{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2015:LB7H4BRDFXBZMH4L4LFSVFIIXJ","short_pith_number":"pith:LB7H4BRD","schema_version":"1.0","canonical_sha256":"587e7e06232dc3961f8be2cb2a9508ba7199bf388d6bcd320e3e4ac42474b304","source":{"kind":"arxiv","id":"1512.03037","version":1},"attestation_state":"computed","paper":{"title":"The independence number of a subset of an abelian group","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"B\\'ela Bajnok, Imre Ruzsa","submitted_at":"2015-12-09T20:39:58Z","abstract_excerpt":"We call a subset $A$ of the (additive) abelian group $G$ {\\it $t$-independent} if for all non-negative integers $h$ and $k$ with $h+k \\leq t$, the sum of $h$ (not necessarily distinct) elements of $A$ does not equal the sum of $k$ (not necessarily distinct) elements of $A$ unless $h=k$ and the two sums contain the same terms in some order. A {\\it weakly $t$-independent} set satisfies this property for sums of distinct terms. We give some exact values and asymptotic bounds for the size of a largest $t$-independent set and weakly $t$-independent set in abelian groups, particularly in the cyclic "},"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":"1512.03037","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2015-12-09T20:39:58Z","cross_cats_sorted":[],"title_canon_sha256":"83180dcceeb641bd7d0e321c56e2d33ff5f43acaf10346e6a6f6b14b154ad83b","abstract_canon_sha256":"682452383014806fb2bcf5853e2aadab3c2dffcfc2b7660f9c03cbcef953ecf5"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:24:38.990670Z","signature_b64":"Bq8ptzJyF9MgE1yevjHfXFDjPu5XigKYA30r9Z5MCWtlMnj7bplNl4zv49p2R4zBkBhOgp8dpduJoiSK/cJrBQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"587e7e06232dc3961f8be2cb2a9508ba7199bf388d6bcd320e3e4ac42474b304","last_reissued_at":"2026-05-18T01:24:38.990270Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:24:38.990270Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"The independence number of a subset of an abelian group","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"B\\'ela Bajnok, Imre Ruzsa","submitted_at":"2015-12-09T20:39:58Z","abstract_excerpt":"We call a subset $A$ of the (additive) abelian group $G$ {\\it $t$-independent} if for all non-negative integers $h$ and $k$ with $h+k \\leq t$, the sum of $h$ (not necessarily distinct) elements of $A$ does not equal the sum of $k$ (not necessarily distinct) elements of $A$ unless $h=k$ and the two sums contain the same terms in some order. A {\\it weakly $t$-independent} set satisfies this property for sums of distinct terms. We give some exact values and asymptotic bounds for the size of a largest $t$-independent set and weakly $t$-independent set in abelian groups, particularly in the cyclic "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1512.03037","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":""},"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":"1512.03037","created_at":"2026-05-18T01:24:38.990342+00:00"},{"alias_kind":"arxiv_version","alias_value":"1512.03037v1","created_at":"2026-05-18T01:24:38.990342+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1512.03037","created_at":"2026-05-18T01:24:38.990342+00:00"},{"alias_kind":"pith_short_12","alias_value":"LB7H4BRDFXBZ","created_at":"2026-05-18T12:29:29.992203+00:00"},{"alias_kind":"pith_short_16","alias_value":"LB7H4BRDFXBZMH4L","created_at":"2026-05-18T12:29:29.992203+00:00"},{"alias_kind":"pith_short_8","alias_value":"LB7H4BRD","created_at":"2026-05-18T12:29:29.992203+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/LB7H4BRDFXBZMH4L4LFSVFIIXJ","json":"https://pith.science/pith/LB7H4BRDFXBZMH4L4LFSVFIIXJ.json","graph_json":"https://pith.science/api/pith-number/LB7H4BRDFXBZMH4L4LFSVFIIXJ/graph.json","events_json":"https://pith.science/api/pith-number/LB7H4BRDFXBZMH4L4LFSVFIIXJ/events.json","paper":"https://pith.science/paper/LB7H4BRD"},"agent_actions":{"view_html":"https://pith.science/pith/LB7H4BRDFXBZMH4L4LFSVFIIXJ","download_json":"https://pith.science/pith/LB7H4BRDFXBZMH4L4LFSVFIIXJ.json","view_paper":"https://pith.science/paper/LB7H4BRD","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1512.03037&json=true","fetch_graph":"https://pith.science/api/pith-number/LB7H4BRDFXBZMH4L4LFSVFIIXJ/graph.json","fetch_events":"https://pith.science/api/pith-number/LB7H4BRDFXBZMH4L4LFSVFIIXJ/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/LB7H4BRDFXBZMH4L4LFSVFIIXJ/action/timestamp_anchor","attest_storage":"https://pith.science/pith/LB7H4BRDFXBZMH4L4LFSVFIIXJ/action/storage_attestation","attest_author":"https://pith.science/pith/LB7H4BRDFXBZMH4L4LFSVFIIXJ/action/author_attestation","sign_citation":"https://pith.science/pith/LB7H4BRDFXBZMH4L4LFSVFIIXJ/action/citation_signature","submit_replication":"https://pith.science/pith/LB7H4BRDFXBZMH4L4LFSVFIIXJ/action/replication_record"}},"created_at":"2026-05-18T01:24:38.990342+00:00","updated_at":"2026-05-18T01:24:38.990342+00:00"}