{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2019:TE2WVGJ4W43DEROTDUCIYE7K5W","short_pith_number":"pith:TE2WVGJ4","schema_version":"1.0","canonical_sha256":"99356a993cb7363245d31d048c13eaeda703fd1ddf9133fbf30c6c9d49c880e3","source":{"kind":"arxiv","id":"1907.05399","version":3},"attestation_state":"computed","paper":{"title":"Optimal destabilization of K-unstable Fano varieties via stability thresholds","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.DG"],"primary_cat":"math.AG","authors_text":"Chuyu Zhou, Harold Blum, Yuchen Liu","submitted_at":"2019-07-11T17:26:41Z","abstract_excerpt":"We show that for a K-unstable Fano variety, any divisorial valuation computing its stability threshold induces a non-trivial special test configuration preserving the stability threshold. When such a divisorial valuation exists, we show that the Fano variety degenerates to a uniquely determined twisted K-polystable Fano variety. We also show that the stability threshold can be approximated by divisorial valuations induced by special test configurations. As an application of the above results and the analytic work of Datar, Sz\\'ekelyhidi, and Ross, we deduce that greatest Ricci lower bounds of "},"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":"1907.05399","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2019-07-11T17:26:41Z","cross_cats_sorted":["math.DG"],"title_canon_sha256":"5b0e7992fe7c6013b1f56b2fd367e5061b76bf9779101c9def35381f55655848","abstract_canon_sha256":"03b9c40765379f016f0ede88b1d8a88429c362a52ab335cacbda57501c6fc595"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T05:26:31.064701Z","signature_b64":"flxoran3qT0Rjn2jXQlBEyOL9Ngpgup9qdJED2QsyxqOyKVWj7GNQ3R+vm0rzOLUbBjmUA/JI7bRMfOmVnF4Bg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"99356a993cb7363245d31d048c13eaeda703fd1ddf9133fbf30c6c9d49c880e3","last_reissued_at":"2026-07-05T05:26:31.064241Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T05:26:31.064241Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Optimal destabilization of K-unstable Fano varieties via stability thresholds","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.DG"],"primary_cat":"math.AG","authors_text":"Chuyu Zhou, Harold Blum, Yuchen Liu","submitted_at":"2019-07-11T17:26:41Z","abstract_excerpt":"We show that for a K-unstable Fano variety, any divisorial valuation computing its stability threshold induces a non-trivial special test configuration preserving the stability threshold. When such a divisorial valuation exists, we show that the Fano variety degenerates to a uniquely determined twisted K-polystable Fano variety. We also show that the stability threshold can be approximated by divisorial valuations induced by special test configurations. As an application of the above results and the analytic work of Datar, Sz\\'ekelyhidi, and Ross, we deduce that greatest Ricci lower bounds of "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1907.05399","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/1907.05399/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":"1907.05399","created_at":"2026-07-05T05:26:31.064303+00:00"},{"alias_kind":"arxiv_version","alias_value":"1907.05399v3","created_at":"2026-07-05T05:26:31.064303+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1907.05399","created_at":"2026-07-05T05:26:31.064303+00:00"},{"alias_kind":"pith_short_12","alias_value":"TE2WVGJ4W43D","created_at":"2026-07-05T05:26:31.064303+00:00"},{"alias_kind":"pith_short_16","alias_value":"TE2WVGJ4W43DEROT","created_at":"2026-07-05T05:26:31.064303+00:00"},{"alias_kind":"pith_short_8","alias_value":"TE2WVGJ4","created_at":"2026-07-05T05:26:31.064303+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/TE2WVGJ4W43DEROTDUCIYE7K5W","json":"https://pith.science/pith/TE2WVGJ4W43DEROTDUCIYE7K5W.json","graph_json":"https://pith.science/api/pith-number/TE2WVGJ4W43DEROTDUCIYE7K5W/graph.json","events_json":"https://pith.science/api/pith-number/TE2WVGJ4W43DEROTDUCIYE7K5W/events.json","paper":"https://pith.science/paper/TE2WVGJ4"},"agent_actions":{"view_html":"https://pith.science/pith/TE2WVGJ4W43DEROTDUCIYE7K5W","download_json":"https://pith.science/pith/TE2WVGJ4W43DEROTDUCIYE7K5W.json","view_paper":"https://pith.science/paper/TE2WVGJ4","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1907.05399&json=true","fetch_graph":"https://pith.science/api/pith-number/TE2WVGJ4W43DEROTDUCIYE7K5W/graph.json","fetch_events":"https://pith.science/api/pith-number/TE2WVGJ4W43DEROTDUCIYE7K5W/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/TE2WVGJ4W43DEROTDUCIYE7K5W/action/timestamp_anchor","attest_storage":"https://pith.science/pith/TE2WVGJ4W43DEROTDUCIYE7K5W/action/storage_attestation","attest_author":"https://pith.science/pith/TE2WVGJ4W43DEROTDUCIYE7K5W/action/author_attestation","sign_citation":"https://pith.science/pith/TE2WVGJ4W43DEROTDUCIYE7K5W/action/citation_signature","submit_replication":"https://pith.science/pith/TE2WVGJ4W43DEROTDUCIYE7K5W/action/replication_record"}},"created_at":"2026-07-05T05:26:31.064303+00:00","updated_at":"2026-07-05T05:26:31.064303+00:00"}