{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2017:WWR6IGB673NJVXOZG2EP37DZIW","short_pith_number":"pith:WWR6IGB6","schema_version":"1.0","canonical_sha256":"b5a3e4183efeda9addd93688fdfc7945a79aa4c81917a96b8ece7de87a090ca3","source":{"kind":"arxiv","id":"1705.01434","version":3},"attestation_state":"computed","paper":{"title":"Collapsing limits of the K\\\"ahler-Ricci flow and the continuity method","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DG","authors_text":"Yashan Zhang","submitted_at":"2017-05-03T13:55:50Z","abstract_excerpt":"We consider the K\\\"ahler-Ricci flow on certain Calabi-Yau fibration, which is a Calabi-Yau fibration with one dimensional base or a product of two Calabi-Yau fibrations with one dimensional bases. Assume the K\\\"ahler-Ricci flow on total space admits a uniform lower bound for Ricci curvature, then the flow converges in Gromov-Hausdorff topology to the metric completion of the regular part of generalized K\\\"ahler-Einstein current on the base, which is a compact length metric space homeomorphic to the base. The analogue results for the continuity method on such Calabi-Yau fibrations are also obta"},"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":"1705.01434","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2017-05-03T13:55:50Z","cross_cats_sorted":[],"title_canon_sha256":"570e7fb739dc944dcb1421cfd37f92e822b57b5a9af91d1c995de83d3dbea407","abstract_canon_sha256":"833a87581e999ef5a7744e46a1f611433e0b7f86712876a20fecdc7c57854773"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:17:54.773027Z","signature_b64":"oSRUgPkePocDrY9IiCQKaQp9r+ekoHj+txv35o6dXJA/H8MPMa/wUukHE2ksCbHWbjotU3XjpOjJ1zrL+/wvDw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"b5a3e4183efeda9addd93688fdfc7945a79aa4c81917a96b8ece7de87a090ca3","last_reissued_at":"2026-05-18T00:17:54.772337Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:17:54.772337Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Collapsing limits of the K\\\"ahler-Ricci flow and the continuity method","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DG","authors_text":"Yashan Zhang","submitted_at":"2017-05-03T13:55:50Z","abstract_excerpt":"We consider the K\\\"ahler-Ricci flow on certain Calabi-Yau fibration, which is a Calabi-Yau fibration with one dimensional base or a product of two Calabi-Yau fibrations with one dimensional bases. Assume the K\\\"ahler-Ricci flow on total space admits a uniform lower bound for Ricci curvature, then the flow converges in Gromov-Hausdorff topology to the metric completion of the regular part of generalized K\\\"ahler-Einstein current on the base, which is a compact length metric space homeomorphic to the base. The analogue results for the continuity method on such Calabi-Yau fibrations are also obta"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1705.01434","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":""},"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":"1705.01434","created_at":"2026-05-18T00:17:54.772444+00:00"},{"alias_kind":"arxiv_version","alias_value":"1705.01434v3","created_at":"2026-05-18T00:17:54.772444+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1705.01434","created_at":"2026-05-18T00:17:54.772444+00:00"},{"alias_kind":"pith_short_12","alias_value":"WWR6IGB673NJ","created_at":"2026-05-18T12:31:53.515858+00:00"},{"alias_kind":"pith_short_16","alias_value":"WWR6IGB673NJVXOZ","created_at":"2026-05-18T12:31:53.515858+00:00"},{"alias_kind":"pith_short_8","alias_value":"WWR6IGB6","created_at":"2026-05-18T12:31:53.515858+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/WWR6IGB673NJVXOZG2EP37DZIW","json":"https://pith.science/pith/WWR6IGB673NJVXOZG2EP37DZIW.json","graph_json":"https://pith.science/api/pith-number/WWR6IGB673NJVXOZG2EP37DZIW/graph.json","events_json":"https://pith.science/api/pith-number/WWR6IGB673NJVXOZG2EP37DZIW/events.json","paper":"https://pith.science/paper/WWR6IGB6"},"agent_actions":{"view_html":"https://pith.science/pith/WWR6IGB673NJVXOZG2EP37DZIW","download_json":"https://pith.science/pith/WWR6IGB673NJVXOZG2EP37DZIW.json","view_paper":"https://pith.science/paper/WWR6IGB6","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1705.01434&json=true","fetch_graph":"https://pith.science/api/pith-number/WWR6IGB673NJVXOZG2EP37DZIW/graph.json","fetch_events":"https://pith.science/api/pith-number/WWR6IGB673NJVXOZG2EP37DZIW/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/WWR6IGB673NJVXOZG2EP37DZIW/action/timestamp_anchor","attest_storage":"https://pith.science/pith/WWR6IGB673NJVXOZG2EP37DZIW/action/storage_attestation","attest_author":"https://pith.science/pith/WWR6IGB673NJVXOZG2EP37DZIW/action/author_attestation","sign_citation":"https://pith.science/pith/WWR6IGB673NJVXOZG2EP37DZIW/action/citation_signature","submit_replication":"https://pith.science/pith/WWR6IGB673NJVXOZG2EP37DZIW/action/replication_record"}},"created_at":"2026-05-18T00:17:54.772444+00:00","updated_at":"2026-05-18T00:17:54.772444+00:00"}