{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2010:2AW55WWGS5PJRNCKNQG5CLWQVB","short_pith_number":"pith:2AW55WWG","schema_version":"1.0","canonical_sha256":"d02ddedac6975e98b44a6c0dd12ed0a87f00566980ed5ec6c0a08b3ab1ec922b","source":{"kind":"arxiv","id":"1009.5835","version":1},"attestation_state":"computed","paper":{"title":"On the Davenport constant and on the structure of extremal zero-sum free sequences","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.NT"],"primary_cat":"math.CO","authors_text":"Alfred Geroldinger, Andreas Philipp, Manfred Liebmann","submitted_at":"2010-09-29T10:43:06Z","abstract_excerpt":"Let $G = C_{n_1} \\oplus ... \\oplus C_{n_r}$ with $1 < n_1 \\t ... \\t n_r$ be a finite abelian group, $\\mathsf d^* (G) = n_1 + ... + n_r - r$, and let $\\mathsf d (G)$ denote the maximal length of a zero-sum free sequence over $G$. Then $\\mathsf d (G) \\ge \\mathsf d^* (G)$, and the standing conjecture is that equality holds for $G = C_n^r$. We show that equality does not hold for $C_2 \\oplus C_{2n}^r$, where $n \\ge 3$ is odd and $r \\ge 4$. This gives new information on the structure of extremal zero-sum free sequences over $C_{2n}^r$."},"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":"1009.5835","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2010-09-29T10:43:06Z","cross_cats_sorted":["math.NT"],"title_canon_sha256":"2915262ad434a5b298244aed214248194e9de3146510bfcdfe9d6b0cd452f2df","abstract_canon_sha256":"d76f90dda094b3c01e75204cf362e86583d4219dd7a2acdcbcc33c5f9efd78e7"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:40:08.809553Z","signature_b64":"Zo4GOl17v+CC0Bs/+hl0g784IZaPSTnXN90qgDxHH88uV2elzFtFrTHuSj0fuqQ4rZgZEq8lkyH0ilwO6/lYAA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"d02ddedac6975e98b44a6c0dd12ed0a87f00566980ed5ec6c0a08b3ab1ec922b","last_reissued_at":"2026-05-18T04:40:08.809066Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:40:08.809066Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"On the Davenport constant and on the structure of extremal zero-sum free sequences","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.NT"],"primary_cat":"math.CO","authors_text":"Alfred Geroldinger, Andreas Philipp, Manfred Liebmann","submitted_at":"2010-09-29T10:43:06Z","abstract_excerpt":"Let $G = C_{n_1} \\oplus ... \\oplus C_{n_r}$ with $1 < n_1 \\t ... \\t n_r$ be a finite abelian group, $\\mathsf d^* (G) = n_1 + ... + n_r - r$, and let $\\mathsf d (G)$ denote the maximal length of a zero-sum free sequence over $G$. Then $\\mathsf d (G) \\ge \\mathsf d^* (G)$, and the standing conjecture is that equality holds for $G = C_n^r$. We show that equality does not hold for $C_2 \\oplus C_{2n}^r$, where $n \\ge 3$ is odd and $r \\ge 4$. This gives new information on the structure of extremal zero-sum free sequences over $C_{2n}^r$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1009.5835","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":"1009.5835","created_at":"2026-05-18T04:40:08.809136+00:00"},{"alias_kind":"arxiv_version","alias_value":"1009.5835v1","created_at":"2026-05-18T04:40:08.809136+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1009.5835","created_at":"2026-05-18T04:40:08.809136+00:00"},{"alias_kind":"pith_short_12","alias_value":"2AW55WWGS5PJ","created_at":"2026-05-18T12:26:03.138858+00:00"},{"alias_kind":"pith_short_16","alias_value":"2AW55WWGS5PJRNCK","created_at":"2026-05-18T12:26:03.138858+00:00"},{"alias_kind":"pith_short_8","alias_value":"2AW55WWG","created_at":"2026-05-18T12:26:03.138858+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/2AW55WWGS5PJRNCKNQG5CLWQVB","json":"https://pith.science/pith/2AW55WWGS5PJRNCKNQG5CLWQVB.json","graph_json":"https://pith.science/api/pith-number/2AW55WWGS5PJRNCKNQG5CLWQVB/graph.json","events_json":"https://pith.science/api/pith-number/2AW55WWGS5PJRNCKNQG5CLWQVB/events.json","paper":"https://pith.science/paper/2AW55WWG"},"agent_actions":{"view_html":"https://pith.science/pith/2AW55WWGS5PJRNCKNQG5CLWQVB","download_json":"https://pith.science/pith/2AW55WWGS5PJRNCKNQG5CLWQVB.json","view_paper":"https://pith.science/paper/2AW55WWG","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1009.5835&json=true","fetch_graph":"https://pith.science/api/pith-number/2AW55WWGS5PJRNCKNQG5CLWQVB/graph.json","fetch_events":"https://pith.science/api/pith-number/2AW55WWGS5PJRNCKNQG5CLWQVB/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/2AW55WWGS5PJRNCKNQG5CLWQVB/action/timestamp_anchor","attest_storage":"https://pith.science/pith/2AW55WWGS5PJRNCKNQG5CLWQVB/action/storage_attestation","attest_author":"https://pith.science/pith/2AW55WWGS5PJRNCKNQG5CLWQVB/action/author_attestation","sign_citation":"https://pith.science/pith/2AW55WWGS5PJRNCKNQG5CLWQVB/action/citation_signature","submit_replication":"https://pith.science/pith/2AW55WWGS5PJRNCKNQG5CLWQVB/action/replication_record"}},"created_at":"2026-05-18T04:40:08.809136+00:00","updated_at":"2026-05-18T04:40:08.809136+00:00"}