{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2023:Y6RGKDOGVAMHIGZDRGUYMPDGRX","short_pith_number":"pith:Y6RGKDOG","schema_version":"1.0","canonical_sha256":"c7a2650dc6a818741b2389a9863c668de62a6d66bc3d50f656b8dcf0e80098de","source":{"kind":"arxiv","id":"2310.20032","version":1},"attestation_state":"computed","paper":{"title":"On the Diameter of Finite Sidon Sets","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Daniel Carter, Kevin O'Bryant, Zach Hunter","submitted_at":"2023-10-30T21:33:06Z","abstract_excerpt":"We prove that the diameter of a Sidon set (also known as a Babcock sequence, Golomb ruler, or $B_2$ set) with $k$ elements is at least $k^2-b k^{3/2}-O(k)$ where $b\\le 1.96365$, a comparatively large improvement on past results. Equivalently, a Sidon set with diameter $n$ has at most $n^{1/2}+0.98183n^{1/4}+O(1)$ elements. The proof is conceptually simple but very computationally intensive, and the proof uses substantial computer assistance. We also provide a proof of $b\\le 1.99058$ that can be verified by hand, which still improves on past results. Finally, we prove that $g$-thin Sidon sets ("},"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":"2310.20032","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.CO","submitted_at":"2023-10-30T21:33:06Z","cross_cats_sorted":[],"title_canon_sha256":"e8bab7c3e5bc654f3ff0360e8892fb34292d1854850968a09869eefe70c86a89","abstract_canon_sha256":"616c5acca0afaa7b85419054bae36d50b0e95ecd4c950093865dd91c68224529"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T07:07:22.889506Z","signature_b64":"kq5R4QL8HwCoAf0nzGdJ5S/ZLhSn4KAmGc7UcMdOmDDVR8pn7AG3UI+gsooD+mjoZ5knBpx9vWatLNpYsWhaCA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"c7a2650dc6a818741b2389a9863c668de62a6d66bc3d50f656b8dcf0e80098de","last_reissued_at":"2026-07-05T07:07:22.889041Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T07:07:22.889041Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"On the Diameter of Finite Sidon Sets","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Daniel Carter, Kevin O'Bryant, Zach Hunter","submitted_at":"2023-10-30T21:33:06Z","abstract_excerpt":"We prove that the diameter of a Sidon set (also known as a Babcock sequence, Golomb ruler, or $B_2$ set) with $k$ elements is at least $k^2-b k^{3/2}-O(k)$ where $b\\le 1.96365$, a comparatively large improvement on past results. Equivalently, a Sidon set with diameter $n$ has at most $n^{1/2}+0.98183n^{1/4}+O(1)$ elements. The proof is conceptually simple but very computationally intensive, and the proof uses substantial computer assistance. We also provide a proof of $b\\le 1.99058$ that can be verified by hand, which still improves on past results. Finally, we prove that $g$-thin Sidon sets ("},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2310.20032","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/2310.20032/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":"2310.20032","created_at":"2026-07-05T07:07:22.889094+00:00"},{"alias_kind":"arxiv_version","alias_value":"2310.20032v1","created_at":"2026-07-05T07:07:22.889094+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2310.20032","created_at":"2026-07-05T07:07:22.889094+00:00"},{"alias_kind":"pith_short_12","alias_value":"Y6RGKDOGVAMH","created_at":"2026-07-05T07:07:22.889094+00:00"},{"alias_kind":"pith_short_16","alias_value":"Y6RGKDOGVAMHIGZD","created_at":"2026-07-05T07:07:22.889094+00:00"},{"alias_kind":"pith_short_8","alias_value":"Y6RGKDOG","created_at":"2026-07-05T07:07:22.889094+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":10,"is_internal_anchor":true}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/Y6RGKDOGVAMHIGZDRGUYMPDGRX","json":"https://pith.science/pith/Y6RGKDOGVAMHIGZDRGUYMPDGRX.json","graph_json":"https://pith.science/api/pith-number/Y6RGKDOGVAMHIGZDRGUYMPDGRX/graph.json","events_json":"https://pith.science/api/pith-number/Y6RGKDOGVAMHIGZDRGUYMPDGRX/events.json","paper":"https://pith.science/paper/Y6RGKDOG"},"agent_actions":{"view_html":"https://pith.science/pith/Y6RGKDOGVAMHIGZDRGUYMPDGRX","download_json":"https://pith.science/pith/Y6RGKDOGVAMHIGZDRGUYMPDGRX.json","view_paper":"https://pith.science/paper/Y6RGKDOG","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2310.20032&json=true","fetch_graph":"https://pith.science/api/pith-number/Y6RGKDOGVAMHIGZDRGUYMPDGRX/graph.json","fetch_events":"https://pith.science/api/pith-number/Y6RGKDOGVAMHIGZDRGUYMPDGRX/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/Y6RGKDOGVAMHIGZDRGUYMPDGRX/action/timestamp_anchor","attest_storage":"https://pith.science/pith/Y6RGKDOGVAMHIGZDRGUYMPDGRX/action/storage_attestation","attest_author":"https://pith.science/pith/Y6RGKDOGVAMHIGZDRGUYMPDGRX/action/author_attestation","sign_citation":"https://pith.science/pith/Y6RGKDOGVAMHIGZDRGUYMPDGRX/action/citation_signature","submit_replication":"https://pith.science/pith/Y6RGKDOGVAMHIGZDRGUYMPDGRX/action/replication_record"}},"created_at":"2026-07-05T07:07:22.889094+00:00","updated_at":"2026-07-05T07:07:22.889094+00:00"}