{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:VKQN7TYGARXOLMTP652TYDJGIB","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":"0b0d17c6ba166174a147c04587e24890763ce799dca130ec2fba547d74cfd1bc","cross_cats_sorted":["math.CO"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2016-08-14T19:13:06Z","title_canon_sha256":"a32f6de34a5c38c8948729f32d8ddf84999b3cf4ac3e17617cd55cfe552ad9fb"},"schema_version":"1.0","source":{"id":"1608.04125","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1608.04125","created_at":"2026-05-18T00:07:28Z"},{"alias_kind":"arxiv_version","alias_value":"1608.04125v3","created_at":"2026-05-18T00:07:28Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1608.04125","created_at":"2026-05-18T00:07:28Z"},{"alias_kind":"pith_short_12","alias_value":"VKQN7TYGARXO","created_at":"2026-05-18T12:30:48Z"},{"alias_kind":"pith_short_16","alias_value":"VKQN7TYGARXOLMTP","created_at":"2026-05-18T12:30:48Z"},{"alias_kind":"pith_short_8","alias_value":"VKQN7TYG","created_at":"2026-05-18T12:30:48Z"}],"graph_snapshots":[{"event_id":"sha256:9daaf4eb45f0277fd525495681a4e79f4e36047b8336250a64818ac13f7715b8","target":"graph","created_at":"2026-05-18T00:07:28Z","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 $\\mathcal S$ be a multiset of integers. We say $\\mathcal S$ is a $\\textit{zero-sum sequence}$ if the sum of its elements is 0. We study zero-sum sequences whose elements lie in the interval $[-k,k]$ such that no subsequence of length $t$ is also zero-sum. Given these restrictions, Augspurger, Minter, Shoukry, Sissokho, Voss show that there are arbitrarily long $t$-avoiding, $k$-bounded zero-sum sequences unless $t$ is divisible by $\\mathrm{LCM}(2,3,4,\\dots,2k-1)$. We confirm a conjecture of these authors that for $k$ and $t$ such that this divisibility condition holds, every zero-sum seque","authors_text":"Aaron Berger","cross_cats":["math.CO"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2016-08-14T19:13:06Z","title":"An Analogue of the Erd\\H{o}s-Ginzburg-Ziv Theorem over $\\mathbb Z$"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1608.04125","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":"sha256:47453b547f23ce2186922e81b2626b529de85835980f6b32710448cc801c4c29","target":"record","created_at":"2026-05-18T00:07:28Z","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":"0b0d17c6ba166174a147c04587e24890763ce799dca130ec2fba547d74cfd1bc","cross_cats_sorted":["math.CO"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2016-08-14T19:13:06Z","title_canon_sha256":"a32f6de34a5c38c8948729f32d8ddf84999b3cf4ac3e17617cd55cfe552ad9fb"},"schema_version":"1.0","source":{"id":"1608.04125","kind":"arxiv","version":3}},"canonical_sha256":"aaa0dfcf06046ee5b26ff7753c0d264060198ebf9c660666d77ee755c60819e6","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"aaa0dfcf06046ee5b26ff7753c0d264060198ebf9c660666d77ee755c60819e6","first_computed_at":"2026-05-18T00:07:28.564417Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:07:28.564417Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"ujZuqTwDwk2unl8RdnSkuLVK+Mu+wE3Rl4dF6Q24SuN4NP8FYXnmU2ZxnC97fdtExkB93ZiwcfT6dDKstUIdDQ==","signature_status":"signed_v1","signed_at":"2026-05-18T00:07:28.565045Z","signed_message":"canonical_sha256_bytes"},"source_id":"1608.04125","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:47453b547f23ce2186922e81b2626b529de85835980f6b32710448cc801c4c29","sha256:9daaf4eb45f0277fd525495681a4e79f4e36047b8336250a64818ac13f7715b8"],"state_sha256":"2d6f5f9d7d09475f13ba3f05224a61b83b5ad9d057ee54a9ae63523a2c4280fe"}