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It is a starting point of zero-sum theory but only has a trivial lower bound $\\mathsf D^*(G) = n_1 + \\cdots + n_r - r + 1$, which equals $\\mathsf D(G)$ over $p$-groups. We investigate the non-dispersive sequences over group $C_n^r$, thereby revealing the growth of $\\mathsf D(G)-\\mathsf D^*(G)$ over non-$p$-groups $G = C_n^r \\oplus "},"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":"1810.08346","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2018-10-19T03:30:49Z","cross_cats_sorted":["math.NT"],"title_canon_sha256":"4f62b56eb22dafbd13fdeb85496e92973a1d09ab8ed32eb8feb412560eda55bb","abstract_canon_sha256":"fdc813fd4e5a81e80aa0668f0fee697d22b508bd070cf89acf0585fb3399659b"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T03:16:41.089145Z","signature_b64":"M/PAtTvDLhNQFiNlNi2ROF0DzdTwZkuXYWBWlhXv6BZ/C6djOWz+fMwhbq2wgT0DIBg7o3M+r+hit9iRafPpBQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"60b4a9f845f8fa4c1902193210d318c06c4549649c8d734758c0d896c5c41eaa","last_reissued_at":"2026-07-05T03:16:41.088737Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T03:16:41.088737Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"On the lower bounds of Davenport constant","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.NT"],"primary_cat":"math.CO","authors_text":"Chao Liu","submitted_at":"2018-10-19T03:30:49Z","abstract_excerpt":"Let $G = C_{n_1} \\oplus \\cdots \\oplus C_{n_r}$ with $1 < n_1 | \\cdots | n_r$ be a finite abelian group. The Davenport constant $\\mathsf D(G)$ is the smallest integer $t$ such that every sequence $S$ over $G$ of length $|S|\\ge t$ has a non-empty zero-sum subsequence. It is a starting point of zero-sum theory but only has a trivial lower bound $\\mathsf D^*(G) = n_1 + \\cdots + n_r - r + 1$, which equals $\\mathsf D(G)$ over $p$-groups. We investigate the non-dispersive sequences over group $C_n^r$, thereby revealing the growth of $\\mathsf D(G)-\\mathsf D^*(G)$ over non-$p$-groups $G = C_n^r \\oplus "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1810.08346","kind":"arxiv","version":2},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/1810.08346/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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":"1810.08346","created_at":"2026-07-05T03:16:41.088794+00:00"},{"alias_kind":"arxiv_version","alias_value":"1810.08346v2","created_at":"2026-07-05T03:16:41.088794+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1810.08346","created_at":"2026-07-05T03:16:41.088794+00:00"},{"alias_kind":"pith_short_12","alias_value":"MC2KT6CF7D5E","created_at":"2026-07-05T03:16:41.088794+00:00"},{"alias_kind":"pith_short_16","alias_value":"MC2KT6CF7D5EYGIC","created_at":"2026-07-05T03:16:41.088794+00:00"},{"alias_kind":"pith_short_8","alias_value":"MC2KT6CF","created_at":"2026-07-05T03:16:41.088794+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/MC2KT6CF7D5EYGICDEZBBUYYYB","json":"https://pith.science/pith/MC2KT6CF7D5EYGICDEZBBUYYYB.json","graph_json":"https://pith.science/api/pith-number/MC2KT6CF7D5EYGICDEZBBUYYYB/graph.json","events_json":"https://pith.science/api/pith-number/MC2KT6CF7D5EYGICDEZBBUYYYB/events.json","paper":"https://pith.science/paper/MC2KT6CF"},"agent_actions":{"view_html":"https://pith.science/pith/MC2KT6CF7D5EYGICDEZBBUYYYB","download_json":"https://pith.science/pith/MC2KT6CF7D5EYGICDEZBBUYYYB.json","view_paper":"https://pith.science/paper/MC2KT6CF","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1810.08346&json=true","fetch_graph":"https://pith.science/api/pith-number/MC2KT6CF7D5EYGICDEZBBUYYYB/graph.json","fetch_events":"https://pith.science/api/pith-number/MC2KT6CF7D5EYGICDEZBBUYYYB/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/MC2KT6CF7D5EYGICDEZBBUYYYB/action/timestamp_anchor","attest_storage":"https://pith.science/pith/MC2KT6CF7D5EYGICDEZBBUYYYB/action/storage_attestation","attest_author":"https://pith.science/pith/MC2KT6CF7D5EYGICDEZBBUYYYB/action/author_attestation","sign_citation":"https://pith.science/pith/MC2KT6CF7D5EYGICDEZBBUYYYB/action/citation_signature","submit_replication":"https://pith.science/pith/MC2KT6CF7D5EYGICDEZBBUYYYB/action/replication_record"}},"created_at":"2026-07-05T03:16:41.088794+00:00","updated_at":"2026-07-05T03:16:41.088794+00:00"}