{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2020:MCLM4SJXQWYT2PSDESLQLDDPRG","short_pith_number":"pith:MCLM4SJX","schema_version":"1.0","canonical_sha256":"6096ce493785b13d3e432497058c6f89bfdf5e5dff45a0853a5b889e6bb83ede","source":{"kind":"arxiv","id":"2012.12193","version":2},"attestation_state":"computed","paper":{"title":"Bridgeland Moduli spaces for Gushel-Mukai threefolds and Kuznetsov's Fano threefold conjecture","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AG","authors_text":"Shizhuo Zhang","submitted_at":"2020-12-22T17:32:40Z","abstract_excerpt":"We study the Hilbert scheme $\\mathcal{H}$ of twisted cubics on a special smooth Gushel-Mukai threefolds $X_{10}$. We show that it is a smooth irreducible projective threefold if $X_{10}$ is general among special Gushel-Mukai threefolds, while it is singular if $X_{10}$ is not general. We construct an irreducible component of a moduli space of Bridgeland stable objects in the Kuznetsov component of $X_{10}$ as a divisorial contraction of $\\mathcal{H}$. We also identify the minimal model of Fano surface $\\mathcal{C}(X_{10}')$ of conics on a smooth ordinary Gushel-Mukai threefold with moduli spac"},"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":"2012.12193","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2020-12-22T17:32:40Z","cross_cats_sorted":[],"title_canon_sha256":"dba205f473e57652b80754cfcc9ce4cd5875393f9795cba42dcb10058f6eab66","abstract_canon_sha256":"e1617a601153c8632cd94f207987ef1a53f5b67475c13d01005a2e21945bea68"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T03:09:16.690063Z","signature_b64":"X5RRJDUA+Lz+Nq7SKasU3Jbo+lhJhQ2hzEoaYrqPduyulNiVmaeu56qPGb98aT0CrI8BHHlU76ooETMvuhoPCQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"6096ce493785b13d3e432497058c6f89bfdf5e5dff45a0853a5b889e6bb83ede","last_reissued_at":"2026-07-05T03:09:16.689665Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T03:09:16.689665Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Bridgeland Moduli spaces for Gushel-Mukai threefolds and Kuznetsov's Fano threefold conjecture","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AG","authors_text":"Shizhuo Zhang","submitted_at":"2020-12-22T17:32:40Z","abstract_excerpt":"We study the Hilbert scheme $\\mathcal{H}$ of twisted cubics on a special smooth Gushel-Mukai threefolds $X_{10}$. We show that it is a smooth irreducible projective threefold if $X_{10}$ is general among special Gushel-Mukai threefolds, while it is singular if $X_{10}$ is not general. We construct an irreducible component of a moduli space of Bridgeland stable objects in the Kuznetsov component of $X_{10}$ as a divisorial contraction of $\\mathcal{H}$. We also identify the minimal model of Fano surface $\\mathcal{C}(X_{10}')$ of conics on a smooth ordinary Gushel-Mukai threefold with moduli spac"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2012.12193","kind":"arxiv","version":2},"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/2012.12193/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":"2012.12193","created_at":"2026-07-05T03:09:16.689715+00:00"},{"alias_kind":"arxiv_version","alias_value":"2012.12193v2","created_at":"2026-07-05T03:09:16.689715+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2012.12193","created_at":"2026-07-05T03:09:16.689715+00:00"},{"alias_kind":"pith_short_12","alias_value":"MCLM4SJXQWYT","created_at":"2026-07-05T03:09:16.689715+00:00"},{"alias_kind":"pith_short_16","alias_value":"MCLM4SJXQWYT2PSD","created_at":"2026-07-05T03:09:16.689715+00:00"},{"alias_kind":"pith_short_8","alias_value":"MCLM4SJX","created_at":"2026-07-05T03:09:16.689715+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":1,"internal_anchor_count":0,"sample":[{"citing_arxiv_id":"2412.06921","citing_title":"On two families of Enriques categories over K3 surfaces","ref_index":69,"is_internal_anchor":false}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/MCLM4SJXQWYT2PSDESLQLDDPRG","json":"https://pith.science/pith/MCLM4SJXQWYT2PSDESLQLDDPRG.json","graph_json":"https://pith.science/api/pith-number/MCLM4SJXQWYT2PSDESLQLDDPRG/graph.json","events_json":"https://pith.science/api/pith-number/MCLM4SJXQWYT2PSDESLQLDDPRG/events.json","paper":"https://pith.science/paper/MCLM4SJX"},"agent_actions":{"view_html":"https://pith.science/pith/MCLM4SJXQWYT2PSDESLQLDDPRG","download_json":"https://pith.science/pith/MCLM4SJXQWYT2PSDESLQLDDPRG.json","view_paper":"https://pith.science/paper/MCLM4SJX","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2012.12193&json=true","fetch_graph":"https://pith.science/api/pith-number/MCLM4SJXQWYT2PSDESLQLDDPRG/graph.json","fetch_events":"https://pith.science/api/pith-number/MCLM4SJXQWYT2PSDESLQLDDPRG/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/MCLM4SJXQWYT2PSDESLQLDDPRG/action/timestamp_anchor","attest_storage":"https://pith.science/pith/MCLM4SJXQWYT2PSDESLQLDDPRG/action/storage_attestation","attest_author":"https://pith.science/pith/MCLM4SJXQWYT2PSDESLQLDDPRG/action/author_attestation","sign_citation":"https://pith.science/pith/MCLM4SJXQWYT2PSDESLQLDDPRG/action/citation_signature","submit_replication":"https://pith.science/pith/MCLM4SJXQWYT2PSDESLQLDDPRG/action/replication_record"}},"created_at":"2026-07-05T03:09:16.689715+00:00","updated_at":"2026-07-05T03:09:16.689715+00:00"}