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We unify the concepts of $F$-harmonic maps, minimal hypersurfaces, maximal spacelike hypersurfaces, and Yang-Mills Fields, and introduce $F$-Yang-Mills fields, $F$-degree, $F$-lower degree, and generalized Yang-Mills-Born-Infeld fields (with the plus sign or with the minus sign) on manifolds. When $F(t)=t, \\frac 1p(2t)^{\\frac p2}, \\sqrt{1+2t} -1,$ and $1-\\sqrt{1-2t},$ the $F$-Yang-Mills field becomes an ordinary Yang-Mills field, $p$-Yang-Mills field, a generalized Yang-Mills-Born-Infeld field with the "},"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":"1003.3777","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2010-03-19T11:53:25Z","cross_cats_sorted":["math-ph","math.AP","math.MP"],"title_canon_sha256":"032d804f617dbc38e5c6b959aa79aaa317ef29e5755af02ad5a5b61a339d992b","abstract_canon_sha256":"ef2bf9961110d63a3c01907284ca3f051c674ec9474f7bbe074f8be618aaf8d2"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:08:25.402169Z","signature_b64":"keGS6TToIkQJLLlSxF+y5IalXQ5DWa+dQJt6NnAauxbNd70jBSFZiE3vJurhcYTO49II9iwX8lT1G/UCANWjDw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"00db11d4b71a4559309355afd788eb03c847fddcd75b0bd7232c3b6395974970","last_reissued_at":"2026-05-18T02:08:25.401297Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:08:25.401297Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"On Vanishing Theorems For Vector Bundle Valued p-Forms And Their Applications","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.AP","math.MP"],"primary_cat":"math.DG","authors_text":"Shihshu Walter Wei, Yuxin Dong","submitted_at":"2010-03-19T11:53:25Z","abstract_excerpt":"Let $F: [0, \\infty) \\to [0, \\infty)$ be a strictly increasing $C^2$ function with $F(0)=0$. 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