{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:PEYC7BCHPFWN4SDDWDPM5JEJIG","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":"a89c47262f81bcad6f21fbdb86cf2ba689459c1edecb7d3977988aea19dc1ed3","cross_cats_sorted":["math.RT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.KT","submitted_at":"2018-07-04T10:00:15Z","title_canon_sha256":"f0e44fe2ce9db71d8b73787caef5b3387110103ba594801b5359c2fc02ea09e4"},"schema_version":"1.0","source":{"id":"1807.01505","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1807.01505","created_at":"2026-05-17T23:50:59Z"},{"alias_kind":"arxiv_version","alias_value":"1807.01505v2","created_at":"2026-05-17T23:50:59Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1807.01505","created_at":"2026-05-17T23:50:59Z"},{"alias_kind":"pith_short_12","alias_value":"PEYC7BCHPFWN","created_at":"2026-05-18T12:32:43Z"},{"alias_kind":"pith_short_16","alias_value":"PEYC7BCHPFWN4SDD","created_at":"2026-05-18T12:32:43Z"},{"alias_kind":"pith_short_8","alias_value":"PEYC7BCH","created_at":"2026-05-18T12:32:43Z"}],"graph_snapshots":[{"event_id":"sha256:0192af41507c1373d93e27ee33677af103e107d7e03ea33f57a6972aae66fe2c","target":"graph","created_at":"2026-05-17T23:50:59Z","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":"We give a general construction of realization functors for $t$-structures on the base of a strong stable derivator. In particular, given such a derivator $\\mathbb D$, a $t$-structure $\\mathbf t=(\\mathcal D^{\\leq0},\\mathcal D^{\\geq0})$ on the triangulated category $\\mathbb D(\\mathbb 1)$, and letting $\\mathcal A=\\mathcal D^{\\leq0}\\cap \\mathcal D^{\\geq0}$ be its heart, we construct, under mild assumptions, a morphism of prederivators \\[ \\mathrm{real}_{\\mathbf t}\\colon \\mathbf{D}_{\\mathcal A}\\to \\mathbb D \\] where $\\mathbf{D}_{\\mathcal A}$ is the natural prederivator enhancing the derived category","authors_text":"Simone Virili","cross_cats":["math.RT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.KT","submitted_at":"2018-07-04T10:00:15Z","title":"Morita theory for stable derivators"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1807.01505","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:e49547ee5b7cfa07e5595dd57e5ccba51b62c198180faef4d5347ec06d5c7040","target":"record","created_at":"2026-05-17T23:50:59Z","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":"a89c47262f81bcad6f21fbdb86cf2ba689459c1edecb7d3977988aea19dc1ed3","cross_cats_sorted":["math.RT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.KT","submitted_at":"2018-07-04T10:00:15Z","title_canon_sha256":"f0e44fe2ce9db71d8b73787caef5b3387110103ba594801b5359c2fc02ea09e4"},"schema_version":"1.0","source":{"id":"1807.01505","kind":"arxiv","version":2}},"canonical_sha256":"79302f8447796cde4863b0decea48941814bf9a5ea13ff161dda3f46f5fb52c8","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"79302f8447796cde4863b0decea48941814bf9a5ea13ff161dda3f46f5fb52c8","first_computed_at":"2026-05-17T23:50:59.583189Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:50:59.583189Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"SBzLQj2OchElrCOqfvYZ2C8b1MHE3Zc5Vgur6aUVhupd5Qivxbh55Y75QEFCPKPjZsMt8HQgzYfnP+FAmHtsBA==","signature_status":"signed_v1","signed_at":"2026-05-17T23:50:59.583650Z","signed_message":"canonical_sha256_bytes"},"source_id":"1807.01505","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:e49547ee5b7cfa07e5595dd57e5ccba51b62c198180faef4d5347ec06d5c7040","sha256:0192af41507c1373d93e27ee33677af103e107d7e03ea33f57a6972aae66fe2c"],"state_sha256":"5edc452025aab58b40d0029a2f67e1ccccaf195119073942f0aef49f43bfe898"}