{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2017:BHF4H5U4F6US3N26T4WQSPZ5RQ","short_pith_number":"pith:BHF4H5U4","schema_version":"1.0","canonical_sha256":"09cbc3f69c2fa92db75e9f2d093f3d8c2b7c7a35508d4ba5ff24b3404783791e","source":{"kind":"arxiv","id":"1708.07597","version":1},"attestation_state":"computed","paper":{"title":"Spectral and Combinatorial Properties of Some Algebraically Defined Graphs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.DM"],"primary_cat":"math.CO","authors_text":"Felix Lazebnik, Sebastian M. Cioab\\u{a}, Shuying Sun","submitted_at":"2017-08-25T01:52:31Z","abstract_excerpt":"Let $k\\ge 3$ be an integer, $q$ be a prime power, and $\\mathbb{F}_q$ denote the field of $q$ elements. Let $f_i, g_i\\in\\mathbb{F}_q[X]$, $3\\le i\\le k$, such that $g_i(-X) = -\\, g_i(X)$. We define a graph $S(k,q) = S(k,q;f_3,g_3,\\cdots,f_k,g_k)$ as a graph with the vertex set $\\mathbb{F}_q^k$ and edges defined as follows: vertices $a = (a_1,a_2,\\ldots,a_k)$ and $b = (b_1,b_2,\\ldots,b_k)$ are adjacent if $a_1\\ne b_1$ and the following $k-2$ relations on their components hold: $$ b_i-a_i = g_i(b_1-a_1)f_i\\Bigl(\\frac{b_2-a_2}{b_1-a_1}\\Bigr)\\;,\\quad 3\\le i\\le k. $$ We show that graphs $S(k,q)$ gene"},"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":"1708.07597","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2017-08-25T01:52:31Z","cross_cats_sorted":["cs.DM"],"title_canon_sha256":"603e6ca15de91ea653cfd68574904c4527cb55ab555ffe5b97bb0d40a65150e8","abstract_canon_sha256":"0edf5f57adaf77089668aeff07bb36b2d8390aadcb0832345819167d08c8ade5"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:36:42.604945Z","signature_b64":"Mx5F+9Hw5Jo7VA1dWm/snS/iw2Tq59IBg/PXP9R3zAl7PAAGSLjT0cJI3L4C/CigSBEX2RWl4mttUaEXDvRnCA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"09cbc3f69c2fa92db75e9f2d093f3d8c2b7c7a35508d4ba5ff24b3404783791e","last_reissued_at":"2026-05-18T00:36:42.604323Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:36:42.604323Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Spectral and Combinatorial Properties of Some Algebraically Defined Graphs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.DM"],"primary_cat":"math.CO","authors_text":"Felix Lazebnik, Sebastian M. Cioab\\u{a}, Shuying Sun","submitted_at":"2017-08-25T01:52:31Z","abstract_excerpt":"Let $k\\ge 3$ be an integer, $q$ be a prime power, and $\\mathbb{F}_q$ denote the field of $q$ elements. Let $f_i, g_i\\in\\mathbb{F}_q[X]$, $3\\le i\\le k$, such that $g_i(-X) = -\\, g_i(X)$. We define a graph $S(k,q) = S(k,q;f_3,g_3,\\cdots,f_k,g_k)$ as a graph with the vertex set $\\mathbb{F}_q^k$ and edges defined as follows: vertices $a = (a_1,a_2,\\ldots,a_k)$ and $b = (b_1,b_2,\\ldots,b_k)$ are adjacent if $a_1\\ne b_1$ and the following $k-2$ relations on their components hold: $$ b_i-a_i = g_i(b_1-a_1)f_i\\Bigl(\\frac{b_2-a_2}{b_1-a_1}\\Bigr)\\;,\\quad 3\\le i\\le k. $$ We show that graphs $S(k,q)$ gene"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1708.07597","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":""},"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":"1708.07597","created_at":"2026-05-18T00:36:42.604415+00:00"},{"alias_kind":"arxiv_version","alias_value":"1708.07597v1","created_at":"2026-05-18T00:36:42.604415+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1708.07597","created_at":"2026-05-18T00:36:42.604415+00:00"},{"alias_kind":"pith_short_12","alias_value":"BHF4H5U4F6US","created_at":"2026-05-18T12:31:08.081275+00:00"},{"alias_kind":"pith_short_16","alias_value":"BHF4H5U4F6US3N26","created_at":"2026-05-18T12:31:08.081275+00:00"},{"alias_kind":"pith_short_8","alias_value":"BHF4H5U4","created_at":"2026-05-18T12:31:08.081275+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/BHF4H5U4F6US3N26T4WQSPZ5RQ","json":"https://pith.science/pith/BHF4H5U4F6US3N26T4WQSPZ5RQ.json","graph_json":"https://pith.science/api/pith-number/BHF4H5U4F6US3N26T4WQSPZ5RQ/graph.json","events_json":"https://pith.science/api/pith-number/BHF4H5U4F6US3N26T4WQSPZ5RQ/events.json","paper":"https://pith.science/paper/BHF4H5U4"},"agent_actions":{"view_html":"https://pith.science/pith/BHF4H5U4F6US3N26T4WQSPZ5RQ","download_json":"https://pith.science/pith/BHF4H5U4F6US3N26T4WQSPZ5RQ.json","view_paper":"https://pith.science/paper/BHF4H5U4","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1708.07597&json=true","fetch_graph":"https://pith.science/api/pith-number/BHF4H5U4F6US3N26T4WQSPZ5RQ/graph.json","fetch_events":"https://pith.science/api/pith-number/BHF4H5U4F6US3N26T4WQSPZ5RQ/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/BHF4H5U4F6US3N26T4WQSPZ5RQ/action/timestamp_anchor","attest_storage":"https://pith.science/pith/BHF4H5U4F6US3N26T4WQSPZ5RQ/action/storage_attestation","attest_author":"https://pith.science/pith/BHF4H5U4F6US3N26T4WQSPZ5RQ/action/author_attestation","sign_citation":"https://pith.science/pith/BHF4H5U4F6US3N26T4WQSPZ5RQ/action/citation_signature","submit_replication":"https://pith.science/pith/BHF4H5U4F6US3N26T4WQSPZ5RQ/action/replication_record"}},"created_at":"2026-05-18T00:36:42.604415+00:00","updated_at":"2026-05-18T00:36:42.604415+00:00"}