{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:Q64HUXC74YFB5X3GUN5GMPKBB3","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":"36213c696249ec74b1e6d157dfbad093986732f20c5b916685b7da3285ced347","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2016-08-10T18:54:38Z","title_canon_sha256":"58672155ab61ab1ebf33085ff8ea87bac17c9d5a4d19fc8d3740647273b48616"},"schema_version":"1.0","source":{"id":"1608.03256","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1608.03256","created_at":"2026-05-18T00:07:33Z"},{"alias_kind":"arxiv_version","alias_value":"1608.03256v3","created_at":"2026-05-18T00:07:33Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1608.03256","created_at":"2026-05-18T00:07:33Z"},{"alias_kind":"pith_short_12","alias_value":"Q64HUXC74YFB","created_at":"2026-05-18T12:30:39Z"},{"alias_kind":"pith_short_16","alias_value":"Q64HUXC74YFB5X3G","created_at":"2026-05-18T12:30:39Z"},{"alias_kind":"pith_short_8","alias_value":"Q64HUXC7","created_at":"2026-05-18T12:30:39Z"}],"graph_snapshots":[{"event_id":"sha256:1167fc30b31fa1b57fdde29a40056b3a0b1f894269c4de0b8cbe78102a308d6c","target":"graph","created_at":"2026-05-18T00:07:33Z","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":"A finite set of integers $A$ is a sum-dominant (also called an More Sums Than Differences or MSTD) set if $|A+A| > |A-A|$. While almost all subsets of $\\{0, \\dots, n\\}$ are not sum-dominant, interestingly a small positive percentage are. We explore sufficient conditions on infinite sets of positive integers such that there are either no sum-dominant subsets, at most finitely many sum-dominant subsets, or infinitely many sum-dominant subsets. In particular, we prove no subset of the Fibonacci numbers is a sum-dominant set, establish conditions such that solutions to a recurrence relation have o","authors_text":"Hung Chu, Nathan McNew, Sean Zhang, Steven J. Miller, Victor Xu","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2016-08-10T18:54:38Z","title":"When Sets Can and Cannot Have MSTD Subsets"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1608.03256","kind":"arxiv","version":3},"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":"sha256:2f1769756531a5f6b3135dcd66f681e97197c0bd9d8c992659769e42dcdc8fbe","target":"record","created_at":"2026-05-18T00:07:33Z","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":"36213c696249ec74b1e6d157dfbad093986732f20c5b916685b7da3285ced347","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2016-08-10T18:54:38Z","title_canon_sha256":"58672155ab61ab1ebf33085ff8ea87bac17c9d5a4d19fc8d3740647273b48616"},"schema_version":"1.0","source":{"id":"1608.03256","kind":"arxiv","version":3}},"canonical_sha256":"87b87a5c5fe60a1edf66a37a663d410ecd7c919cf4078d94abf9b12a174f4cbf","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"87b87a5c5fe60a1edf66a37a663d410ecd7c919cf4078d94abf9b12a174f4cbf","first_computed_at":"2026-05-18T00:07:33.304050Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:07:33.304050Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"3rrf8O9gryjsN/j6309xrY//74EfP4sN5n8L2kuY8puGDCYStpGm0aT9fRoGZVR/WOLeYJfbI+qh2dOJxFdJDA==","signature_status":"signed_v1","signed_at":"2026-05-18T00:07:33.304727Z","signed_message":"canonical_sha256_bytes"},"source_id":"1608.03256","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:2f1769756531a5f6b3135dcd66f681e97197c0bd9d8c992659769e42dcdc8fbe","sha256:1167fc30b31fa1b57fdde29a40056b3a0b1f894269c4de0b8cbe78102a308d6c"],"state_sha256":"f9fa2bf475124da262ad27bc977da172eb409625be23e4fbd7844e2c7fd87808"}