{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2019:XFKTF7JGQVXLECX7VNDUPT2FLE","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":"3be044f9571fbf10649bebc1d6529ef16ea28f489ab38d0183142382be97331d","cross_cats_sorted":["cs.IT","math.IT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2019-08-21T19:45:51Z","title_canon_sha256":"ebc9a047556ff625c4b2535245e43b2ef1bd1fc8c19b41e97fc8a9cc40049491"},"schema_version":"1.0","source":{"id":"1908.08097","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1908.08097","created_at":"2026-07-05T01:17:38Z"},{"alias_kind":"arxiv_version","alias_value":"1908.08097v3","created_at":"2026-07-05T01:17:38Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1908.08097","created_at":"2026-07-05T01:17:38Z"},{"alias_kind":"pith_short_12","alias_value":"XFKTF7JGQVXL","created_at":"2026-07-05T01:17:38Z"},{"alias_kind":"pith_short_16","alias_value":"XFKTF7JGQVXLECX7","created_at":"2026-07-05T01:17:38Z"},{"alias_kind":"pith_short_8","alias_value":"XFKTF7JG","created_at":"2026-07-05T01:17:38Z"}],"graph_snapshots":[{"event_id":"sha256:8beb33afe8ebe014fd16f4cb63b0799c9f3688ed6fbf32b727bc382e368deb44","target":"graph","created_at":"2026-07-05T01:17:38Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/1908.08097/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"For $q=p^m$ with $p$ prime and $k\\mid q-1$, we consider the generalized Paley graph $\\Gamma(k,q) = Cay(\\mathbb{F}_q, R_k)$, with $R_k=\\{ x^k : x \\in \\mathbb{F}_q^* \\}$, and the irreducible $p$-ary cyclic code $\\mathcal{C}(k,q) = \\{(\\textrm{Tr}_{q/p}(\\gamma \\omega^{ik})_{i=0}^{n-1})\\}_{\\gamma \\in \\mathbb{F}_q}$, with $\\omega$ a primitive element of $\\mathbb{F}_q$ and $n=\\tfrac{q-1}{k}$. We first express the spectra of $\\Gamma(k,q)$ in terms of Gaussian periods. Then, we show that the spectra of $\\Gamma(k,q)$ and $\\mathcal{C}(k,q)$ are mutually determined by each other if further $k\\mid \\tfrac{q","authors_text":"Denis E. Videla, Ricardo A. Podest\\'a","cross_cats":["cs.IT","math.IT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2019-08-21T19:45:51Z","title":"Spectral properties of generalized Paley graphs and their associated irreducible cyclic codes"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1908.08097","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":"sha256:86b6b3427d4fe46e4f35b1c3df5244cc5841d279943d8844411cd3aa96df29af","target":"record","created_at":"2026-07-05T01:17:38Z","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":"3be044f9571fbf10649bebc1d6529ef16ea28f489ab38d0183142382be97331d","cross_cats_sorted":["cs.IT","math.IT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2019-08-21T19:45:51Z","title_canon_sha256":"ebc9a047556ff625c4b2535245e43b2ef1bd1fc8c19b41e97fc8a9cc40049491"},"schema_version":"1.0","source":{"id":"1908.08097","kind":"arxiv","version":3}},"canonical_sha256":"b95532fd26856eb20affab4747cf45591ee58eb5e1247c2f6e8636ac9aa84b7e","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"b95532fd26856eb20affab4747cf45591ee58eb5e1247c2f6e8636ac9aa84b7e","first_computed_at":"2026-07-05T01:17:38.224446Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T01:17:38.224446Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"cByTP99uQm0xvgJWtv2bHlixqxlPpmhGeXpSmcF4iVlx/sk6sGRxS2UZN3TegNAs6DP7Nm/aXJMkfiEegifiAw==","signature_status":"signed_v1","signed_at":"2026-07-05T01:17:38.224875Z","signed_message":"canonical_sha256_bytes"},"source_id":"1908.08097","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:86b6b3427d4fe46e4f35b1c3df5244cc5841d279943d8844411cd3aa96df29af","sha256:8beb33afe8ebe014fd16f4cb63b0799c9f3688ed6fbf32b727bc382e368deb44"],"state_sha256":"3e5d429fc24fb987eb3359f36096fcbf9f4e5492cd46bd4304eeaeff0c5c72b1"}