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We show that an oscillation probability for \\nu_e \\to \\nu_\\mu can be written in the form P(\\nu_e \\to \\nu_\\mu) =A_{e\\mu} cos \\delta + B_{e\\mu} sin \\delta + C_{e\\mu} without any approximation using the CP phase \\delta. This result holds not only in constant matter but also in arbitrary matter. Another probability for \\nu_\\mu \\to \\nu_\\tau can be written in the form P(\\nu_\\mu \\to \\nu_\\tau)= A_{\\mu\\tau} cos \\delta + B_{\\mu\\tau} sin \\delta\n + C_{\\mu\\tau} + D_{\\mu\\tau}"},"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":"hep-ph/0207174","kind":"arxiv","version":2},"metadata":{"license":"","primary_cat":"hep-ph","submitted_at":"2002-07-14T19:01:03Z","cross_cats_sorted":[],"title_canon_sha256":"9a7ac867ebab5f06aef2b26ee885b8fdbb13cd7c9f2915c38b0739ed46805600","abstract_canon_sha256":"b3b1b7249e5bb907b77cb0d032e9398878419531c5828c9edf883aa612945c91"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:06:14.102398Z","signature_b64":"MA1H1C01qahJo94WZf9s7VUOisgRVxTezz72wNWpl07T8zViAbST0/odGApTomNacWKwDx47TWAZmdhaPIjwAQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"4cee075005ca0b19bbeba547aecbbbb77b4058810a3748f0e2ad003961c71b16","last_reissued_at":"2026-05-18T01:06:14.101890Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:06:14.101890Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Overall Feature of CP dependence for Neutrino Oscillation Probability in Arbitrary Matter Profile","license":"","headline":"","cross_cats":[],"primary_cat":"hep-ph","authors_text":"Akira Takamura, Hidekazu Yokomakura, Keiichi Kimura","submitted_at":"2002-07-14T19:01:03Z","abstract_excerpt":"We study the CP dependence of neutrino oscillation probability for all channels in arbitrary matter profile within three generations. 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