{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2020:7A365DI3UV2QEMRHSPOVMZ7MRG","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":"a3040ab5dd3934eb280707464af51a56a17e72dfeccfe784fa6cffdcba27b1c6","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2020-04-06T16:40:09Z","title_canon_sha256":"09b916779485689093eea0769aade7697bd029eda2651311da5e7caad2129b1a"},"schema_version":"1.0","source":{"id":"2004.02798","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2004.02798","created_at":"2026-07-05T01:59:11Z"},{"alias_kind":"arxiv_version","alias_value":"2004.02798v3","created_at":"2026-07-05T01:59:11Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2004.02798","created_at":"2026-07-05T01:59:11Z"},{"alias_kind":"pith_short_12","alias_value":"7A365DI3UV2Q","created_at":"2026-07-05T01:59:11Z"},{"alias_kind":"pith_short_16","alias_value":"7A365DI3UV2QEMRH","created_at":"2026-07-05T01:59:11Z"},{"alias_kind":"pith_short_8","alias_value":"7A365DI3","created_at":"2026-07-05T01:59:11Z"}],"graph_snapshots":[{"event_id":"sha256:139d5123db2ae9479a9f6ff4a84c1a1e025becb21d680ea21456c4b996df33a1","target":"graph","created_at":"2026-07-05T01:59:11Z","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/2004.02798/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We prove that ideal sheaves of lines in a Fano threefold $X$ of Picard rank one and index two are stable objects in the Kuznetsov component $\\mathsf{Ku}(X)$, with respect to the stability conditions constructed by Bayer, Lahoz, Macr\\`i and Stellari, giving a modular description to the Hilbert scheme of lines in $X$. When $X$ is a cubic threefold, we show that the Serre functor of $\\mathsf{Ku}(X)$ preserves these stability conditions. As an application, we obtain the smoothness of non-empty moduli spaces of stable objects in $\\mathsf{Ku}(X)$. When $X$ is a quartic double solid, we describe a co","authors_text":"Laura Pertusi, Song Yang","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2020-04-06T16:40:09Z","title":"Some remarks on Fano threefolds of index two and stability conditions"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2004.02798","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:bb860c35fa2693ca848fbb48f9584b310a11baeb2f8ec5125ab1e096a6dc301c","target":"record","created_at":"2026-07-05T01:59:11Z","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":"a3040ab5dd3934eb280707464af51a56a17e72dfeccfe784fa6cffdcba27b1c6","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2020-04-06T16:40:09Z","title_canon_sha256":"09b916779485689093eea0769aade7697bd029eda2651311da5e7caad2129b1a"},"schema_version":"1.0","source":{"id":"2004.02798","kind":"arxiv","version":3}},"canonical_sha256":"f837ee8d1ba57502322793dd5667ec89a0bacb52af9fe06ef1a090c4375d0613","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"f837ee8d1ba57502322793dd5667ec89a0bacb52af9fe06ef1a090c4375d0613","first_computed_at":"2026-07-05T01:59:11.158838Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T01:59:11.158838Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"mYxCCh8TOsMp1ngOGPdFUF9LiXRy7pkw0jkoQFS2bbPJvORCLbz4vxAYwVUvaeCuBuhAsauCYW6K/UO0Q1UfCA==","signature_status":"signed_v1","signed_at":"2026-07-05T01:59:11.159194Z","signed_message":"canonical_sha256_bytes"},"source_id":"2004.02798","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:bb860c35fa2693ca848fbb48f9584b310a11baeb2f8ec5125ab1e096a6dc301c","sha256:139d5123db2ae9479a9f6ff4a84c1a1e025becb21d680ea21456c4b996df33a1"],"state_sha256":"e3a5c4a17198f282ee84f7cd8b9163140bab58ebae292163327db1b40b94626b"}