{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2019:WRU33AFCG374IIYYPFQNU7FL3J","short_pith_number":"pith:WRU33AFC","schema_version":"1.0","canonical_sha256":"b469bd80a236ffc423187960da7cabda7f0934562e74255ad270d59ba3f0f65d","source":{"kind":"arxiv","id":"1907.02408","version":3},"attestation_state":"computed","paper":{"title":"Openness of K-semistability for Fano varieties","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.DG"],"primary_cat":"math.AG","authors_text":"Chenyang Xu, Harold Blum, Yuchen Liu","submitted_at":"2019-07-04T14:03:37Z","abstract_excerpt":"In this paper, we prove the openness of K-semistability in families of log Fano pairs by showing that the stability threshold is a constructible function on the fibers. We also prove that any special test configuration arises from a log canonical place of a bounded complement and establish properties of any minimizer of the stability threshold."},"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":"1907.02408","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2019-07-04T14:03:37Z","cross_cats_sorted":["math.DG"],"title_canon_sha256":"c92b4e0b404998d495c04a5e2285fa02aab2152250e19881b2a9a7ff97e5c275","abstract_canon_sha256":"db8dce85e3d6de7beaa5dcd36a0ad73daaef3670583743246271571ff599cf8f"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T03:27:24.032501Z","signature_b64":"5OSOEmw3f3kOtnaMBFZguqF/flWHJvS/7/veaVSW/Q4MPnAF94hkBw8xc3g65RGuDVBTPbx3m1DS7JRpr5eMDg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"b469bd80a236ffc423187960da7cabda7f0934562e74255ad270d59ba3f0f65d","last_reissued_at":"2026-07-05T03:27:24.032112Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T03:27:24.032112Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Openness of K-semistability for Fano varieties","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.DG"],"primary_cat":"math.AG","authors_text":"Chenyang Xu, Harold Blum, Yuchen Liu","submitted_at":"2019-07-04T14:03:37Z","abstract_excerpt":"In this paper, we prove the openness of K-semistability in families of log Fano pairs by showing that the stability threshold is a constructible function on the fibers. We also prove that any special test configuration arises from a log canonical place of a bounded complement and establish properties of any minimizer of the stability threshold."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1907.02408","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/1907.02408/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":"1907.02408","created_at":"2026-07-05T03:27:24.032169+00:00"},{"alias_kind":"arxiv_version","alias_value":"1907.02408v3","created_at":"2026-07-05T03:27:24.032169+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1907.02408","created_at":"2026-07-05T03:27:24.032169+00:00"},{"alias_kind":"pith_short_12","alias_value":"WRU33AFCG374","created_at":"2026-07-05T03:27:24.032169+00:00"},{"alias_kind":"pith_short_16","alias_value":"WRU33AFCG374IIYY","created_at":"2026-07-05T03:27:24.032169+00:00"},{"alias_kind":"pith_short_8","alias_value":"WRU33AFC","created_at":"2026-07-05T03:27:24.032169+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/WRU33AFCG374IIYYPFQNU7FL3J","json":"https://pith.science/pith/WRU33AFCG374IIYYPFQNU7FL3J.json","graph_json":"https://pith.science/api/pith-number/WRU33AFCG374IIYYPFQNU7FL3J/graph.json","events_json":"https://pith.science/api/pith-number/WRU33AFCG374IIYYPFQNU7FL3J/events.json","paper":"https://pith.science/paper/WRU33AFC"},"agent_actions":{"view_html":"https://pith.science/pith/WRU33AFCG374IIYYPFQNU7FL3J","download_json":"https://pith.science/pith/WRU33AFCG374IIYYPFQNU7FL3J.json","view_paper":"https://pith.science/paper/WRU33AFC","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1907.02408&json=true","fetch_graph":"https://pith.science/api/pith-number/WRU33AFCG374IIYYPFQNU7FL3J/graph.json","fetch_events":"https://pith.science/api/pith-number/WRU33AFCG374IIYYPFQNU7FL3J/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/WRU33AFCG374IIYYPFQNU7FL3J/action/timestamp_anchor","attest_storage":"https://pith.science/pith/WRU33AFCG374IIYYPFQNU7FL3J/action/storage_attestation","attest_author":"https://pith.science/pith/WRU33AFCG374IIYYPFQNU7FL3J/action/author_attestation","sign_citation":"https://pith.science/pith/WRU33AFCG374IIYYPFQNU7FL3J/action/citation_signature","submit_replication":"https://pith.science/pith/WRU33AFCG374IIYYPFQNU7FL3J/action/replication_record"}},"created_at":"2026-07-05T03:27:24.032169+00:00","updated_at":"2026-07-05T03:27:24.032169+00:00"}