{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:Z2PPYDQP2UIXNFP25AEHAWMB3V","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":"4ae858c262565ee170598d77f59887f65776cf2be6576256766a8f0b30ab34cb","cross_cats_sorted":["math.NT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2014-05-17T07:18:47Z","title_canon_sha256":"060efd0f4e93f66d65252bb7e6cf6198fe2ee91fd7a4f7fa9e10703ccd213b5d"},"schema_version":"1.0","source":{"id":"1405.4363","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1405.4363","created_at":"2026-05-18T01:06:23Z"},{"alias_kind":"arxiv_version","alias_value":"1405.4363v2","created_at":"2026-05-18T01:06:23Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1405.4363","created_at":"2026-05-18T01:06:23Z"},{"alias_kind":"pith_short_12","alias_value":"Z2PPYDQP2UIX","created_at":"2026-05-18T12:28:59Z"},{"alias_kind":"pith_short_16","alias_value":"Z2PPYDQP2UIXNFP2","created_at":"2026-05-18T12:28:59Z"},{"alias_kind":"pith_short_8","alias_value":"Z2PPYDQP","created_at":"2026-05-18T12:28:59Z"}],"graph_snapshots":[{"event_id":"sha256:db0bc5ec2c212a866b5f64bb23acfa2450d8eb3627ef323dedac6fa64b1a6073","target":"graph","created_at":"2026-05-18T01:06:23Z","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":"Given an additively written abelian group $G$ and a set $X\\subseteq G$, we let $\\mathscr{B}(X)$ denote the monoid of zero-sum sequences over $X$ and $\\mathsf{D}(X)$ the Davenport constant of $\\mathscr{B}(X)$, namely the supremum of the positive integers $n$ for which there exists a sequence $x_1 \\cdots x_n$ of $\\mathscr{B}(X)$ such that $\\sum_{i \\in I} x_i \\ne 0$ for each non-empty proper subset $I$ of $\\{1, \\ldots, n\\}$. In this paper, we mainly investigate the case when $G$ is a power of $\\mathbb{Z}$ and $X$ is a box (i.e., a product of intervals of $G$). Some mixed sets (e.g., the product o","authors_text":"Alain Plagne, Salvatore Tringali","cross_cats":["math.NT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2014-05-17T07:18:47Z","title":"The Davenport constant of a box"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1405.4363","kind":"arxiv","version":2},"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":"sha256:0cb7226dd43114e867717aa6d302b4df251069fc1a77bc300d07ddd97386ffc7","target":"record","created_at":"2026-05-18T01:06:23Z","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":"4ae858c262565ee170598d77f59887f65776cf2be6576256766a8f0b30ab34cb","cross_cats_sorted":["math.NT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2014-05-17T07:18:47Z","title_canon_sha256":"060efd0f4e93f66d65252bb7e6cf6198fe2ee91fd7a4f7fa9e10703ccd213b5d"},"schema_version":"1.0","source":{"id":"1405.4363","kind":"arxiv","version":2}},"canonical_sha256":"ce9efc0e0fd5117695fae808705981dd7613404b949073aeb876121df5a1883d","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"ce9efc0e0fd5117695fae808705981dd7613404b949073aeb876121df5a1883d","first_computed_at":"2026-05-18T01:06:23.199947Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:06:23.199947Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"MInU6E92U678Tkh2Rd2f4XXv5CD34TCIH8MPr+qigeAREkZ7dEGDB9FwwIaejra5MtqmKao3ISnKffGYgtcQAA==","signature_status":"signed_v1","signed_at":"2026-05-18T01:06:23.200511Z","signed_message":"canonical_sha256_bytes"},"source_id":"1405.4363","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:0cb7226dd43114e867717aa6d302b4df251069fc1a77bc300d07ddd97386ffc7","sha256:db0bc5ec2c212a866b5f64bb23acfa2450d8eb3627ef323dedac6fa64b1a6073"],"state_sha256":"19c74ff7ac0794cf5ea27e6f0a66e9a633915c6129205519386eb28de10e53ec"}