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We establish the long-time convergence of the flow to a limiting metric $h_{\\infty}$ and use it to solve the prescribed Hermitian-Yang-Mills tensor equation\n  $$\\Lambda_{\\omega_g}\\left(\\sqrt R^{h_\\infty}\\right)=P,\n  $$\n  for a general "},"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":"2606.21062","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/publicdomain/zero/1.0/","primary_cat":"math.DG","submitted_at":"2026-06-19T03:21:33Z","cross_cats_sorted":[],"title_canon_sha256":"ab983bab24bf61bbbd2132da9fa7e88bf5c9bcb0c992bf5b61406f0d26f44cba","abstract_canon_sha256":"673233c41194d17b7611eaa99515d34d29913de4974045b18e0963784a505acd"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-06-23T01:12:28.645484Z","signature_b64":"/UjNt1miuZSh9A+vGIpO7+W3WKWjjw3yTJECIFwW5SLL98S9l37kBW6LMrL2VkThWdqMBTVJ0y+pVYvjgoJqDA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"fff4daa479ce7f76718badb35590af18a8c4b609d5149039b54a99c6282be01b","last_reissued_at":"2026-06-23T01:12:28.644989Z","signature_status":"signed_v1","first_computed_at":"2026-06-23T01:12:28.644989Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"The prescribed Hermitian-Yang-Mills flow I","license":"http://creativecommons.org/publicdomain/zero/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DG","authors_text":"Shing-Tung Yau, Xaokui Yang, Zhiyao Xiong","submitted_at":"2026-06-19T03:21:33Z","abstract_excerpt":"In this paper, we introduce a broad class of flows, including the prescribed Hermitian-Yang-Mills flow:\n  $$\\frac{\\partial h}{\\partial t}=-\\Lambda_{\\omega_g}\\left(\\sqrt R^h\\right)+P$$\n  where $P\\in\\Gamma(M,E^*\\otimes\\bar{E}^*)$ is a prescribed Hermitian tensor associated with a holomorphic vector bundle $E$ over a K\\\"ahler (or Hermitian) manifold $(M,\\omega_g)$. We establish the long-time convergence of the flow to a limiting metric $h_{\\infty}$ and use it to solve the prescribed Hermitian-Yang-Mills tensor equation\n  $$\\Lambda_{\\omega_g}\\left(\\sqrt R^{h_\\infty}\\right)=P,\n  $$\n  for a general "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2606.21062","kind":"arxiv","version":1},"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/2606.21062/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":"2606.21062","created_at":"2026-06-23T01:12:28.645065+00:00"},{"alias_kind":"arxiv_version","alias_value":"2606.21062v1","created_at":"2026-06-23T01:12:28.645065+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2606.21062","created_at":"2026-06-23T01:12:28.645065+00:00"},{"alias_kind":"pith_short_12","alias_value":"772NVJDZZZ7X","created_at":"2026-06-23T01:12:28.645065+00:00"},{"alias_kind":"pith_short_16","alias_value":"772NVJDZZZ7XM4ML","created_at":"2026-06-23T01:12:28.645065+00:00"},{"alias_kind":"pith_short_8","alias_value":"772NVJDZ","created_at":"2026-06-23T01:12:28.645065+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":1,"internal_anchor_count":1,"sample":[{"citing_arxiv_id":"2606.30121","citing_title":"Iterative construction of Hermitian-Einstein metrics on stable bundles","ref_index":14,"is_internal_anchor":true}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/772NVJDZZZ7XM4MLVWZVLEFPDC","json":"https://pith.science/pith/772NVJDZZZ7XM4MLVWZVLEFPDC.json","graph_json":"https://pith.science/api/pith-number/772NVJDZZZ7XM4MLVWZVLEFPDC/graph.json","events_json":"https://pith.science/api/pith-number/772NVJDZZZ7XM4MLVWZVLEFPDC/events.json","paper":"https://pith.science/paper/772NVJDZ"},"agent_actions":{"view_html":"https://pith.science/pith/772NVJDZZZ7XM4MLVWZVLEFPDC","download_json":"https://pith.science/pith/772NVJDZZZ7XM4MLVWZVLEFPDC.json","view_paper":"https://pith.science/paper/772NVJDZ","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2606.21062&json=true","fetch_graph":"https://pith.science/api/pith-number/772NVJDZZZ7XM4MLVWZVLEFPDC/graph.json","fetch_events":"https://pith.science/api/pith-number/772NVJDZZZ7XM4MLVWZVLEFPDC/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/772NVJDZZZ7XM4MLVWZVLEFPDC/action/timestamp_anchor","attest_storage":"https://pith.science/pith/772NVJDZZZ7XM4MLVWZVLEFPDC/action/storage_attestation","attest_author":"https://pith.science/pith/772NVJDZZZ7XM4MLVWZVLEFPDC/action/author_attestation","sign_citation":"https://pith.science/pith/772NVJDZZZ7XM4MLVWZVLEFPDC/action/citation_signature","submit_replication":"https://pith.science/pith/772NVJDZZZ7XM4MLVWZVLEFPDC/action/replication_record"}},"created_at":"2026-06-23T01:12:28.645065+00:00","updated_at":"2026-06-23T01:12:28.645065+00:00"}