{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2023:ISQYUKGVWPEEGQZZDPPRQVJQCB","short_pith_number":"pith:ISQYUKGV","schema_version":"1.0","canonical_sha256":"44a18a28d5b3c84343391bdf185530106e56290ac448bd1341459f7c2a1d50f0","source":{"kind":"arxiv","id":"2312.13653","version":3},"attestation_state":"computed","paper":{"title":"Singular cscK metrics on smoothable varieties","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AG","math.AP","math.DG"],"primary_cat":"math.CV","authors_text":"Antonio Trusiani, Chung-Ming Pan, Tat Dat T\\^o","submitted_at":"2023-12-21T08:26:59Z","abstract_excerpt":"We prove the lower semi-continuity of the coercivity threshold of Mabuchi functional along a degenerate family of normal compact K\\\"ahler varieties with klt singularities. Moreover, we establish the existence of singular cscK metrics on $\\mathbb{Q}$-Gorenstein smoothable klt varieties when the Mabuchi functional is coercive, these arise as a limit of cscK metrics on close-by fibres. The proof relies on developing a novel strong topology of pluripotential theory in families and establishing uniform estimates for cscK metrics."},"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":"2312.13653","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CV","submitted_at":"2023-12-21T08:26:59Z","cross_cats_sorted":["math.AG","math.AP","math.DG"],"title_canon_sha256":"4fc311a7c994a7e4fcb98b49d9d23acd1296c023be950054695c06d7ee0e3c30","abstract_canon_sha256":"fcf409a48f39bd4f121f81f493aa200efbf66e329d803b0606d24632098dc53a"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T11:23:14.962629Z","signature_b64":"lxDpSqL8eDGG0rEaP8+IOEVOtBpuQrC5M9WGrk5VUV4F34yW+xysewjobfzUWHvopWcFc8jN++ZY89T8DayHDw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"44a18a28d5b3c84343391bdf185530106e56290ac448bd1341459f7c2a1d50f0","last_reissued_at":"2026-07-05T11:23:14.962109Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T11:23:14.962109Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Singular cscK metrics on smoothable varieties","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AG","math.AP","math.DG"],"primary_cat":"math.CV","authors_text":"Antonio Trusiani, Chung-Ming Pan, Tat Dat T\\^o","submitted_at":"2023-12-21T08:26:59Z","abstract_excerpt":"We prove the lower semi-continuity of the coercivity threshold of Mabuchi functional along a degenerate family of normal compact K\\\"ahler varieties with klt singularities. Moreover, we establish the existence of singular cscK metrics on $\\mathbb{Q}$-Gorenstein smoothable klt varieties when the Mabuchi functional is coercive, these arise as a limit of cscK metrics on close-by fibres. The proof relies on developing a novel strong topology of pluripotential theory in families and establishing uniform estimates for cscK metrics."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2312.13653","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/2312.13653/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":"2312.13653","created_at":"2026-07-05T11:23:14.962169+00:00"},{"alias_kind":"arxiv_version","alias_value":"2312.13653v3","created_at":"2026-07-05T11:23:14.962169+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2312.13653","created_at":"2026-07-05T11:23:14.962169+00:00"},{"alias_kind":"pith_short_12","alias_value":"ISQYUKGVWPEE","created_at":"2026-07-05T11:23:14.962169+00:00"},{"alias_kind":"pith_short_16","alias_value":"ISQYUKGVWPEEGQZZ","created_at":"2026-07-05T11:23:14.962169+00:00"},{"alias_kind":"pith_short_8","alias_value":"ISQYUKGV","created_at":"2026-07-05T11:23:14.962169+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":1,"internal_anchor_count":0,"sample":[{"citing_arxiv_id":"2606.02816","citing_title":"On the geometry of non-collapsed polarized cscK surfaces","ref_index":94,"is_internal_anchor":false}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/ISQYUKGVWPEEGQZZDPPRQVJQCB","json":"https://pith.science/pith/ISQYUKGVWPEEGQZZDPPRQVJQCB.json","graph_json":"https://pith.science/api/pith-number/ISQYUKGVWPEEGQZZDPPRQVJQCB/graph.json","events_json":"https://pith.science/api/pith-number/ISQYUKGVWPEEGQZZDPPRQVJQCB/events.json","paper":"https://pith.science/paper/ISQYUKGV"},"agent_actions":{"view_html":"https://pith.science/pith/ISQYUKGVWPEEGQZZDPPRQVJQCB","download_json":"https://pith.science/pith/ISQYUKGVWPEEGQZZDPPRQVJQCB.json","view_paper":"https://pith.science/paper/ISQYUKGV","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2312.13653&json=true","fetch_graph":"https://pith.science/api/pith-number/ISQYUKGVWPEEGQZZDPPRQVJQCB/graph.json","fetch_events":"https://pith.science/api/pith-number/ISQYUKGVWPEEGQZZDPPRQVJQCB/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/ISQYUKGVWPEEGQZZDPPRQVJQCB/action/timestamp_anchor","attest_storage":"https://pith.science/pith/ISQYUKGVWPEEGQZZDPPRQVJQCB/action/storage_attestation","attest_author":"https://pith.science/pith/ISQYUKGVWPEEGQZZDPPRQVJQCB/action/author_attestation","sign_citation":"https://pith.science/pith/ISQYUKGVWPEEGQZZDPPRQVJQCB/action/citation_signature","submit_replication":"https://pith.science/pith/ISQYUKGVWPEEGQZZDPPRQVJQCB/action/replication_record"}},"created_at":"2026-07-05T11:23:14.962169+00:00","updated_at":"2026-07-05T11:23:14.962169+00:00"}