{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2008:KUD5VGVCBHILEDYNMSJJYIFYZS","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":"6233a6bfdb10ac180eca504e4bccf41c042ec46b0d9599783be73605156bbe3e","cross_cats_sorted":["math.RA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2008-10-29T03:41:27Z","title_canon_sha256":"51f98a765f4361a767178b0e4b5fea4c16e4dfd515e51cfb23cdda857ea50432"},"schema_version":"1.0","source":{"id":"0810.5190","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0810.5190","created_at":"2026-05-18T03:35:52Z"},{"alias_kind":"arxiv_version","alias_value":"0810.5190v2","created_at":"2026-05-18T03:35:52Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0810.5190","created_at":"2026-05-18T03:35:52Z"},{"alias_kind":"pith_short_12","alias_value":"KUD5VGVCBHIL","created_at":"2026-05-18T12:25:57Z"},{"alias_kind":"pith_short_16","alias_value":"KUD5VGVCBHILEDYN","created_at":"2026-05-18T12:25:57Z"},{"alias_kind":"pith_short_8","alias_value":"KUD5VGVC","created_at":"2026-05-18T12:25:57Z"}],"graph_snapshots":[{"event_id":"sha256:7f11d6301ca1eeee9e65ea23688b42c31d95beb7f89e1ec9333a4bdf46fd3ccb","target":"graph","created_at":"2026-05-18T03:35:52Z","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 $A$ be a hereditary algebra over an algebraically closed field $k$ and $A^{(m)}$ be the $m$-replicated algebra of $A$. Given an $A^{(m)}$-module $T$, we denote by $\\delta (T)$ the number of non isomorphic indecomposable summands of $T$. In this paper, we prove that a partial tilting $A^{(m)}$-module $T$ is a tilting $A^{(m)}$-module if and only if $\\delta (T)=\\delta (A^{(m)})$, and that every partial tilting $A^{(m)}$-module has complements. As an application, we deduce that the tilting quiver $\\mathscr{K}_{A^{(m)}}$ of $A^{(m)}$ is connected. Moreover, we investigate the number of complem","authors_text":"Shunhua Zhang","cross_cats":["math.RA"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2008-10-29T03:41:27Z","title":"Partial tilting modules over $m$-replicated algebras"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0810.5190","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":"sha256:42af6e577f32e7916463cfeeefd5badba57584de27aac253b4c0db6fd2cd14f5","target":"record","created_at":"2026-05-18T03:35:52Z","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":"6233a6bfdb10ac180eca504e4bccf41c042ec46b0d9599783be73605156bbe3e","cross_cats_sorted":["math.RA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2008-10-29T03:41:27Z","title_canon_sha256":"51f98a765f4361a767178b0e4b5fea4c16e4dfd515e51cfb23cdda857ea50432"},"schema_version":"1.0","source":{"id":"0810.5190","kind":"arxiv","version":2}},"canonical_sha256":"5507da9aa209d0b20f0d64929c20b8ccbd1f2682f26aa2920939f05dbed14c0d","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"5507da9aa209d0b20f0d64929c20b8ccbd1f2682f26aa2920939f05dbed14c0d","first_computed_at":"2026-05-18T03:35:52.210080Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:35:52.210080Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Et3Xq5vQSFgPutWk3Aaq2vBH45+so9ALP/Xz6Da9UmZzh1Pn3rmQZnwtpG62HZnueVBAwN+6ib5EHaVb/A6RDQ==","signature_status":"signed_v1","signed_at":"2026-05-18T03:35:52.210925Z","signed_message":"canonical_sha256_bytes"},"source_id":"0810.5190","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:42af6e577f32e7916463cfeeefd5badba57584de27aac253b4c0db6fd2cd14f5","sha256:7f11d6301ca1eeee9e65ea23688b42c31d95beb7f89e1ec9333a4bdf46fd3ccb"],"state_sha256":"5fef43db5b3c9c3646d827d51a78f7ec1d88f3e1ddb1ba6df31493133227e5fb"}