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But a precise measurement for $\\theta^{}_{23}$ and $\\delta$ will probably force us to modify the neutrino mixing $U^{(0)}$ from such a symmetry. Here we perform a study for modifications to $U^{(0)}$ in the forms of $U^{(1)\\dagger} U^{(0)}$ and $U^{(0)} U^{(1)}$ where $U^{(1)}= R^{(1)}_{ij}$ (for $ij = 12, 23$ and 13) with $R^{(1)}_{ij}$ deno"},"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":"1803.04603","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-ph","submitted_at":"2018-03-13T02:50:19Z","cross_cats_sorted":[],"title_canon_sha256":"fd04d71541437783e5da67289ac6371913efac74b7f4383940dccdac3c67cd0d","abstract_canon_sha256":"2a95c7bb1cd4351e3c1285b40bc15e3b4524db511adadcc2323b0e06de6afe3d"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:04:49.538985Z","signature_b64":"8DAbTyjx1I1Dr7XCPgt0hYX+ZwPG9L0JPLj9FPqJJf8yrqrDg0K3JJ8NoWvmddZR8F72WsdUqbB9V0V2uYIhDQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"9bc18535daf75e525d017c17dae8866e210a16dd879ca6f38bd4b2327dc7138e","last_reissued_at":"2026-05-18T00:04:49.538300Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:04:49.538300Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Modifications to the neutrino mixing from the mu-tau reflection symmetry","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"hep-ph","authors_text":"Zhen-hua Zhao","submitted_at":"2018-03-13T02:50:19Z","abstract_excerpt":"The $\\mu$-$\\tau$ reflection symmetry serves as a unique basis for understanding the observed neutrino mixing as it can lead us to the interesting results $\\theta^{}_{23} = \\pi/4$ and $\\delta = -\\pi/2$ which stand close to the current experimental results. 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