{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:XLNF3U3B53ZTGERNELGDZUJSMT","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":"93b529125f3a6cd6fbb9778ffe1f78ff20585b5233017195126829b6aa4cfb0c","cross_cats_sorted":["math.NT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2014-05-12T02:57:42Z","title_canon_sha256":"a3d6d7869082ae4b939edd888f2750d49c46655ba2f076c4f04f3748eb5ad7fd"},"schema_version":"1.0","source":{"id":"1405.3194","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1405.3194","created_at":"2026-05-18T00:02:46Z"},{"alias_kind":"arxiv_version","alias_value":"1405.3194v2","created_at":"2026-05-18T00:02:46Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1405.3194","created_at":"2026-05-18T00:02:46Z"},{"alias_kind":"pith_short_12","alias_value":"XLNF3U3B53ZT","created_at":"2026-05-18T12:28:57Z"},{"alias_kind":"pith_short_16","alias_value":"XLNF3U3B53ZTGERN","created_at":"2026-05-18T12:28:57Z"},{"alias_kind":"pith_short_8","alias_value":"XLNF3U3B","created_at":"2026-05-18T12:28:57Z"}],"graph_snapshots":[{"event_id":"sha256:1dd5f36f526dc44f50c994533e1ce5eff77b13ebe3a98015e1cc42c982bfc0b8","target":"graph","created_at":"2026-05-18T00:02:46Z","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":"A number of new terminating series involving $\\sin(n^2/k)$ and $\\cos(n^2/k)$ are presented and connected to Gauss quadratic sums. Several new closed forms of generic Gauss quadratic sums are obtained and previously known results are generalized.","authors_text":"Larry Glasser, Michael S. Milgram","cross_cats":["math.NT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2014-05-12T02:57:42Z","title":"On Quadratic Gauss Sums and Variations Thereof"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1405.3194","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":"sha256:06b04538a4cb962211ad29d4aff673ea31fae497d1b657b6877b517298602e64","target":"record","created_at":"2026-05-18T00:02:46Z","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":"93b529125f3a6cd6fbb9778ffe1f78ff20585b5233017195126829b6aa4cfb0c","cross_cats_sorted":["math.NT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2014-05-12T02:57:42Z","title_canon_sha256":"a3d6d7869082ae4b939edd888f2750d49c46655ba2f076c4f04f3748eb5ad7fd"},"schema_version":"1.0","source":{"id":"1405.3194","kind":"arxiv","version":2}},"canonical_sha256":"bada5dd361eef333122d22cc3cd13264db5cf1ec752b85a15426bbf4647db97e","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"bada5dd361eef333122d22cc3cd13264db5cf1ec752b85a15426bbf4647db97e","first_computed_at":"2026-05-18T00:02:46.147606Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:02:46.147606Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"wVzUz7JVa5N8gnmaKSnpoT1yvCeHIiUTlqP0DfhsDjyI8zOG2tz7EeqxKMc3iHI4irwVmsbo7esu/Wn0aR4/Dg==","signature_status":"signed_v1","signed_at":"2026-05-18T00:02:46.148082Z","signed_message":"canonical_sha256_bytes"},"source_id":"1405.3194","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:06b04538a4cb962211ad29d4aff673ea31fae497d1b657b6877b517298602e64","sha256:1dd5f36f526dc44f50c994533e1ce5eff77b13ebe3a98015e1cc42c982bfc0b8"],"state_sha256":"824bacfa06f06913e55f1639bfc35aa51cde42348584dafc5d6a787a941a76f8"}