{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2019:VBDBHTTBSWMI6IEBHNL5C3P5W6","short_pith_number":"pith:VBDBHTTB","schema_version":"1.0","canonical_sha256":"a84613ce6195988f20813b57d16dfdb786e3e929d0045ec756faf48fe9ca37c9","source":{"kind":"arxiv","id":"1908.00649","version":3},"attestation_state":"computed","paper":{"title":"Locally finitely presented and coherent hearts","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.KT","math.RA","math.RT"],"primary_cat":"math.CT","authors_text":"Carlos E. Parra, Manuel Saor\\'in, Simone Virili","submitted_at":"2019-08-01T22:44:29Z","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"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1908.00649","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CT","submitted_at":"2019-08-01T22:44:29Z","cross_cats_sorted":["math.KT","math.RA","math.RT"],"title_canon_sha256":"d3647c428f4988e7aae1162554e8f49525edbcce88c077d3d21a8775172b527a","abstract_canon_sha256":"1679743d2404077ed9f41d4825298f955f9c2ca87057de32c106c96f60829a28"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T04:44:17.466465Z","signature_b64":"1CO0BXI8gi7oFbLSgIyYq0T9dD/VS9FqpyD3gFE8xq6zDjLKb6WQCLHVJEVmbrprAnFAGqWBngSUy0ExYYgDCw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"a84613ce6195988f20813b57d16dfdb786e3e929d0045ec756faf48fe9ca37c9","last_reissued_at":"2026-07-05T04:44:17.465966Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T04:44:17.465966Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Locally finitely presented and coherent hearts","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.KT","math.RA","math.RT"],"primary_cat":"math.CT","authors_text":"Carlos E. Parra, Manuel Saor\\'in, Simone Virili","submitted_at":"2019-08-01T22:44:29Z","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"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1908.00649","kind":"arxiv","version":3},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/1908.00649/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"},"aliases":[{"alias_kind":"arxiv","alias_value":"1908.00649","created_at":"2026-07-05T04:44:17.466024+00:00"},{"alias_kind":"arxiv_version","alias_value":"1908.00649v3","created_at":"2026-07-05T04:44:17.466024+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1908.00649","created_at":"2026-07-05T04:44:17.466024+00:00"},{"alias_kind":"pith_short_12","alias_value":"VBDBHTTBSWMI","created_at":"2026-07-05T04:44:17.466024+00:00"},{"alias_kind":"pith_short_16","alias_value":"VBDBHTTBSWMI6IEB","created_at":"2026-07-05T04:44:17.466024+00:00"},{"alias_kind":"pith_short_8","alias_value":"VBDBHTTB","created_at":"2026-07-05T04:44:17.466024+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/VBDBHTTBSWMI6IEBHNL5C3P5W6","json":"https://pith.science/pith/VBDBHTTBSWMI6IEBHNL5C3P5W6.json","graph_json":"https://pith.science/api/pith-number/VBDBHTTBSWMI6IEBHNL5C3P5W6/graph.json","events_json":"https://pith.science/api/pith-number/VBDBHTTBSWMI6IEBHNL5C3P5W6/events.json","paper":"https://pith.science/paper/VBDBHTTB"},"agent_actions":{"view_html":"https://pith.science/pith/VBDBHTTBSWMI6IEBHNL5C3P5W6","download_json":"https://pith.science/pith/VBDBHTTBSWMI6IEBHNL5C3P5W6.json","view_paper":"https://pith.science/paper/VBDBHTTB","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1908.00649&json=true","fetch_graph":"https://pith.science/api/pith-number/VBDBHTTBSWMI6IEBHNL5C3P5W6/graph.json","fetch_events":"https://pith.science/api/pith-number/VBDBHTTBSWMI6IEBHNL5C3P5W6/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/VBDBHTTBSWMI6IEBHNL5C3P5W6/action/timestamp_anchor","attest_storage":"https://pith.science/pith/VBDBHTTBSWMI6IEBHNL5C3P5W6/action/storage_attestation","attest_author":"https://pith.science/pith/VBDBHTTBSWMI6IEBHNL5C3P5W6/action/author_attestation","sign_citation":"https://pith.science/pith/VBDBHTTBSWMI6IEBHNL5C3P5W6/action/citation_signature","submit_replication":"https://pith.science/pith/VBDBHTTBSWMI6IEBHNL5C3P5W6/action/replication_record"}},"created_at":"2026-07-05T04:44:17.466024+00:00","updated_at":"2026-07-05T04:44:17.466024+00:00"}