{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2018:SYVGO4JC3KRRQMLQ5UDJXYLIPP","short_pith_number":"pith:SYVGO4JC","schema_version":"1.0","canonical_sha256":"962a677122daa3183170ed069be1687bef94a092b0fba3d2b47191014be177d0","source":{"kind":"arxiv","id":"1810.05262","version":6},"attestation_state":"computed","paper":{"title":"Sidon sets and $C_4$-saturated graphs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Carlos Alberto Trujillo, David Fernando Daza, Fenando Andr\\'es Benavides","submitted_at":"2018-10-11T21:38:06Z","abstract_excerpt":"The problem of determining the Tur\\'an number of $C_4$ is a well studied problem that dates back to a paper of Erd\\\"os from 1938. It is known that Sidon sets can be used to construct $C_4$-free graphs. If $\\A$ is a Sidon set in the abelian group $X$, the sum graph $G_{X, \\A}$ with vertex set $X$ and edges set $E=\\{\\{x, y\\}:x\\neq y, x+y\\in \\A\\}$ is $C_4$-free. Using the sum graph of a Sidon set of type Singer we verify a conjecture of Erd\\\"os and Simonovits concerning the number of copies of $C_4$ in a graph with $ex(q^2+q+1, C_4)+1$ edges. Further, we give a sufficient condition for the sum gr"},"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":"1810.05262","kind":"arxiv","version":6},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2018-10-11T21:38:06Z","cross_cats_sorted":[],"title_canon_sha256":"d07a135674c72b13bbaa13ed8e2eac377fd9cdc539a82364834408b17d5ca272","abstract_canon_sha256":"5b2eba9cfebee0028490522942333cb1613f3a8ab03a61867b7d7af6ae3ca1cb"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:50:59.153057Z","signature_b64":"dZamIYK2A/VEM257nWTVX5uU7xioAkurImajFG0i69TS193VvhSclGaCFH4YmQyQazl7SXun7RlKbTvph2SMCg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"962a677122daa3183170ed069be1687bef94a092b0fba3d2b47191014be177d0","last_reissued_at":"2026-05-17T23:50:59.152559Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:50:59.152559Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Sidon sets and $C_4$-saturated graphs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Carlos Alberto Trujillo, David Fernando Daza, Fenando Andr\\'es Benavides","submitted_at":"2018-10-11T21:38:06Z","abstract_excerpt":"The problem of determining the Tur\\'an number of $C_4$ is a well studied problem that dates back to a paper of Erd\\\"os from 1938. It is known that Sidon sets can be used to construct $C_4$-free graphs. If $\\A$ is a Sidon set in the abelian group $X$, the sum graph $G_{X, \\A}$ with vertex set $X$ and edges set $E=\\{\\{x, y\\}:x\\neq y, x+y\\in \\A\\}$ is $C_4$-free. Using the sum graph of a Sidon set of type Singer we verify a conjecture of Erd\\\"os and Simonovits concerning the number of copies of $C_4$ in a graph with $ex(q^2+q+1, C_4)+1$ edges. Further, we give a sufficient condition for the sum gr"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1810.05262","kind":"arxiv","version":6},"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":"1810.05262","created_at":"2026-05-17T23:50:59.152642+00:00"},{"alias_kind":"arxiv_version","alias_value":"1810.05262v6","created_at":"2026-05-17T23:50:59.152642+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1810.05262","created_at":"2026-05-17T23:50:59.152642+00:00"},{"alias_kind":"pith_short_12","alias_value":"SYVGO4JC3KRR","created_at":"2026-05-18T12:32:53.628368+00:00"},{"alias_kind":"pith_short_16","alias_value":"SYVGO4JC3KRRQMLQ","created_at":"2026-05-18T12:32:53.628368+00:00"},{"alias_kind":"pith_short_8","alias_value":"SYVGO4JC","created_at":"2026-05-18T12:32:53.628368+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":1,"internal_anchor_count":1,"sample":[{"citing_arxiv_id":"2501.11736","citing_title":"Cardinalities of $g$-difference sets","ref_index":15,"is_internal_anchor":true}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/SYVGO4JC3KRRQMLQ5UDJXYLIPP","json":"https://pith.science/pith/SYVGO4JC3KRRQMLQ5UDJXYLIPP.json","graph_json":"https://pith.science/api/pith-number/SYVGO4JC3KRRQMLQ5UDJXYLIPP/graph.json","events_json":"https://pith.science/api/pith-number/SYVGO4JC3KRRQMLQ5UDJXYLIPP/events.json","paper":"https://pith.science/paper/SYVGO4JC"},"agent_actions":{"view_html":"https://pith.science/pith/SYVGO4JC3KRRQMLQ5UDJXYLIPP","download_json":"https://pith.science/pith/SYVGO4JC3KRRQMLQ5UDJXYLIPP.json","view_paper":"https://pith.science/paper/SYVGO4JC","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1810.05262&json=true","fetch_graph":"https://pith.science/api/pith-number/SYVGO4JC3KRRQMLQ5UDJXYLIPP/graph.json","fetch_events":"https://pith.science/api/pith-number/SYVGO4JC3KRRQMLQ5UDJXYLIPP/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/SYVGO4JC3KRRQMLQ5UDJXYLIPP/action/timestamp_anchor","attest_storage":"https://pith.science/pith/SYVGO4JC3KRRQMLQ5UDJXYLIPP/action/storage_attestation","attest_author":"https://pith.science/pith/SYVGO4JC3KRRQMLQ5UDJXYLIPP/action/author_attestation","sign_citation":"https://pith.science/pith/SYVGO4JC3KRRQMLQ5UDJXYLIPP/action/citation_signature","submit_replication":"https://pith.science/pith/SYVGO4JC3KRRQMLQ5UDJXYLIPP/action/replication_record"}},"created_at":"2026-05-17T23:50:59.152642+00:00","updated_at":"2026-05-17T23:50:59.152642+00:00"}