7b7f2f7c33c6ed4869ae6","schema_version":"1.0","event_id":"sha256:132022d26f1c7eb528bb278c1368916719c5ed5e05d7b7f2f7c33c6ed4869ae6"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2015:67VSJS3QOHJHH6SGWQTHTW3MTH","target":"graph","payload":{"graph_snapshot":{"paper":{"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","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Mikhail Klin, \\v{S}tefan Gy\\\"urki","submitted_at":"2015-07-14T09:21:57Z","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."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1507.03783","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T01:36:57Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"uKtT8v0av9EuFEViML9tKLOFGFlzXprZB4l1HWIe+PyeHNexT08805P1VuZ2oYldXbi4I7wOyqocSzll5cOADA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-29T13:14:07.459470Z"},"content_sha256":"ea623df4f654298c6038b314cfb36311cb5211fadb75409be5c04c74b52b146c","schema_version":"1.0","event_id":"sha256:ea623df4f654298c6038b314cfb36311cb5211fadb75409be5c04c74b52b146c"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/67VSJS3QOHJHH6SGWQTHTW3MTH/bundle.json","state_url":"https://pith.science/pith/67VSJS3QOHJHH6SGWQTHTW3MTH/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/67VSJS3QOHJHH6SGWQTHTW3MTH/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-06-29T13:14:07Z","links":{"resolver":"https://pith.science/pith/67VSJS3QOHJHH6SGWQTHTW3MTH","bundle":"https://pith.science/pith/67VSJS3QOHJHH6SGWQTHTW3MTH/bundle.json","state":"https://pith.science/pith/67VSJS3QOHJHH6SGWQTHTW3MTH/state.json","well_known_bundle":"https://pith.science/.well-known/pith/67VSJS3QOHJHH6SGWQTHTW3MTH/bundle.json"},"state":{"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"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"DgDTE5dLMc5ujD2bX4UZqryJutnlv0e1dp1lZR/0XaxtyVH5p4qpzyggUzGHDMCJDDsAWTJUBqfrODuu4/sRAQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-29T13:14:07.461470Z","bundle_sha256":"9c9ae47722a21b9210fd9be8580e3a20817c27e9a0f88243d80c92708f6f5578"}}