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Let $E$ be a holomorphic vector bundle over a compact K\\\"ahler manifold $(M,\\omega_g)$.\n  Suppose that for every proper coherent subsheaf $F\\subset E$, the following inequality holds:\n  $$\n  deg_{\\omega_g}(F)<deg_{\\omega_g}(E).\n  $$\n  Then, for any initial Hermitian metric $h_0$ on $E$ and any positive-definite Hermitian tensor $P\\in \\Gamma(M,E^*\\otimes \\overline E^*)$, the prescribed Hermitian-Yang-Mills flow\n  $$ \\ \\frac{\\partial h}{\\partial t} = -\\Lambda_{\\omega_g}\\left(\\"},"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":"2606.21073","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/publicdomain/zero/1.0/","primary_cat":"math.DG","submitted_at":"2026-06-19T03:41:33Z","cross_cats_sorted":[],"title_canon_sha256":"55d4268247f9e4a03c3cecc7e1a317539fc55fa54036eb968cd20b5fec233f76","abstract_canon_sha256":"8b721a3635195a529ab3784e9fe6b163794b5724f6f6af099f5b716bce723549"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-06-23T01:12:28.972644Z","signature_b64":"rVSD5dbH59yyiMR9oRInDp8sEkKlLcbvIwpdCvYnb9zoHISOopYj0ps3hPXpN1WOHuaYtReO+RHewv4mkVu8Dg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"528f53bda975c8f22110f747969a1f9e89adfc6d6591efde03214e71fde21a12","last_reissued_at":"2026-06-23T01:12:28.972181Z","signature_status":"signed_v1","first_computed_at":"2026-06-23T01:12:28.972181Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"The prescribed Hermitian-Yang-Mills flow II","license":"http://creativecommons.org/publicdomain/zero/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DG","authors_text":"Shing-Tung Yau, Xiaokui Yang, Zhiyao Xiong","submitted_at":"2026-06-19T03:41:33Z","abstract_excerpt":"We prove an analogue of the classical Donaldson-Uhlenbeck-Yau theorem by using the prescribed Hermitian-Yang-Mills flow. 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