{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2019:VBDBHTTBSWMI6IEBHNL5C3P5W6","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":"1679743d2404077ed9f41d4825298f955f9c2ca87057de32c106c96f60829a28","cross_cats_sorted":["math.KT","math.RA","math.RT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CT","submitted_at":"2019-08-01T22:44:29Z","title_canon_sha256":"d3647c428f4988e7aae1162554e8f49525edbcce88c077d3d21a8775172b527a"},"schema_version":"1.0","source":{"id":"1908.00649","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1908.00649","created_at":"2026-07-05T04:44:17Z"},{"alias_kind":"arxiv_version","alias_value":"1908.00649v3","created_at":"2026-07-05T04:44:17Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1908.00649","created_at":"2026-07-05T04:44:17Z"},{"alias_kind":"pith_short_12","alias_value":"VBDBHTTBSWMI","created_at":"2026-07-05T04:44:17Z"},{"alias_kind":"pith_short_16","alias_value":"VBDBHTTBSWMI6IEB","created_at":"2026-07-05T04:44:17Z"},{"alias_kind":"pith_short_8","alias_value":"VBDBHTTB","created_at":"2026-07-05T04:44:17Z"}],"graph_snapshots":[{"event_id":"sha256:08359d902ae7c40768bd4aa516578ef8abc3c19b8522e93c2ad91602d6375275","target":"graph","created_at":"2026-07-05T04:44:17Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/1908.00649/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Starting with a Grothendieck category $\\mathcal{G}$ and a torsion pair $\\mathbf{t}=(\\mathcal{T},\\mathcal{F})$ in $\\mathcal G$, we study the local finite presentability and local coherence of the heart $\\mathcal{H}_{\\mathbf{t}}$ of the associated Happel-Reiten-Smal{\\o} $t$-structure in the derived category $\\mathrm{Der} (\\mathcal{G})$. We start by showing that, in this general setting, the torsion pair $\\mathbf t$ is of finite type, if and only if it is quasi-cotilting, if and only if it is cosilting. We then proceed to study those $\\mathbf t$ for which $\\mathcal{H}_{\\mathbf{t}}$ is locally fin","authors_text":"Carlos E. Parra, Manuel Saor\\'in, Simone Virili","cross_cats":["math.KT","math.RA","math.RT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CT","submitted_at":"2019-08-01T22:44:29Z","title":"Locally finitely presented and coherent hearts"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1908.00649","kind":"arxiv","version":3},"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":"sha256:353968727482e7ac7e84959b7f6cf45228e7e4350645a580482458089b134fce","target":"record","created_at":"2026-07-05T04:44:17Z","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":"1679743d2404077ed9f41d4825298f955f9c2ca87057de32c106c96f60829a28","cross_cats_sorted":["math.KT","math.RA","math.RT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CT","submitted_at":"2019-08-01T22:44:29Z","title_canon_sha256":"d3647c428f4988e7aae1162554e8f49525edbcce88c077d3d21a8775172b527a"},"schema_version":"1.0","source":{"id":"1908.00649","kind":"arxiv","version":3}},"canonical_sha256":"a84613ce6195988f20813b57d16dfdb786e3e929d0045ec756faf48fe9ca37c9","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"a84613ce6195988f20813b57d16dfdb786e3e929d0045ec756faf48fe9ca37c9","first_computed_at":"2026-07-05T04:44:17.465966Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T04:44:17.465966Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"1CO0BXI8gi7oFbLSgIyYq0T9dD/VS9FqpyD3gFE8xq6zDjLKb6WQCLHVJEVmbrprAnFAGqWBngSUy0ExYYgDCw==","signature_status":"signed_v1","signed_at":"2026-07-05T04:44:17.466465Z","signed_message":"canonical_sha256_bytes"},"source_id":"1908.00649","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:353968727482e7ac7e84959b7f6cf45228e7e4350645a580482458089b134fce","sha256:08359d902ae7c40768bd4aa516578ef8abc3c19b8522e93c2ad91602d6375275"],"state_sha256":"0d06efe78b2e57deb0788d2ca44bb073cbc528f897320681684b2a6a6a2c3e4c"}