{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:7MLL2IVKKAD3ET4ZP5R27MHOY4","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":"a4ad62f90651643a3b91d9c4c3152cb505e4a7f2f23ee84f18ad7266aab2de37","cross_cats_sorted":["math.RA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2017-03-14T22:06:22Z","title_canon_sha256":"4c1194af9dbcfc7caf4a520cd0a1c22e0bc63b3d6c74d1aadb6b682c852f31c5"},"schema_version":"1.0","source":{"id":"1703.04745","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1703.04745","created_at":"2026-05-18T00:48:39Z"},{"alias_kind":"arxiv_version","alias_value":"1703.04745v1","created_at":"2026-05-18T00:48:39Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1703.04745","created_at":"2026-05-18T00:48:39Z"},{"alias_kind":"pith_short_12","alias_value":"7MLL2IVKKAD3","created_at":"2026-05-18T12:31:05Z"},{"alias_kind":"pith_short_16","alias_value":"7MLL2IVKKAD3ET4Z","created_at":"2026-05-18T12:31:05Z"},{"alias_kind":"pith_short_8","alias_value":"7MLL2IVK","created_at":"2026-05-18T12:31:05Z"}],"graph_snapshots":[{"event_id":"sha256:167b9c6ab97116e5d815c6ac79b3c3b696705bf284adaab38b468c8bfdf0cd38","target":"graph","created_at":"2026-05-18T00:48:39Z","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 a $1$-tilting module whose tilting torsion pair $({\\mathcal T}, {\\mathcal F})$ has the property that the heart ${\\mathcal H}_t$ of the induced $t$-structure (in the derived category ${\\mathcal D}({\\rm Mod} \\mbox{-} R)$ is Grothendieck. It is proved that such tilting torsion pairs are characterized in several ways: (1) the $1$-tilting module $T$ is pure projective; (2) ${\\mathcal T}$ is a definable subcategory of ${\\rm Mod} \\mbox{-} R$ with enough pure projectives, and (3) both classes ${\\mathcal T}$ and ${\\mathcal F}$ are finitely axiomatizable.\n  This study addresses the question o","authors_text":"Ivo Herzog, Jan Trlifaj, Jan \\v{S}aroch, Pavel P\\v{r}\\'ihoda, Silvana Bazzoni","cross_cats":["math.RA"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2017-03-14T22:06:22Z","title":"Pure Projective Tilting Modules"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1703.04745","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":"sha256:6179d73e094977b2422933c5c2e8da93e053e69a4bbc344f0ffea1cd70f3f7b4","target":"record","created_at":"2026-05-18T00:48:39Z","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":"a4ad62f90651643a3b91d9c4c3152cb505e4a7f2f23ee84f18ad7266aab2de37","cross_cats_sorted":["math.RA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2017-03-14T22:06:22Z","title_canon_sha256":"4c1194af9dbcfc7caf4a520cd0a1c22e0bc63b3d6c74d1aadb6b682c852f31c5"},"schema_version":"1.0","source":{"id":"1703.04745","kind":"arxiv","version":1}},"canonical_sha256":"fb16bd22aa5007b24f997f63afb0eec7211b116c26ddcece454676998a09e270","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"fb16bd22aa5007b24f997f63afb0eec7211b116c26ddcece454676998a09e270","first_computed_at":"2026-05-18T00:48:39.342089Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:48:39.342089Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"4AxP6kBuaQNFxWw403PA+sYsEzBWOO0yVMnVMyp+wZ0q5JziJ3H64iVTRM/NGhS5+4zQ0WVFCcmyvjkN92e0CA==","signature_status":"signed_v1","signed_at":"2026-05-18T00:48:39.342538Z","signed_message":"canonical_sha256_bytes"},"source_id":"1703.04745","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:6179d73e094977b2422933c5c2e8da93e053e69a4bbc344f0ffea1cd70f3f7b4","sha256:167b9c6ab97116e5d815c6ac79b3c3b696705bf284adaab38b468c8bfdf0cd38"],"state_sha256":"33036900015f47c49387120e4f78a1f8082309a5bc23fc7d708313ce0a86dbd7"}