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We call $S$ is unsplittable, if there do not exist $g$ in $S$ and $x,y \\in G$ such that $g=x+y$ and $Sg^{-1}xy$ is also a minimal zero-sum sequence. In this paper we show that if $S$ is an unsplittable minimal zero-sum sequence of length $|S|= \\frac{p-1}{2}$, then $S=g^{\\frac{p-11}{2}}(\\frac{p+3}{2}g)^4(\\frac{p-1}{2}g)$ or $g^{\\frac{p-7}{2}}(\\frac{p+5}{2}g)^2(\\frac{"},"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":"1409.1970","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2014-09-06T01:20:47Z","cross_cats_sorted":[],"title_canon_sha256":"98420c3f9319fdefa3aba8f8f9f23046ae840c6abb64143cd52274e2d4f9d0e9","abstract_canon_sha256":"7ab66d7f17e500361fa9711de2a5b44d4783571adb748cb45ec324a86d869056"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:43:18.288987Z","signature_b64":"AsueIO9qWlJNeCzMmQPofQ6Qdu03qyUzKDt/DsUx02pKE6lSK8gxc1wvdmNPndml/eYvuQsDylD0KP7Y7nu/CA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"687eafd8a5f4b995ad46f1b67a0b8c783dd4003891f38444a1dc3d37bfa2bade","last_reissued_at":"2026-05-18T02:43:18.288528Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:43:18.288528Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"On the unsplittable minimal zero-sum sequences over finite cyclic groups of prime order","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Fang Sun, Jiangtao Peng","submitted_at":"2014-09-06T01:20:47Z","abstract_excerpt":"Let $p > 155$ be a prime and let $G$ be a cyclic group of order $p$. Let $S$ be a minimal zero-sum sequence with elements over $G$, i.e., the sum of elements in $S$ is zero, but no proper nontrivial subsequence of $S$ has sum zero. We call $S$ is unsplittable, if there do not exist $g$ in $S$ and $x,y \\in G$ such that $g=x+y$ and $Sg^{-1}xy$ is also a minimal zero-sum sequence. In this paper we show that if $S$ is an unsplittable minimal zero-sum sequence of length $|S|= \\frac{p-1}{2}$, then $S=g^{\\frac{p-11}{2}}(\\frac{p+3}{2}g)^4(\\frac{p-1}{2}g)$ or $g^{\\frac{p-7}{2}}(\\frac{p+5}{2}g)^2(\\frac{"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1409.1970","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":"1409.1970","created_at":"2026-05-18T02:43:18.288597+00:00"},{"alias_kind":"arxiv_version","alias_value":"1409.1970v1","created_at":"2026-05-18T02:43:18.288597+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1409.1970","created_at":"2026-05-18T02:43:18.288597+00:00"},{"alias_kind":"pith_short_12","alias_value":"NB7K7WFF6S4Z","created_at":"2026-05-18T12:28:41.024544+00:00"},{"alias_kind":"pith_short_16","alias_value":"NB7K7WFF6S4ZLLKG","created_at":"2026-05-18T12:28:41.024544+00:00"},{"alias_kind":"pith_short_8","alias_value":"NB7K7WFF","created_at":"2026-05-18T12:28:41.024544+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/NB7K7WFF6S4ZLLKG6G3HUC4MPA","json":"https://pith.science/pith/NB7K7WFF6S4ZLLKG6G3HUC4MPA.json","graph_json":"https://pith.science/api/pith-number/NB7K7WFF6S4ZLLKG6G3HUC4MPA/graph.json","events_json":"https://pith.science/api/pith-number/NB7K7WFF6S4ZLLKG6G3HUC4MPA/events.json","paper":"https://pith.science/paper/NB7K7WFF"},"agent_actions":{"view_html":"https://pith.science/pith/NB7K7WFF6S4ZLLKG6G3HUC4MPA","download_json":"https://pith.science/pith/NB7K7WFF6S4ZLLKG6G3HUC4MPA.json","view_paper":"https://pith.science/paper/NB7K7WFF","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1409.1970&json=true","fetch_graph":"https://pith.science/api/pith-number/NB7K7WFF6S4ZLLKG6G3HUC4MPA/graph.json","fetch_events":"https://pith.science/api/pith-number/NB7K7WFF6S4ZLLKG6G3HUC4MPA/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/NB7K7WFF6S4ZLLKG6G3HUC4MPA/action/timestamp_anchor","attest_storage":"https://pith.science/pith/NB7K7WFF6S4ZLLKG6G3HUC4MPA/action/storage_attestation","attest_author":"https://pith.science/pith/NB7K7WFF6S4ZLLKG6G3HUC4MPA/action/author_attestation","sign_citation":"https://pith.science/pith/NB7K7WFF6S4ZLLKG6G3HUC4MPA/action/citation_signature","submit_replication":"https://pith.science/pith/NB7K7WFF6S4ZLLKG6G3HUC4MPA/action/replication_record"}},"created_at":"2026-05-18T02:43:18.288597+00:00","updated_at":"2026-05-18T02:43:18.288597+00:00"}