{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2019:WEA6ZO2TH4T44X5IOIVEVVHMR6","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":"c41a042a7c0b1683be592a80493fc8fb49d627bbb85057668457ca09fbd4dfe9","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2019-07-25T21:12:21Z","title_canon_sha256":"47b55a3487293206b8bdadafff61c1e00833e1184a7ac1f713b0dfb4634ecf4e"},"schema_version":"1.0","source":{"id":"1907.11236","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1907.11236","created_at":"2026-05-17T23:39:29Z"},{"alias_kind":"arxiv_version","alias_value":"1907.11236v1","created_at":"2026-05-17T23:39:29Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1907.11236","created_at":"2026-05-17T23:39:29Z"},{"alias_kind":"pith_short_12","alias_value":"WEA6ZO2TH4T4","created_at":"2026-05-18T12:33:30Z"},{"alias_kind":"pith_short_16","alias_value":"WEA6ZO2TH4T44X5I","created_at":"2026-05-18T12:33:30Z"},{"alias_kind":"pith_short_8","alias_value":"WEA6ZO2T","created_at":"2026-05-18T12:33:30Z"}],"graph_snapshots":[{"event_id":"sha256:34311f3a5fccdf8339d9d82afa7bb5bd123c624cae3d67956e4ff9d3825f82a7","target":"graph","created_at":"2026-05-17T23:39:29Z","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":"For an abelian group $G$ and an integer $t > 0$, the modified Erd\\H{o}s-Ginzburg-Ziv constant $s'_t(G)$ is the smallest integer $\\ell$ such that any zero-sum sequence of length at least $\\ell$ with elements in $G$ contains a zero-sum subsequence (not necessarily consecutive) of length $t$. We compute bounds for $s'_{t}(G)$ for $G = \\left(\\mathbb{Z}/n\\mathbb{Z}\\right)^2$ and $G = \\left(\\mathbb{Z}/n_1\\mathbb{Z} \\times \\mathbb{Z}/n_2\\mathbb{Z}\\right)$. We also compute bounds for $G = \\left(\\mathbb{Z}/p\\mathbb{Z}\\right)^d$ where the subsequence can be any length in $\\{p, \\dots, (d-1)p\\}$. Lastly, ","authors_text":"Trajan Hammonds","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2019-07-25T21:12:21Z","title":"Modified Erd\\H{o}s-Ginzburg-Ziv Constants for $(\\mathbb{Z}/n\\mathbb{Z})^2$"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1907.11236","kind":"arxiv","version":1},"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":"sha256:50928ac5523fe19e68a4c28e5e0915165df1bdff2f5b02f83e7bed8ac19d7cbb","target":"record","created_at":"2026-05-17T23:39:29Z","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":"c41a042a7c0b1683be592a80493fc8fb49d627bbb85057668457ca09fbd4dfe9","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2019-07-25T21:12:21Z","title_canon_sha256":"47b55a3487293206b8bdadafff61c1e00833e1184a7ac1f713b0dfb4634ecf4e"},"schema_version":"1.0","source":{"id":"1907.11236","kind":"arxiv","version":1}},"canonical_sha256":"b101ecbb533f27ce5fa8722a4ad4ec8fabab0f02e5f37356351c3473970f1939","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"b101ecbb533f27ce5fa8722a4ad4ec8fabab0f02e5f37356351c3473970f1939","first_computed_at":"2026-05-17T23:39:29.731455Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:39:29.731455Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"nYJ8r3CFJBLEvcc7cGVCXQyciJp71MoDzP7hUItcfubczNCtNJBN28KMPQhKdDNPSymiKMxpbMKbC3UfuxIsCQ==","signature_status":"signed_v1","signed_at":"2026-05-17T23:39:29.731969Z","signed_message":"canonical_sha256_bytes"},"source_id":"1907.11236","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:50928ac5523fe19e68a4c28e5e0915165df1bdff2f5b02f83e7bed8ac19d7cbb","sha256:34311f3a5fccdf8339d9d82afa7bb5bd123c624cae3d67956e4ff9d3825f82a7"],"state_sha256":"1a3787faca6d2f9ab59fba3e9a5af9c54cc3e81b76835ba91c8f75044c4b2427"}