{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:65C3VMQ3K5XQQABGR3U7NAIXMC","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":"5792ac8878c586ddf217b106b84da61ada0a9b19ec77474da6318c89d4ffa012","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2012-08-05T01:22:59Z","title_canon_sha256":"9f93d1cb70d80ef35e9597f3359d3a1d7407e2e873e941ffa209085c43c10a90"},"schema_version":"1.0","source":{"id":"1208.0971","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1208.0971","created_at":"2026-05-18T03:49:20Z"},{"alias_kind":"arxiv_version","alias_value":"1208.0971v1","created_at":"2026-05-18T03:49:20Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1208.0971","created_at":"2026-05-18T03:49:20Z"},{"alias_kind":"pith_short_12","alias_value":"65C3VMQ3K5XQ","created_at":"2026-05-18T12:26:56Z"},{"alias_kind":"pith_short_16","alias_value":"65C3VMQ3K5XQQABG","created_at":"2026-05-18T12:26:56Z"},{"alias_kind":"pith_short_8","alias_value":"65C3VMQ3","created_at":"2026-05-18T12:26:56Z"}],"graph_snapshots":[{"event_id":"sha256:f46e734c383aa9c4ba6566fcdcdacde97cbc687793f6711b10eba4a948075a78","target":"graph","created_at":"2026-05-18T03:49:20Z","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":"In this paper, generalizing the result in \\cite{GXY}, we construct strongly regular Cayley graphs by using union of cyclotomic classes of $\\F_q$ and Gauss sums of index $w$, where $w\\geq 2$ is even. In particular, we obtain three infinite families of strongly regular graphs with new parameters.","authors_text":"Fan Wu","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2012-08-05T01:22:59Z","title":"Constructions of Strongly Regular Cayley Graphs using Even Index Gauss Sums"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1208.0971","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":"sha256:5de17dccfab66a60510dd76c5284f76db00c549234ea875d35b5f4e846de54b3","target":"record","created_at":"2026-05-18T03:49:20Z","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":"5792ac8878c586ddf217b106b84da61ada0a9b19ec77474da6318c89d4ffa012","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2012-08-05T01:22:59Z","title_canon_sha256":"9f93d1cb70d80ef35e9597f3359d3a1d7407e2e873e941ffa209085c43c10a90"},"schema_version":"1.0","source":{"id":"1208.0971","kind":"arxiv","version":1}},"canonical_sha256":"f745bab21b576f0800268ee9f6811760a4d42dec2bca9e350404f65fd109af68","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"f745bab21b576f0800268ee9f6811760a4d42dec2bca9e350404f65fd109af68","first_computed_at":"2026-05-18T03:49:20.982587Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:49:20.982587Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"R8nWf1vuT5Y8W2sMGRyah46egxKtssjQx6Kn1xMWyQyrq9YwhJjBBDpmdb5/GbZrLvgpYv9RE8iTnSYK7NIADw==","signature_status":"signed_v1","signed_at":"2026-05-18T03:49:20.983246Z","signed_message":"canonical_sha256_bytes"},"source_id":"1208.0971","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:5de17dccfab66a60510dd76c5284f76db00c549234ea875d35b5f4e846de54b3","sha256:f46e734c383aa9c4ba6566fcdcdacde97cbc687793f6711b10eba4a948075a78"],"state_sha256":"79e539ca0276f7e12917984a6e836b3030030cc036cc6ff2952669a175be6b1b"}