{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2017:KOQUHKBWAYRNMV7ABQY2KAR7D3","short_pith_number":"pith:KOQUHKBW","canonical_record":{"source":{"id":"1706.06281","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2017-06-20T06:15:45Z","cross_cats_sorted":[],"title_canon_sha256":"c247f6e5dde83065dbdf5d5b69730a5bff37a983176b799e90fc8d75886a6ec3","abstract_canon_sha256":"19bd7fedf90c6181d92a0a2b26b849ac595937cfd577f9a56f23fe9f0ce0f253"},"schema_version":"1.0"},"canonical_sha256":"53a143a8360622d657e00c31a5023f1ef2ebe3f39c85775b863f1969bc17eca9","source":{"kind":"arxiv","id":"1706.06281","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1706.06281","created_at":"2026-05-18T00:19:03Z"},{"alias_kind":"arxiv_version","alias_value":"1706.06281v2","created_at":"2026-05-18T00:19:03Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1706.06281","created_at":"2026-05-18T00:19:03Z"},{"alias_kind":"pith_short_12","alias_value":"KOQUHKBWAYRN","created_at":"2026-05-18T12:31:24Z"},{"alias_kind":"pith_short_16","alias_value":"KOQUHKBWAYRNMV7A","created_at":"2026-05-18T12:31:24Z"},{"alias_kind":"pith_short_8","alias_value":"KOQUHKBW","created_at":"2026-05-18T12:31:24Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2017:KOQUHKBWAYRNMV7ABQY2KAR7D3","target":"record","payload":{"canonical_record":{"source":{"id":"1706.06281","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2017-06-20T06:15:45Z","cross_cats_sorted":[],"title_canon_sha256":"c247f6e5dde83065dbdf5d5b69730a5bff37a983176b799e90fc8d75886a6ec3","abstract_canon_sha256":"19bd7fedf90c6181d92a0a2b26b849ac595937cfd577f9a56f23fe9f0ce0f253"},"schema_version":"1.0"},"canonical_sha256":"53a143a8360622d657e00c31a5023f1ef2ebe3f39c85775b863f1969bc17eca9","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:19:03.995465Z","signature_b64":"KO/o+UlAV3m7ikp7PkctJ2vRjg+zg3UNYTblm+g63ZcnwQs1TbpAaBI6rtentS167mk6CiRE2sPEklYpgdkgCQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"53a143a8360622d657e00c31a5023f1ef2ebe3f39c85775b863f1969bc17eca9","last_reissued_at":"2026-05-18T00:19:03.994773Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:19:03.994773Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1706.06281","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T00:19:03Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"wsdaJGHBdAW89nT6QBPkJcNPjQHaDuiozDHth1uk7n7vFZF+o+mGOKKrhuSvrI6wgo4YI+ZaoJ/LFBcQSjWfCQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-26T00:19:15.923042Z"},"content_sha256":"a90c012ef1ea71ca25d70244da733652467a8346c6a8b49a932b64fcd3829f90","schema_version":"1.0","event_id":"sha256:a90c012ef1ea71ca25d70244da733652467a8346c6a8b49a932b64fcd3829f90"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2017:KOQUHKBWAYRNMV7ABQY2KAR7D3","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Non-commutative association schemes and their fusion association schemes","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Hadi Kharaghani, Sho Suda","submitted_at":"2017-06-20T06:15:45Z","abstract_excerpt":"We give a sufficient condition for a non-commutative association scheme to have a fusion association scheme, and construct non-commutative association schemes from symmetric balanced generalized weighing matrices and generalized Hadamard matrices. We then apply the criterion to these non-commutative association schemes to obtain symmetric fusion association schemes."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1706.06281","kind":"arxiv","version":2},"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":"2026-05-18T00:19:03Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"/AwfaXpTnkfU+Iu8VB6Cw2zy8BNcujbQjwSQ1p9tZxIsXZuiLKuHjghFLKVu+HCpwGMptAA08aYARlxWtbMSBg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-26T00:19:15.923690Z"},"content_sha256":"d6496695bd2ba3eabfc478931907af55046b45fcc18ed3fca99e642e6e30ca9c","schema_version":"1.0","event_id":"sha256:d6496695bd2ba3eabfc478931907af55046b45fcc18ed3fca99e642e6e30ca9c"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/KOQUHKBWAYRNMV7ABQY2KAR7D3/bundle.json","state_url":"https://pith.science/pith/KOQUHKBWAYRNMV7ABQY2KAR7D3/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/KOQUHKBWAYRNMV7ABQY2KAR7D3/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":"2026-05-26T00:19:15Z","links":{"resolver":"https://pith.science/pith/KOQUHKBWAYRNMV7ABQY2KAR7D3","bundle":"https://pith.science/pith/KOQUHKBWAYRNMV7ABQY2KAR7D3/bundle.json","state":"https://pith.science/pith/KOQUHKBWAYRNMV7ABQY2KAR7D3/state.json","well_known_bundle":"https://pith.science/.well-known/pith/KOQUHKBWAYRNMV7ABQY2KAR7D3/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:KOQUHKBWAYRNMV7ABQY2KAR7D3","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":"19bd7fedf90c6181d92a0a2b26b849ac595937cfd577f9a56f23fe9f0ce0f253","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2017-06-20T06:15:45Z","title_canon_sha256":"c247f6e5dde83065dbdf5d5b69730a5bff37a983176b799e90fc8d75886a6ec3"},"schema_version":"1.0","source":{"id":"1706.06281","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1706.06281","created_at":"2026-05-18T00:19:03Z"},{"alias_kind":"arxiv_version","alias_value":"1706.06281v2","created_at":"2026-05-18T00:19:03Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1706.06281","created_at":"2026-05-18T00:19:03Z"},{"alias_kind":"pith_short_12","alias_value":"KOQUHKBWAYRN","created_at":"2026-05-18T12:31:24Z"},{"alias_kind":"pith_short_16","alias_value":"KOQUHKBWAYRNMV7A","created_at":"2026-05-18T12:31:24Z"},{"alias_kind":"pith_short_8","alias_value":"KOQUHKBW","created_at":"2026-05-18T12:31:24Z"}],"graph_snapshots":[{"event_id":"sha256:d6496695bd2ba3eabfc478931907af55046b45fcc18ed3fca99e642e6e30ca9c","target":"graph","created_at":"2026-05-18T00:19:03Z","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 give a sufficient condition for a non-commutative association scheme to have a fusion association scheme, and construct non-commutative association schemes from symmetric balanced generalized weighing matrices and generalized Hadamard matrices. We then apply the criterion to these non-commutative association schemes to obtain symmetric fusion association schemes.","authors_text":"Hadi Kharaghani, Sho Suda","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2017-06-20T06:15:45Z","title":"Non-commutative association schemes and their fusion association schemes"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1706.06281","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:a90c012ef1ea71ca25d70244da733652467a8346c6a8b49a932b64fcd3829f90","target":"record","created_at":"2026-05-18T00:19:03Z","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":"19bd7fedf90c6181d92a0a2b26b849ac595937cfd577f9a56f23fe9f0ce0f253","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2017-06-20T06:15:45Z","title_canon_sha256":"c247f6e5dde83065dbdf5d5b69730a5bff37a983176b799e90fc8d75886a6ec3"},"schema_version":"1.0","source":{"id":"1706.06281","kind":"arxiv","version":2}},"canonical_sha256":"53a143a8360622d657e00c31a5023f1ef2ebe3f39c85775b863f1969bc17eca9","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"53a143a8360622d657e00c31a5023f1ef2ebe3f39c85775b863f1969bc17eca9","first_computed_at":"2026-05-18T00:19:03.994773Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:19:03.994773Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"KO/o+UlAV3m7ikp7PkctJ2vRjg+zg3UNYTblm+g63ZcnwQs1TbpAaBI6rtentS167mk6CiRE2sPEklYpgdkgCQ==","signature_status":"signed_v1","signed_at":"2026-05-18T00:19:03.995465Z","signed_message":"canonical_sha256_bytes"},"source_id":"1706.06281","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:a90c012ef1ea71ca25d70244da733652467a8346c6a8b49a932b64fcd3829f90","sha256:d6496695bd2ba3eabfc478931907af55046b45fcc18ed3fca99e642e6e30ca9c"],"state_sha256":"de9b1afc3a92efe4a628feb5eb44ce253405e00bb9aba0ea83c23b8502a6ffc2"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"cNDghmbB29gaMdqt4ZjwkXZeTP1bYT0VvsuAVGZF7QNQ2gCybvUebsZFKFyThjJK50SO0qFZxHtMCQn8VFsdCw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-26T00:19:15.926955Z","bundle_sha256":"4a30743d4fc9ebb9e7ae2851f86d2cc4c9dd971dd16e2e5cc88ffbcfef4c23c0"}}