{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2016:667XYCHTQH3QJZTVT46MUUZH3N","short_pith_number":"pith:667XYCHT","schema_version":"1.0","canonical_sha256":"f7bf7c08f381f704e6759f3cca5327db561fbbfde26b1bab172cd0b4a3e23a05","source":{"kind":"arxiv","id":"1603.03068","version":5},"attestation_state":"computed","paper":{"title":"Sum-avoiding sets in groups","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Terence Tao, Van Vu","submitted_at":"2016-03-09T21:43:24Z","abstract_excerpt":"Let $A$ be a finite subset of an arbitrary additive group $G$, and let $\\phi(A)$ denote the cardinality of the largest subset $B$ in $A$ that is sum-avoiding in $A$ (that is to say, $b_1+b_2 \\not \\in A$ for all distinct $b_1,b_2 \\in B$). The question of controlling the size of $A$ in terms of $\\phi(A)$ in the case when $G$ was torsion-free was posed by Erd\\H{o}s and Moser. When $G$ has torsion, $A$ can be arbitrarily large for fixed $\\phi(A)$ due to the presence of subgroups. Nevertheless, we provide a qualitative answer to an analogue of the Erd\\H{o}s-Moser problem in this setting, by establi"},"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":"1603.03068","kind":"arxiv","version":5},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.CO","submitted_at":"2016-03-09T21:43:24Z","cross_cats_sorted":[],"title_canon_sha256":"5fc0596db6a051f68173d7d0cc862267e0133d40e8bcbc956649640f01e3d22e","abstract_canon_sha256":"40a7e497ef6141c9358ac51dd594778153d4994208386392be4efae4e90634cb"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:52:41.800981Z","signature_b64":"IP/UuX63DGREd5jdALGQxWVliy8U7SU3KfWFI/MaqrOjV9lMOKcS2fTJnkHEEAG2XcIw2/sHiFxr5GPr/0c3DQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"f7bf7c08f381f704e6759f3cca5327db561fbbfde26b1bab172cd0b4a3e23a05","last_reissued_at":"2026-05-18T00:52:41.800499Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:52:41.800499Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Sum-avoiding sets in groups","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Terence Tao, Van Vu","submitted_at":"2016-03-09T21:43:24Z","abstract_excerpt":"Let $A$ be a finite subset of an arbitrary additive group $G$, and let $\\phi(A)$ denote the cardinality of the largest subset $B$ in $A$ that is sum-avoiding in $A$ (that is to say, $b_1+b_2 \\not \\in A$ for all distinct $b_1,b_2 \\in B$). The question of controlling the size of $A$ in terms of $\\phi(A)$ in the case when $G$ was torsion-free was posed by Erd\\H{o}s and Moser. When $G$ has torsion, $A$ can be arbitrarily large for fixed $\\phi(A)$ due to the presence of subgroups. Nevertheless, we provide a qualitative answer to an analogue of the Erd\\H{o}s-Moser problem in this setting, by establi"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1603.03068","kind":"arxiv","version":5},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"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":"1603.03068","created_at":"2026-05-18T00:52:41.800574+00:00"},{"alias_kind":"arxiv_version","alias_value":"1603.03068v5","created_at":"2026-05-18T00:52:41.800574+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1603.03068","created_at":"2026-05-18T00:52:41.800574+00:00"},{"alias_kind":"pith_short_12","alias_value":"667XYCHTQH3Q","created_at":"2026-05-18T12:30:01.593930+00:00"},{"alias_kind":"pith_short_16","alias_value":"667XYCHTQH3QJZTV","created_at":"2026-05-18T12:30:01.593930+00:00"},{"alias_kind":"pith_short_8","alias_value":"667XYCHT","created_at":"2026-05-18T12:30:01.593930+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/667XYCHTQH3QJZTVT46MUUZH3N","json":"https://pith.science/pith/667XYCHTQH3QJZTVT46MUUZH3N.json","graph_json":"https://pith.science/api/pith-number/667XYCHTQH3QJZTVT46MUUZH3N/graph.json","events_json":"https://pith.science/api/pith-number/667XYCHTQH3QJZTVT46MUUZH3N/events.json","paper":"https://pith.science/paper/667XYCHT"},"agent_actions":{"view_html":"https://pith.science/pith/667XYCHTQH3QJZTVT46MUUZH3N","download_json":"https://pith.science/pith/667XYCHTQH3QJZTVT46MUUZH3N.json","view_paper":"https://pith.science/paper/667XYCHT","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1603.03068&json=true","fetch_graph":"https://pith.science/api/pith-number/667XYCHTQH3QJZTVT46MUUZH3N/graph.json","fetch_events":"https://pith.science/api/pith-number/667XYCHTQH3QJZTVT46MUUZH3N/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/667XYCHTQH3QJZTVT46MUUZH3N/action/timestamp_anchor","attest_storage":"https://pith.science/pith/667XYCHTQH3QJZTVT46MUUZH3N/action/storage_attestation","attest_author":"https://pith.science/pith/667XYCHTQH3QJZTVT46MUUZH3N/action/author_attestation","sign_citation":"https://pith.science/pith/667XYCHTQH3QJZTVT46MUUZH3N/action/citation_signature","submit_replication":"https://pith.science/pith/667XYCHTQH3QJZTVT46MUUZH3N/action/replication_record"}},"created_at":"2026-05-18T00:52:41.800574+00:00","updated_at":"2026-05-18T00:52:41.800574+00:00"}