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We prove that the one-parameter subgroups of $\\mathcal{U}(n)$ are the optimal paths, provided the spectrum of the exponent is bounded by $\\pi$. Moreover, if L is strictly convex, we prove that one-parameter subgroups are the unique optimal curves"},"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":"1107.2439","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2011-07-13T00:10:45Z","cross_cats_sorted":["math.FA"],"title_canon_sha256":"7676e86facb3b32ceb35846f3a3c27c2fb4dd500b2fe622a3baf9d004005efeb","abstract_canon_sha256":"de485ac7177fc69db45f78eac4dcb23f1bc3829842c24295099530bab2ce47dd"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:18:23.010970Z","signature_b64":"5hngbo+65bgU6lplptFZqDBzOYNI0Ce1s20pc3i9NjQw+YbTWy+FgzbEXpmII/IgWo3G2zTxBBZulPIh9gz5BQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"10760e942e1b935d5dc600a357dde6692bb4b0cd5f2030d2504de2b8b7551aa5","last_reissued_at":"2026-05-18T04:18:23.010516Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:18:23.010516Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Optimal paths for symmetric actions in the unitary group","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.FA"],"primary_cat":"math.DG","authors_text":"Alejandro Varela, Gabriel Larotonda, Jorge Antezana","submitted_at":"2011-07-13T00:10:45Z","abstract_excerpt":"Given a positive and unitarily invariant Lagrangian L defined in the algebra of Hermitian matrices, and a fixed interval $[a,b]\\subset\\mathbb R$, we study the action defined in the Lie group of $n\\times n$ unitary matrices $\\mathcal{U}(n)$ by $$ S(\\alpha)=\\int_a^b L(\\dot\\alpha(t))\\,dt\\,, $$ where $\\alpha:[a,b]\\to\\mathcal{U}(n)$ is a rectifiable curve. We prove that the one-parameter subgroups of $\\mathcal{U}(n)$ are the optimal paths, provided the spectrum of the exponent is bounded by $\\pi$. 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