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We compute the spectra of $\\Gamma(3,q)$ and $\\Gamma(4,q)$ and from them we obtain the spectra of $\\Gamma^+(3,q)$ and $\\Gamma^+(4,q)$ also. Then we show that, in the non-semiprimitive case, the spectrum of $\\Gamma(3,p^{3\\ell})$ and $\\Gamma(4,p^{4\\ell})$ with $p$ prime can be recursively obtained, under certain arithmetic conditions"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"2204.08509","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2022-04-18T18:43:37Z","cross_cats_sorted":[],"title_canon_sha256":"f33153a0b34fe5cc1e2d486f2bdc79d63edcc4b2c7b419ed28692ff3c64f75db","abstract_canon_sha256":"67819bf377e71c0d9d437221b24389acb9bea638893d8fcc65e4a92ac89edb87"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T04:15:30.529502Z","signature_b64":"obGK3OB3yok/6ImUEISUYvt3KpFRseahPGtvyPkHA127Psa1utQjIa26MalK7xdvgli4k2Oi7CFGpi5GbcTVCg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"45cfcd3f26046fa79a4ab0321b9b4d0cf5582fe2d8e7951940479cf09104c789","last_reissued_at":"2026-07-05T04:15:30.529060Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T04:15:30.529060Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Generalized Paley graphs equienergetic with their complements","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Denis E. Videla, Ricardo A. Podest\\'a","submitted_at":"2022-04-18T18:43:37Z","abstract_excerpt":"We consider generalized Paley graphs $\\Gamma(k,q)$, generalized Paley sum graphs $\\Gamma^+(k,q)$, and their corresponding complements $\\bar \\Gamma(k,q)$ and $\\bar \\Gamma^+(k,q)$, for $k=3,4$. Denote by $\\Gamma = \\Gamma^*(k,q)$ either $\\Gamma(k,q)$ or $\\Gamma^+(k,q)$. We compute the spectra of $\\Gamma(3,q)$ and $\\Gamma(4,q)$ and from them we obtain the spectra of $\\Gamma^+(3,q)$ and $\\Gamma^+(4,q)$ also. Then we show that, in the non-semiprimitive case, the spectrum of $\\Gamma(3,p^{3\\ell})$ and $\\Gamma(4,p^{4\\ell})$ with $p$ prime can be recursively obtained, under certain arithmetic conditions"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2204.08509","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2204.08509/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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"},"aliases":[{"alias_kind":"arxiv","alias_value":"2204.08509","created_at":"2026-07-05T04:15:30.529112+00:00"},{"alias_kind":"arxiv_version","alias_value":"2204.08509v1","created_at":"2026-07-05T04:15:30.529112+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2204.08509","created_at":"2026-07-05T04:15:30.529112+00:00"},{"alias_kind":"pith_short_12","alias_value":"IXH42PZGARX2","created_at":"2026-07-05T04:15:30.529112+00:00"},{"alias_kind":"pith_short_16","alias_value":"IXH42PZGARX2PGSK","created_at":"2026-07-05T04:15:30.529112+00:00"},{"alias_kind":"pith_short_8","alias_value":"IXH42PZG","created_at":"2026-07-05T04:15:30.529112+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/IXH42PZGARX2PGSKWAZBXG2NBT","json":"https://pith.science/pith/IXH42PZGARX2PGSKWAZBXG2NBT.json","graph_json":"https://pith.science/api/pith-number/IXH42PZGARX2PGSKWAZBXG2NBT/graph.json","events_json":"https://pith.science/api/pith-number/IXH42PZGARX2PGSKWAZBXG2NBT/events.json","paper":"https://pith.science/paper/IXH42PZG"},"agent_actions":{"view_html":"https://pith.science/pith/IXH42PZGARX2PGSKWAZBXG2NBT","download_json":"https://pith.science/pith/IXH42PZGARX2PGSKWAZBXG2NBT.json","view_paper":"https://pith.science/paper/IXH42PZG","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2204.08509&json=true","fetch_graph":"https://pith.science/api/pith-number/IXH42PZGARX2PGSKWAZBXG2NBT/graph.json","fetch_events":"https://pith.science/api/pith-number/IXH42PZGARX2PGSKWAZBXG2NBT/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/IXH42PZGARX2PGSKWAZBXG2NBT/action/timestamp_anchor","attest_storage":"https://pith.science/pith/IXH42PZGARX2PGSKWAZBXG2NBT/action/storage_attestation","attest_author":"https://pith.science/pith/IXH42PZGARX2PGSKWAZBXG2NBT/action/author_attestation","sign_citation":"https://pith.science/pith/IXH42PZGARX2PGSKWAZBXG2NBT/action/citation_signature","submit_replication":"https://pith.science/pith/IXH42PZGARX2PGSKWAZBXG2NBT/action/replication_record"}},"created_at":"2026-07-05T04:15:30.529112+00:00","updated_at":"2026-07-05T04:15:30.529112+00:00"}