{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:SOBFS4WJQIZ23UNY4GSNUO232K","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":"3282218e86c3ef1d0c14398dcab2365889c93969c9e0a2d6587ad16b1481b2f7","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2015-04-28T10:17:59Z","title_canon_sha256":"2a6c825263abd2725091918c7404dd46d9f403add70720e64fdb47d116e2d644"},"schema_version":"1.0","source":{"id":"1504.07411","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1504.07411","created_at":"2026-05-18T01:36:47Z"},{"alias_kind":"arxiv_version","alias_value":"1504.07411v2","created_at":"2026-05-18T01:36:47Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1504.07411","created_at":"2026-05-18T01:36:47Z"},{"alias_kind":"pith_short_12","alias_value":"SOBFS4WJQIZ2","created_at":"2026-05-18T12:29:42Z"},{"alias_kind":"pith_short_16","alias_value":"SOBFS4WJQIZ23UNY","created_at":"2026-05-18T12:29:42Z"},{"alias_kind":"pith_short_8","alias_value":"SOBFS4WJ","created_at":"2026-05-18T12:29:42Z"}],"graph_snapshots":[{"event_id":"sha256:db5b92c850eabecb0c707f6e0147a8f5a480e95f0665a4b6d927f7d7f29ee363","target":"graph","created_at":"2026-05-18T01:36:47Z","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":"Let $A$ and $B$ be sets of nonnegative integers. For a positive integer $n$ let $R_{A}(n)$ denote the number of representations of $n$ as the sum of two terms from $A$. Let $\\displaystyle s_{A}(x) = \\max_{n \\le x}R_{A}(n)$ and $\\displaystyle d_{A,B}(x) = \\max_{\\hbox{t: $a_{t} \\le x$ or $b_{t} \\le x$}}|a_{t} - b_{t}|$. In this paper we study the connection between $s_{A}(x)$, $s_{B}(x)$ and $d_{A,B}(x)$. We improve a result of Haddad and Helou about the Erd\\H{o}s - Tur\\'an conjecture.","authors_text":"Csaba S\\'andor, S\\'andor Z. Kiss","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2015-04-28T10:17:59Z","title":"On the maximum values of the additive representation functions"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1504.07411","kind":"arxiv","version":2},"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":"sha256:5b42fad8e65726498e6948511a99f49800d612b076a4a8132e51da26b7878099","target":"record","created_at":"2026-05-18T01:36:47Z","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":"3282218e86c3ef1d0c14398dcab2365889c93969c9e0a2d6587ad16b1481b2f7","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2015-04-28T10:17:59Z","title_canon_sha256":"2a6c825263abd2725091918c7404dd46d9f403add70720e64fdb47d116e2d644"},"schema_version":"1.0","source":{"id":"1504.07411","kind":"arxiv","version":2}},"canonical_sha256":"93825972c98233add1b8e1a4da3b5bd283e46e0775c3ecd3d074ed94eb3cefb6","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"93825972c98233add1b8e1a4da3b5bd283e46e0775c3ecd3d074ed94eb3cefb6","first_computed_at":"2026-05-18T01:36:47.855766Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:36:47.855766Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"pJgJDIkzWRaDOOVbQEc/DdFCNI3AGIRX1hX6PUr51kOfAvp2ksQhzw8h7IEm1p7Gn0rHlvCjWo0LxmQxkYkXDQ==","signature_status":"signed_v1","signed_at":"2026-05-18T01:36:47.856437Z","signed_message":"canonical_sha256_bytes"},"source_id":"1504.07411","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:5b42fad8e65726498e6948511a99f49800d612b076a4a8132e51da26b7878099","sha256:db5b92c850eabecb0c707f6e0147a8f5a480e95f0665a4b6d927f7d7f29ee363"],"state_sha256":"a4645ac9dd0535f08faf1f150bb7ed55d2a1aaba170b801638f8415c5629d458"}