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Next, we point out that the $L^\\infty$ bound on Ricci curvature is an obstruction to the extension of the pseudo-Calabi flow. Finally, we show that if there is a cscK metric in its K\\\"ahler class, then for any initial potential in a small $C^"},"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":"1004.2663","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2010-04-15T16:22:05Z","cross_cats_sorted":["math.AP"],"title_canon_sha256":"5e398b28a8882857a2d366d9ed17541fb5fc6ad60ed37115358fecda55873a80","abstract_canon_sha256":"e928c51c96d25941ac3ec8891bd3dacad2b9326cc3c175a460e35ae56dc0d488"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:31:31.181831Z","signature_b64":"L0ZbztL0LyLBiDNre1TuVUTPZGFBC11FSBwZVCAHnEFB3YlQEYGbC3pOw4YYTTrgJBrraKgVWryoHPeckCA5CA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"1d516acffa952419299ec516f982110ebe465b340841bf54cf85132b243d280b","last_reissued_at":"2026-05-18T03:31:31.181424Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:31:31.181424Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Pseudo-Calabi Flow","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AP"],"primary_cat":"math.DG","authors_text":"Kai Zheng, Xiuxiong Chen","submitted_at":"2010-04-15T16:22:05Z","abstract_excerpt":"We first define Pseudo-Calabi flow, as {equation*}\n  {{aligned}{{\\partial \\varphi}\\over {\\partial t}}&= -f(\\varphi), \\triangle_varphi f(\\varphi) &= S(\\varphi) - \\ul S.{aligned}. \\end{equation*} Then we prove the well-posedness of this flow including the short time existence, the regularity of the solution and the continuous dependence on the initial data. Next, we point out that the $L^\\infty$ bound on Ricci curvature is an obstruction to the extension of the pseudo-Calabi flow. Finally, we show that if there is a cscK metric in its K\\\"ahler class, then for any initial potential in a small $C^"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1004.2663","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":"1004.2663","created_at":"2026-05-18T03:31:31.181480+00:00"},{"alias_kind":"arxiv_version","alias_value":"1004.2663v3","created_at":"2026-05-18T03:31:31.181480+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1004.2663","created_at":"2026-05-18T03:31:31.181480+00:00"},{"alias_kind":"pith_short_12","alias_value":"DVIWVT72SUSB","created_at":"2026-05-18T12:26:06.534383+00:00"},{"alias_kind":"pith_short_16","alias_value":"DVIWVT72SUSBSKM6","created_at":"2026-05-18T12:26:06.534383+00:00"},{"alias_kind":"pith_short_8","alias_value":"DVIWVT72","created_at":"2026-05-18T12:26:06.534383+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/DVIWVT72SUSBSKM6YULPTAQRB2","json":"https://pith.science/pith/DVIWVT72SUSBSKM6YULPTAQRB2.json","graph_json":"https://pith.science/api/pith-number/DVIWVT72SUSBSKM6YULPTAQRB2/graph.json","events_json":"https://pith.science/api/pith-number/DVIWVT72SUSBSKM6YULPTAQRB2/events.json","paper":"https://pith.science/paper/DVIWVT72"},"agent_actions":{"view_html":"https://pith.science/pith/DVIWVT72SUSBSKM6YULPTAQRB2","download_json":"https://pith.science/pith/DVIWVT72SUSBSKM6YULPTAQRB2.json","view_paper":"https://pith.science/paper/DVIWVT72","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1004.2663&json=true","fetch_graph":"https://pith.science/api/pith-number/DVIWVT72SUSBSKM6YULPTAQRB2/graph.json","fetch_events":"https://pith.science/api/pith-number/DVIWVT72SUSBSKM6YULPTAQRB2/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/DVIWVT72SUSBSKM6YULPTAQRB2/action/timestamp_anchor","attest_storage":"https://pith.science/pith/DVIWVT72SUSBSKM6YULPTAQRB2/action/storage_attestation","attest_author":"https://pith.science/pith/DVIWVT72SUSBSKM6YULPTAQRB2/action/author_attestation","sign_citation":"https://pith.science/pith/DVIWVT72SUSBSKM6YULPTAQRB2/action/citation_signature","submit_replication":"https://pith.science/pith/DVIWVT72SUSBSKM6YULPTAQRB2/action/replication_record"}},"created_at":"2026-05-18T03:31:31.181480+00:00","updated_at":"2026-05-18T03:31:31.181480+00:00"}