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In this article, we address the following question: If $ g $ is a Riemannian metric having (i) positive scalar curvature (PSC metric) on $ M $ and nonnegative mean curvature on $ \\partial M $; and (ii) the $ g $-angle between normal vector field $ \\nu_{g} $ along $ \\partial M $ and $ \\partial_{\\xi} \\in \\Gamma(TI) $ being less than $ \\frac{\\pi}{4} $, then there exists a met"},"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":"2507.07005","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2025-07-09T16:35:06Z","cross_cats_sorted":[],"title_canon_sha256":"dce8c54b5b428968821c254a1aa2ab9d88dd87a6d0ccdb745a40b6e7e1028083","abstract_canon_sha256":"1c25e5749f679895beea639bfb4c098eda84872db889bd4119673a873243ff76"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T11:34:27.574472Z","signature_b64":"VYH4yEc6POkrtwdZzVwESp4cpMw+7CfzGIGNHmMfKZsRFdCEETX1HXWUH8i1K/UE7UPkyuwp4q55eTq7w1DdAw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"4d3812911b545145e661575efe5f0276fdb597f1f304d44c628a924ee5d9f9a7","last_reissued_at":"2026-07-05T11:34:27.573982Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T11:34:27.573982Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Scalar and Mean Curvature Comparison on Compact Cylinder","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DG","authors_text":"Jie Xu","submitted_at":"2025-07-09T16:35:06Z","abstract_excerpt":"Let $ X $ be a closed, oriented Riemannian manifold. Denote by $ (M = X \\times I, \\partial M = X \\times \\lbrace 0 \\rbrace \\cup X \\times \\lbrace 1 \\rbrace, g) $ a compact cylinder with smooth boundary, $ \\dim M \\geqslant 3 $. 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