{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2017:OH6DLLH6NFL6S63FPNL7NCDM4P","short_pith_number":"pith:OH6DLLH6","schema_version":"1.0","canonical_sha256":"71fc35acfe6957e97b657b57f6886ce3fa3f4201d49c5641faf6e4546d1b7a54","source":{"kind":"arxiv","id":"1702.00807","version":1},"attestation_state":"computed","paper":{"title":"Zero-sum invariants of finite abelian groups","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.NT"],"primary_cat":"math.CO","authors_text":"Guoqing Wang, Jiangtao Peng, Weidong Gao, Yuanlin Li","submitted_at":"2017-02-02T19:26:50Z","abstract_excerpt":"The purpose of the article is to provide an unified way to formulate zero-sum invariants. Let $G$ be a finite additive abelian group. Let $B(G)$ denote the set consisting of all nonempty zero-sum sequences over G. For\n  $\\Omega \\subset B(G$), let $d_{\\Omega}(G)$ be the smallest integer $t$ such that every sequence $S$ over $G$ of length $|S|\\geq t$ has a subsequence in $\\Omega$.We provide some first results and open problems on $d_{\\Omega}(G)$."},"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":"1702.00807","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2017-02-02T19:26:50Z","cross_cats_sorted":["math.NT"],"title_canon_sha256":"0e24f30401f644073b9e27618152feed56b25ea83d00951188170867773b8807","abstract_canon_sha256":"8927dd9fd9b92b8872afc807c9cd7e4274914aa77ef7a7f5018ad8dc5bf3b3c5"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:51:29.723984Z","signature_b64":"0buCOEYtBrafsrf58kyqY9VlCeqnR37LevGlQ/j4NtGNQ4JQ6N82F2TKxweAMdqDwKOXUI63/lsWiRhFTjirDw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"71fc35acfe6957e97b657b57f6886ce3fa3f4201d49c5641faf6e4546d1b7a54","last_reissued_at":"2026-05-18T00:51:29.723407Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:51:29.723407Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Zero-sum invariants of finite abelian groups","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.NT"],"primary_cat":"math.CO","authors_text":"Guoqing Wang, Jiangtao Peng, Weidong Gao, Yuanlin Li","submitted_at":"2017-02-02T19:26:50Z","abstract_excerpt":"The purpose of the article is to provide an unified way to formulate zero-sum invariants. Let $G$ be a finite additive abelian group. Let $B(G)$ denote the set consisting of all nonempty zero-sum sequences over G. For\n  $\\Omega \\subset B(G$), let $d_{\\Omega}(G)$ be the smallest integer $t$ such that every sequence $S$ over $G$ of length $|S|\\geq t$ has a subsequence in $\\Omega$.We provide some first results and open problems on $d_{\\Omega}(G)$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1702.00807","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":"1702.00807","created_at":"2026-05-18T00:51:29.723492+00:00"},{"alias_kind":"arxiv_version","alias_value":"1702.00807v1","created_at":"2026-05-18T00:51:29.723492+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1702.00807","created_at":"2026-05-18T00:51:29.723492+00:00"},{"alias_kind":"pith_short_12","alias_value":"OH6DLLH6NFL6","created_at":"2026-05-18T12:31:34.259226+00:00"},{"alias_kind":"pith_short_16","alias_value":"OH6DLLH6NFL6S63F","created_at":"2026-05-18T12:31:34.259226+00:00"},{"alias_kind":"pith_short_8","alias_value":"OH6DLLH6","created_at":"2026-05-18T12:31:34.259226+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/OH6DLLH6NFL6S63FPNL7NCDM4P","json":"https://pith.science/pith/OH6DLLH6NFL6S63FPNL7NCDM4P.json","graph_json":"https://pith.science/api/pith-number/OH6DLLH6NFL6S63FPNL7NCDM4P/graph.json","events_json":"https://pith.science/api/pith-number/OH6DLLH6NFL6S63FPNL7NCDM4P/events.json","paper":"https://pith.science/paper/OH6DLLH6"},"agent_actions":{"view_html":"https://pith.science/pith/OH6DLLH6NFL6S63FPNL7NCDM4P","download_json":"https://pith.science/pith/OH6DLLH6NFL6S63FPNL7NCDM4P.json","view_paper":"https://pith.science/paper/OH6DLLH6","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1702.00807&json=true","fetch_graph":"https://pith.science/api/pith-number/OH6DLLH6NFL6S63FPNL7NCDM4P/graph.json","fetch_events":"https://pith.science/api/pith-number/OH6DLLH6NFL6S63FPNL7NCDM4P/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/OH6DLLH6NFL6S63FPNL7NCDM4P/action/timestamp_anchor","attest_storage":"https://pith.science/pith/OH6DLLH6NFL6S63FPNL7NCDM4P/action/storage_attestation","attest_author":"https://pith.science/pith/OH6DLLH6NFL6S63FPNL7NCDM4P/action/author_attestation","sign_citation":"https://pith.science/pith/OH6DLLH6NFL6S63FPNL7NCDM4P/action/citation_signature","submit_replication":"https://pith.science/pith/OH6DLLH6NFL6S63FPNL7NCDM4P/action/replication_record"}},"created_at":"2026-05-18T00:51:29.723492+00:00","updated_at":"2026-05-18T00:51:29.723492+00:00"}