{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:SYVGO4JC3KRRQMLQ5UDJXYLIPP","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":"5b2eba9cfebee0028490522942333cb1613f3a8ab03a61867b7d7af6ae3ca1cb","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2018-10-11T21:38:06Z","title_canon_sha256":"d07a135674c72b13bbaa13ed8e2eac377fd9cdc539a82364834408b17d5ca272"},"schema_version":"1.0","source":{"id":"1810.05262","kind":"arxiv","version":6}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1810.05262","created_at":"2026-05-17T23:50:59Z"},{"alias_kind":"arxiv_version","alias_value":"1810.05262v6","created_at":"2026-05-17T23:50:59Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1810.05262","created_at":"2026-05-17T23:50:59Z"},{"alias_kind":"pith_short_12","alias_value":"SYVGO4JC3KRR","created_at":"2026-05-18T12:32:53Z"},{"alias_kind":"pith_short_16","alias_value":"SYVGO4JC3KRRQMLQ","created_at":"2026-05-18T12:32:53Z"},{"alias_kind":"pith_short_8","alias_value":"SYVGO4JC","created_at":"2026-05-18T12:32:53Z"}],"graph_snapshots":[{"event_id":"sha256:2684460ac204900073be254beec03f2bf72c62421c86e393bd63f6996a6c2169","target":"graph","created_at":"2026-05-17T23:50:59Z","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":"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","authors_text":"Carlos Alberto Trujillo, David Fernando Daza, Fenando Andr\\'es Benavides","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2018-10-11T21:38:06Z","title":"Sidon sets and $C_4$-saturated graphs"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1810.05262","kind":"arxiv","version":6},"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:c807a3485617f03a5db053d0170d92198c286644ed0eb47818a90e8841f06c7d","target":"record","created_at":"2026-05-17T23:50:59Z","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":"5b2eba9cfebee0028490522942333cb1613f3a8ab03a61867b7d7af6ae3ca1cb","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2018-10-11T21:38:06Z","title_canon_sha256":"d07a135674c72b13bbaa13ed8e2eac377fd9cdc539a82364834408b17d5ca272"},"schema_version":"1.0","source":{"id":"1810.05262","kind":"arxiv","version":6}},"canonical_sha256":"962a677122daa3183170ed069be1687bef94a092b0fba3d2b47191014be177d0","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"962a677122daa3183170ed069be1687bef94a092b0fba3d2b47191014be177d0","first_computed_at":"2026-05-17T23:50:59.152559Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:50:59.152559Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"dZamIYK2A/VEM257nWTVX5uU7xioAkurImajFG0i69TS193VvhSclGaCFH4YmQyQazl7SXun7RlKbTvph2SMCg==","signature_status":"signed_v1","signed_at":"2026-05-17T23:50:59.153057Z","signed_message":"canonical_sha256_bytes"},"source_id":"1810.05262","source_kind":"arxiv","source_version":6}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:c807a3485617f03a5db053d0170d92198c286644ed0eb47818a90e8841f06c7d","sha256:2684460ac204900073be254beec03f2bf72c62421c86e393bd63f6996a6c2169"],"state_sha256":"60764de8bc23f783cb7a19c6321e0e77f8245f906b1f5a50609bd0b986b31340"}