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We confirm a conjecture of these authors that for $k$ and $t$ such that this divisibility condition holds, every zero-sum seque"},"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":"1608.04125","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2016-08-14T19:13:06Z","cross_cats_sorted":["math.CO"],"title_canon_sha256":"a32f6de34a5c38c8948729f32d8ddf84999b3cf4ac3e17617cd55cfe552ad9fb","abstract_canon_sha256":"0b0d17c6ba166174a147c04587e24890763ce799dca130ec2fba547d74cfd1bc"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:07:28.565045Z","signature_b64":"ujZuqTwDwk2unl8RdnSkuLVK+Mu+wE3Rl4dF6Q24SuN4NP8FYXnmU2ZxnC97fdtExkB93ZiwcfT6dDKstUIdDQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"aaa0dfcf06046ee5b26ff7753c0d264060198ebf9c660666d77ee755c60819e6","last_reissued_at":"2026-05-18T00:07:28.564417Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:07:28.564417Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"An Analogue of the Erd\\H{o}s-Ginzburg-Ziv Theorem over $\\mathbb Z$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CO"],"primary_cat":"math.NT","authors_text":"Aaron Berger","submitted_at":"2016-08-14T19:13:06Z","abstract_excerpt":"Let $\\mathcal S$ be a multiset of integers. 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