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If $\\Sigma$ is strictly stable, then, in a sufficiently small free-boundary adapted tubular neighborhood $K_r$, the relative cycle $\\llbracket\\Sigma\\rrbracket$ is the unique mass minimizer in its relative $\\mathbb Z_2$-homology class in $(K_r,K_r\\cap\\partial N)$.\n  We further prove a relative flat-neighborhood version, and"},"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":"2605.25585","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2026-05-25T08:34:58Z","cross_cats_sorted":[],"title_canon_sha256":"cd2ff0fde64d168ff667f0a56deaef3204de9cfac2c51e0851a015114d528a14","abstract_canon_sha256":"6ebca1241d6d17c9d35495710a1f1af1aebb8d4c7d5a393ae1099e8e5d0b9c6f"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-26T02:04:44.313516Z","signature_b64":"UvlUfPINyfxZsPTCR+c1J1BjKlEev0HOvdie8IchnUxNMZHjGYi1RMYwUPQKz615fYNx2fqqmMlrajWrefxZCQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"37143c9b02c32b0662f3e105a68a8bf509735308b45a78ebcfa7dcd904a85445","last_reissued_at":"2026-05-26T02:04:44.312657Z","signature_status":"signed_v1","first_computed_at":"2026-05-26T02:04:44.312657Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"A Local Minimizing Property of Strictly Stable Free Boundary Minimal Hypersurfaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DG","authors_text":"Hangyue Zhu, Xiaoxiang Jiao","submitted_at":"2026-05-25T08:34:58Z","abstract_excerpt":"We prove a local minimizing property for strictly stable free-boundary minimal hypersurfaces in the relative current setting. 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