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For every sequence $T$ of elements in $\\mathcal{S}$ (repetition allowed), let $\\sigma(T) \\in \\mathcal{S}$ denote the sum of all terms of $T$. Define the Davenport constant $D(\\mathcal{S})$ of $\\mathcal{S}$ to be the least positive integer $d$ such that every sequence $T$ over $\\mathcal{S}$ of length at least $d$ contains a proper subsequence $T'$ with $\\sigma(T')=\\sigma(T)$, and define "},"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":"1309.5588","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2013-09-22T10:52:07Z","cross_cats_sorted":["math.AC","math.NT"],"title_canon_sha256":"d70c2acb22670f28e9e28887f317b0ee09ea13484da07b1f7cf188ef19fa2657","abstract_canon_sha256":"3399f03db75f263c43504d423b638fed14be8dfff4df9675a4338662a73bdb9b"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:09:47.630716Z","signature_b64":"OF7r+xd6J9atHKFHf5ns+Dg/tyjH4EL6SrvOvHikMv0M0LE0gWDfBIgLEfF0sx+CKb5XJM12iAI6MlWOpsoVDg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"d89f9fc79772bfa5262c3317d56e34791f103ec75e3b05f514cc0519fae099bc","last_reissued_at":"2026-05-18T03:09:47.629918Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:09:47.629918Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Erd\\H{o}s-Ginzburg-Ziv theorem for finite commutative semigroups","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AC","math.NT"],"primary_cat":"math.CO","authors_text":"Guoqing Wang, Sukumar Das Adhikari, Weidong Gao","submitted_at":"2013-09-22T10:52:07Z","abstract_excerpt":"Let $\\mathcal{S}$ be a finite commutative semigroup written additively, and let $\\exp(\\mathcal{S})$ be its exponent which is defined as the least common multiple of all periods of the elements in $\\mathcal{S}$. For every sequence $T$ of elements in $\\mathcal{S}$ (repetition allowed), let $\\sigma(T) \\in \\mathcal{S}$ denote the sum of all terms of $T$. Define the Davenport constant $D(\\mathcal{S})$ of $\\mathcal{S}$ to be the least positive integer $d$ such that every sequence $T$ over $\\mathcal{S}$ of length at least $d$ contains a proper subsequence $T'$ with $\\sigma(T')=\\sigma(T)$, and define "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1309.5588","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":""},"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":"1309.5588","created_at":"2026-05-18T03:09:47.630061+00:00"},{"alias_kind":"arxiv_version","alias_value":"1309.5588v2","created_at":"2026-05-18T03:09:47.630061+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1309.5588","created_at":"2026-05-18T03:09:47.630061+00:00"},{"alias_kind":"pith_short_12","alias_value":"3CPZ7R4XOK72","created_at":"2026-05-18T12:27:32.513160+00:00"},{"alias_kind":"pith_short_16","alias_value":"3CPZ7R4XOK72KJRM","created_at":"2026-05-18T12:27:32.513160+00:00"},{"alias_kind":"pith_short_8","alias_value":"3CPZ7R4X","created_at":"2026-05-18T12:27:32.513160+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/3CPZ7R4XOK72KJRMGML5K3RUPE","json":"https://pith.science/pith/3CPZ7R4XOK72KJRMGML5K3RUPE.json","graph_json":"https://pith.science/api/pith-number/3CPZ7R4XOK72KJRMGML5K3RUPE/graph.json","events_json":"https://pith.science/api/pith-number/3CPZ7R4XOK72KJRMGML5K3RUPE/events.json","paper":"https://pith.science/paper/3CPZ7R4X"},"agent_actions":{"view_html":"https://pith.science/pith/3CPZ7R4XOK72KJRMGML5K3RUPE","download_json":"https://pith.science/pith/3CPZ7R4XOK72KJRMGML5K3RUPE.json","view_paper":"https://pith.science/paper/3CPZ7R4X","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1309.5588&json=true","fetch_graph":"https://pith.science/api/pith-number/3CPZ7R4XOK72KJRMGML5K3RUPE/graph.json","fetch_events":"https://pith.science/api/pith-number/3CPZ7R4XOK72KJRMGML5K3RUPE/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/3CPZ7R4XOK72KJRMGML5K3RUPE/action/timestamp_anchor","attest_storage":"https://pith.science/pith/3CPZ7R4XOK72KJRMGML5K3RUPE/action/storage_attestation","attest_author":"https://pith.science/pith/3CPZ7R4XOK72KJRMGML5K3RUPE/action/author_attestation","sign_citation":"https://pith.science/pith/3CPZ7R4XOK72KJRMGML5K3RUPE/action/citation_signature","submit_replication":"https://pith.science/pith/3CPZ7R4XOK72KJRMGML5K3RUPE/action/replication_record"}},"created_at":"2026-05-18T03:09:47.630061+00:00","updated_at":"2026-05-18T03:09:47.630061+00:00"}