{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2008:TQGH5U5L3EBXK5PAINNPL7RIFI","short_pith_number":"pith:TQGH5U5L","canonical_record":{"source":{"id":"0808.3676","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2008-08-27T11:09:03Z","cross_cats_sorted":[],"title_canon_sha256":"aa4285aeb04468a43816c7f19a2810f10e51e912edc9bb6b97f6106e8130e239","abstract_canon_sha256":"99f027c920004ce03743c767da45be15bde9a480ec37d7c9d13daf304cb34ade"},"schema_version":"1.0"},"canonical_sha256":"9c0c7ed3abd9037575e0435af5fe282a38becac8d1bd73078c5f76d994535db2","source":{"kind":"arxiv","id":"0808.3676","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0808.3676","created_at":"2026-05-18T00:32:31Z"},{"alias_kind":"arxiv_version","alias_value":"0808.3676v3","created_at":"2026-05-18T00:32:31Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0808.3676","created_at":"2026-05-18T00:32:31Z"},{"alias_kind":"pith_short_12","alias_value":"TQGH5U5L3EBX","created_at":"2026-05-18T12:25:58Z"},{"alias_kind":"pith_short_16","alias_value":"TQGH5U5L3EBXK5PA","created_at":"2026-05-18T12:25:58Z"},{"alias_kind":"pith_short_8","alias_value":"TQGH5U5L","created_at":"2026-05-18T12:25:58Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2008:TQGH5U5L3EBXK5PAINNPL7RIFI","target":"record","payload":{"canonical_record":{"source":{"id":"0808.3676","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2008-08-27T11:09:03Z","cross_cats_sorted":[],"title_canon_sha256":"aa4285aeb04468a43816c7f19a2810f10e51e912edc9bb6b97f6106e8130e239","abstract_canon_sha256":"99f027c920004ce03743c767da45be15bde9a480ec37d7c9d13daf304cb34ade"},"schema_version":"1.0"},"canonical_sha256":"9c0c7ed3abd9037575e0435af5fe282a38becac8d1bd73078c5f76d994535db2","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:32:31.883160Z","signature_b64":"64iwM2mLDLDvpbwRz2NV1t5Z0nXD47OotoJUuOclrWyjfXvMqu3H5hEXALNjrPo1/F0x80ICIwZMfPjWJFYJDQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"9c0c7ed3abd9037575e0435af5fe282a38becac8d1bd73078c5f76d994535db2","last_reissued_at":"2026-05-18T00:32:31.882522Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:32:31.882522Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"0808.3676","source_version":3,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T00:32:31Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"CdeSQsrDpPUfRJ2wnlw0mh8fjB/IXgAbpJrXE68foRoJN2pNzDUckV+kwyEkAlhBAKbd8AN0t4uLnGGZSinuDQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-01T19:02:13.550144Z"},"content_sha256":"fae7574d62ff50067f0050695b046b7c2949e2bd7882f9ae06a0220273d16254","schema_version":"1.0","event_id":"sha256:fae7574d62ff50067f0050695b046b7c2949e2bd7882f9ae06a0220273d16254"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2008:TQGH5U5L3EBXK5PAINNPL7RIFI","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Pseudocyclic association schemes and strongly regular graphs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Akihiro Munemasa, Takuya Ikuta","submitted_at":"2008-08-27T11:09:03Z","abstract_excerpt":"Let X be a pseudocyclic association scheme in which all the nontrivial relations are strongly regular graphs with the same eigenvalues. We prove that the principal part of the first eigenmatrix of X is a linear combination of an incidence matrix of a symmetric design and the all-ones matrix. Amorphous pseudocyclic association schemes are examples of such association schemes whose associated symmetric design is trivial. We present several non-amorphous examples, which are either cyclotomic association schemes, or their fusion schemes. Special properties of symmetric designs guarantee the existe"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0808.3676","kind":"arxiv","version":3},"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":"2026-05-18T00:32:31Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"52yeMXlLX2R3nyeBTdm8Dor8LasV6jYaE2G+q4fJvc2Q23LkdKOonN0FTl9Gt5ESgzCQVG+8YUaAikuxqxhNDQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-01T19:02:13.550514Z"},"content_sha256":"d4ffeaf04af2a6a074ae146f7493c00670cc49e1a0fa7adf702b5ed4b9fa21f7","schema_version":"1.0","event_id":"sha256:d4ffeaf04af2a6a074ae146f7493c00670cc49e1a0fa7adf702b5ed4b9fa21f7"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/TQGH5U5L3EBXK5PAINNPL7RIFI/bundle.json","state_url":"https://pith.science/pith/TQGH5U5L3EBXK5PAINNPL7RIFI/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/TQGH5U5L3EBXK5PAINNPL7RIFI/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":"2026-06-01T19:02:13Z","links":{"resolver":"https://pith.science/pith/TQGH5U5L3EBXK5PAINNPL7RIFI","bundle":"https://pith.science/pith/TQGH5U5L3EBXK5PAINNPL7RIFI/bundle.json","state":"https://pith.science/pith/TQGH5U5L3EBXK5PAINNPL7RIFI/state.json","well_known_bundle":"https://pith.science/.well-known/pith/TQGH5U5L3EBXK5PAINNPL7RIFI/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2008:TQGH5U5L3EBXK5PAINNPL7RIFI","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":"99f027c920004ce03743c767da45be15bde9a480ec37d7c9d13daf304cb34ade","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2008-08-27T11:09:03Z","title_canon_sha256":"aa4285aeb04468a43816c7f19a2810f10e51e912edc9bb6b97f6106e8130e239"},"schema_version":"1.0","source":{"id":"0808.3676","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0808.3676","created_at":"2026-05-18T00:32:31Z"},{"alias_kind":"arxiv_version","alias_value":"0808.3676v3","created_at":"2026-05-18T00:32:31Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0808.3676","created_at":"2026-05-18T00:32:31Z"},{"alias_kind":"pith_short_12","alias_value":"TQGH5U5L3EBX","created_at":"2026-05-18T12:25:58Z"},{"alias_kind":"pith_short_16","alias_value":"TQGH5U5L3EBXK5PA","created_at":"2026-05-18T12:25:58Z"},{"alias_kind":"pith_short_8","alias_value":"TQGH5U5L","created_at":"2026-05-18T12:25:58Z"}],"graph_snapshots":[{"event_id":"sha256:d4ffeaf04af2a6a074ae146f7493c00670cc49e1a0fa7adf702b5ed4b9fa21f7","target":"graph","created_at":"2026-05-18T00:32:31Z","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 X be a pseudocyclic association scheme in which all the nontrivial relations are strongly regular graphs with the same eigenvalues. We prove that the principal part of the first eigenmatrix of X is a linear combination of an incidence matrix of a symmetric design and the all-ones matrix. Amorphous pseudocyclic association schemes are examples of such association schemes whose associated symmetric design is trivial. We present several non-amorphous examples, which are either cyclotomic association schemes, or their fusion schemes. Special properties of symmetric designs guarantee the existe","authors_text":"Akihiro Munemasa, Takuya Ikuta","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2008-08-27T11:09:03Z","title":"Pseudocyclic association schemes and strongly regular graphs"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0808.3676","kind":"arxiv","version":3},"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:fae7574d62ff50067f0050695b046b7c2949e2bd7882f9ae06a0220273d16254","target":"record","created_at":"2026-05-18T00:32:31Z","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":"99f027c920004ce03743c767da45be15bde9a480ec37d7c9d13daf304cb34ade","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2008-08-27T11:09:03Z","title_canon_sha256":"aa4285aeb04468a43816c7f19a2810f10e51e912edc9bb6b97f6106e8130e239"},"schema_version":"1.0","source":{"id":"0808.3676","kind":"arxiv","version":3}},"canonical_sha256":"9c0c7ed3abd9037575e0435af5fe282a38becac8d1bd73078c5f76d994535db2","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"9c0c7ed3abd9037575e0435af5fe282a38becac8d1bd73078c5f76d994535db2","first_computed_at":"2026-05-18T00:32:31.882522Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:32:31.882522Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"64iwM2mLDLDvpbwRz2NV1t5Z0nXD47OotoJUuOclrWyjfXvMqu3H5hEXALNjrPo1/F0x80ICIwZMfPjWJFYJDQ==","signature_status":"signed_v1","signed_at":"2026-05-18T00:32:31.883160Z","signed_message":"canonical_sha256_bytes"},"source_id":"0808.3676","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:fae7574d62ff50067f0050695b046b7c2949e2bd7882f9ae06a0220273d16254","sha256:d4ffeaf04af2a6a074ae146f7493c00670cc49e1a0fa7adf702b5ed4b9fa21f7"],"state_sha256":"dcecde125cd3177b74aa9c1142dc2a72c6335d6ae9ae18aef9967d4feb6fd2c2"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"vlUWSj8aN/cgyNrrqyuBv/Wa0GQXGVbci/9+juNMSl0D2CNE68Mp4mLomYcj1Oho/rQafQB/tP/ZCgET++K4DQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-01T19:02:13.552480Z","bundle_sha256":"bf4a65fc7cf00c45abde90884d9068f8d7f5f75619d877cfc0bd4a08ab2c2cf8"}}