{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2010:4OVSURT7BW7MK6OLCQDJXKWFUF","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":"a2211033487bf5fb8315a9f1db6a25fbc51d8b3a32795dc99ca2f9dd5e539015","cross_cats_sorted":["math.RA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2010-12-10T04:00:47Z","title_canon_sha256":"165e5f13b6fe18443eca05309fbee4c00d6852f5fb338f5a892dd270aba0ab31"},"schema_version":"1.0","source":{"id":"1012.2176","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1012.2176","created_at":"2026-05-18T02:58:01Z"},{"alias_kind":"arxiv_version","alias_value":"1012.2176v1","created_at":"2026-05-18T02:58:01Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1012.2176","created_at":"2026-05-18T02:58:01Z"},{"alias_kind":"pith_short_12","alias_value":"4OVSURT7BW7M","created_at":"2026-05-18T12:26:04Z"},{"alias_kind":"pith_short_16","alias_value":"4OVSURT7BW7MK6OL","created_at":"2026-05-18T12:26:04Z"},{"alias_kind":"pith_short_8","alias_value":"4OVSURT7","created_at":"2026-05-18T12:26:04Z"}],"graph_snapshots":[{"event_id":"sha256:ffd10b010ff08aa5bca1ff9c72972cb4a28847e0f47fb4c78dde181632cb5f85","target":"graph","created_at":"2026-05-18T02:58:01Z","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 $T$ be an infinitely generated tilting module of projective dimension at most one over an arbitrary associative ring $A$, and let $B$ be the endomorphism ring of $T$. In this paper, we prove that if $T$ is good then there exists a ring $C$, a homological ring epimorphism $B\\ra C$ and a recollement among the (unbounded) derived module categories $\\D{C}$ of $C$, $\\D{B}$ of $B$, and $\\D{A}$ of $A$. In particular, the kernel of the total left derived functor $T\\otimes_B^{\\mathbb L}-$ is triangle equivalent to the derived module category $\\D{C}$. Conversely, if the functor $T\\otimes_B^{\\mathbb ","authors_text":"Changchang Xi, Hongxing Chen","cross_cats":["math.RA"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2010-12-10T04:00:47Z","title":"Good tilting modules and recollements of derived module categories"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1012.2176","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":"sha256:8c5b280e0b472cb3e460cfa64f6303fe9b13d481008079dc4c5c9c6546e404d4","target":"record","created_at":"2026-05-18T02:58:01Z","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":"a2211033487bf5fb8315a9f1db6a25fbc51d8b3a32795dc99ca2f9dd5e539015","cross_cats_sorted":["math.RA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2010-12-10T04:00:47Z","title_canon_sha256":"165e5f13b6fe18443eca05309fbee4c00d6852f5fb338f5a892dd270aba0ab31"},"schema_version":"1.0","source":{"id":"1012.2176","kind":"arxiv","version":1}},"canonical_sha256":"e3ab2a467f0dbec579cb14069baac5a17ba2c85c0cc090c101438fe7fe289beb","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"e3ab2a467f0dbec579cb14069baac5a17ba2c85c0cc090c101438fe7fe289beb","first_computed_at":"2026-05-18T02:58:01.396397Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:58:01.396397Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"rLtk6/QR1wwrdCeBxw44cozgNvLZJAJiBIGupIFkpERiQLLGTu8RonfVTNKe42VZcuxTup2r4MMVrylu42ZQAw==","signature_status":"signed_v1","signed_at":"2026-05-18T02:58:01.396871Z","signed_message":"canonical_sha256_bytes"},"source_id":"1012.2176","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:8c5b280e0b472cb3e460cfa64f6303fe9b13d481008079dc4c5c9c6546e404d4","sha256:ffd10b010ff08aa5bca1ff9c72972cb4a28847e0f47fb4c78dde181632cb5f85"],"state_sha256":"175b8c77c473c12703385ced89c9df6deb23b608993681be40ba5521ed7f2f35"}