{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:BQZIQA6NCUWQSGW3NN5B5B3Y7G","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":"9fc5eb65649be6a50341e3a4123ce81a11f50ad165063aeca9c8aa4399105924","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2017-12-26T10:13:01Z","title_canon_sha256":"9575324ef04c5deed026559a97bbc860225048390e713087dc20c5b269f62323"},"schema_version":"1.0","source":{"id":"1712.09226","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1712.09226","created_at":"2026-05-18T00:27:14Z"},{"alias_kind":"arxiv_version","alias_value":"1712.09226v1","created_at":"2026-05-18T00:27:14Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1712.09226","created_at":"2026-05-18T00:27:14Z"},{"alias_kind":"pith_short_12","alias_value":"BQZIQA6NCUWQ","created_at":"2026-05-18T12:31:08Z"},{"alias_kind":"pith_short_16","alias_value":"BQZIQA6NCUWQSGW3","created_at":"2026-05-18T12:31:08Z"},{"alias_kind":"pith_short_8","alias_value":"BQZIQA6N","created_at":"2026-05-18T12:31:08Z"}],"graph_snapshots":[{"event_id":"sha256:5fe8d96f463b226970610cff557c201f9e8070193b0a75f3beda16131359910f","target":"graph","created_at":"2026-05-18T00:27:14Z","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 $A$ be a nonempty finite subset of an additive abelian group $G$. Define $A + A := \\{a + b : a, b \\in A\\}$ and $A \\dotplus A := \\{a + b : a, b \\in A~\\text{and}~ a \\neq b\\}$. The set $A$ is called a {\\em sum-dominant (SD) set} if $|A + A| > |A - A|$, and it is called a {\\em restricted sum-domonant (RSD) set} if $|A \\dotplus A| > |A - A|$. In this paper, we prove that for infinitely many positive integers $k$, there are infinitely many RSD sets of integers of cardinality $k$. We also provide an explicit construction of infinite sequence of RSD sets.","authors_text":"Raj Kumar Mistri, R. Thangadurai","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2017-12-26T10:13:01Z","title":"Restricted-sum-dominant sets"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1712.09226","kind":"arxiv","version":1},"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":"sha256:94f87ab8c0e555042da8f7baa407be646fe428b7e444feda48c6269f9184bd8e","target":"record","created_at":"2026-05-18T00:27:14Z","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":"9fc5eb65649be6a50341e3a4123ce81a11f50ad165063aeca9c8aa4399105924","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2017-12-26T10:13:01Z","title_canon_sha256":"9575324ef04c5deed026559a97bbc860225048390e713087dc20c5b269f62323"},"schema_version":"1.0","source":{"id":"1712.09226","kind":"arxiv","version":1}},"canonical_sha256":"0c328803cd152d091adb6b7a1e8778f9b6465d74f401da95d7f69634fddb7876","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"0c328803cd152d091adb6b7a1e8778f9b6465d74f401da95d7f69634fddb7876","first_computed_at":"2026-05-18T00:27:14.160463Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:27:14.160463Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"/sIS1XKqgftPGOJLjq3C6xjVgzcYiMIVGX5P7L6bEOkrhKAyR88d6Nh1pxJM+NKI4OyiSIIyq5su2juiUnLeBQ==","signature_status":"signed_v1","signed_at":"2026-05-18T00:27:14.161076Z","signed_message":"canonical_sha256_bytes"},"source_id":"1712.09226","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:94f87ab8c0e555042da8f7baa407be646fe428b7e444feda48c6269f9184bd8e","sha256:5fe8d96f463b226970610cff557c201f9e8070193b0a75f3beda16131359910f"],"state_sha256":"105647f32db62270f29c391f62b8cb4aac05330ab5159298e643a2bea94a97ed"}