{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:XO26BU3CVGD5O43TUTZPSYYCRL","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":"b9dd236fbbcd1ac65ac1ee309a58443903c3fc34165fcd005ca6db1a4e0f48fd","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2014-02-02T17:36:07Z","title_canon_sha256":"f3e24a7f2d5627418a7b2ba0350a2fafefb8d01fc3d7181b171d9b468d1fa0bb"},"schema_version":"1.0","source":{"id":"1402.0221","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1402.0221","created_at":"2026-05-18T03:00:24Z"},{"alias_kind":"arxiv_version","alias_value":"1402.0221v1","created_at":"2026-05-18T03:00:24Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1402.0221","created_at":"2026-05-18T03:00:24Z"},{"alias_kind":"pith_short_12","alias_value":"XO26BU3CVGD5","created_at":"2026-05-18T12:28:57Z"},{"alias_kind":"pith_short_16","alias_value":"XO26BU3CVGD5O43T","created_at":"2026-05-18T12:28:57Z"},{"alias_kind":"pith_short_8","alias_value":"XO26BU3C","created_at":"2026-05-18T12:28:57Z"}],"graph_snapshots":[{"event_id":"sha256:31747a7340a228bd34f56b89927f415e77d7431c8f2f8f6b6ec4f0260fc39e67","target":"graph","created_at":"2026-05-18T03:00:24Z","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":"Let $G$ be a finite cyclic group. Every sequence $S$ of length $l$ over $G$ can be written in the form $S=(x_1g)\\cdot\\ldots\\cdot(x_lg)$ where $g\\in G$ and $x_1, \\ldots, x_l\\in[1, \\ord(g)]$, and the index $\\ind(S)$ of $S$ is defined to be the minimum of $(x_1+\\cdots+x_l)/\\ord(g)$ over all possible $g\\in G$ such that $\\langle g \\rangle =G$. Recently the second and the third authors determined the index of any minimal zero-sum sequence $S$ of length 5 over a cyclic group of a prime order where $S=g^2(x_2g)(x_3g)(x_4g)$. In this paper, we determine the index of any minimal zero-sum sequence $S$ of","authors_text":"Jiangtao Peng, Li-meng Xia, Yuanlin Li","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2014-02-02T17:36:07Z","title":"Minimal zero-sum sequence of length five over finite cyclic groups of prime power order"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1402.0221","kind":"arxiv","version":1},"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":"sha256:8e642a7f8bd4f9a71cfa0269dae6ba7dcef4fe81445516478d24897ddf3a7f76","target":"record","created_at":"2026-05-18T03:00:24Z","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":"b9dd236fbbcd1ac65ac1ee309a58443903c3fc34165fcd005ca6db1a4e0f48fd","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2014-02-02T17:36:07Z","title_canon_sha256":"f3e24a7f2d5627418a7b2ba0350a2fafefb8d01fc3d7181b171d9b468d1fa0bb"},"schema_version":"1.0","source":{"id":"1402.0221","kind":"arxiv","version":1}},"canonical_sha256":"bbb5e0d362a987d77373a4f2f963028af3ebf740cfb2175d17b7ee5d53c8ff0b","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"bbb5e0d362a987d77373a4f2f963028af3ebf740cfb2175d17b7ee5d53c8ff0b","first_computed_at":"2026-05-18T03:00:24.282962Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:00:24.282962Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"jVb6GUE+gR27R/7h9r+6rzieYy2VrWnjoJ04oOtp4XpuNlLjcCcneqsSjYd3n63y4VkSd06gCuOwTt91G9MTAw==","signature_status":"signed_v1","signed_at":"2026-05-18T03:00:24.283727Z","signed_message":"canonical_sha256_bytes"},"source_id":"1402.0221","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:8e642a7f8bd4f9a71cfa0269dae6ba7dcef4fe81445516478d24897ddf3a7f76","sha256:31747a7340a228bd34f56b89927f415e77d7431c8f2f8f6b6ec4f0260fc39e67"],"state_sha256":"7ae32a2055a698d033db69977fbe4312c6bd597f5591b704902996b401a5062c"}