{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:VMS2NTSFBI5IX74N3AGDASB7XC","merge_version":"pith-open-graph-merge-v1","event_count":2,"valid_event_count":2,"invalid_event_count":0,"equivocation_count":0,"current":{"canonical_record":{"metadata":{"abstract_canon_sha256":"5db0c9d81c9003263110ce78b7573057b74c4098f5d8cfc63bf08e161dac5d82","cross_cats_sorted":["hep-ex"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-ph","submitted_at":"2015-07-31T23:33:41Z","title_canon_sha256":"cc4be6f262a82cb7e8536d16ec95c565280501a3eb92321ef943bf368d99b5d3"},"schema_version":"1.0","source":{"id":"1508.00052","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1508.00052","created_at":"2026-05-18T01:19:48Z"},{"alias_kind":"arxiv_version","alias_value":"1508.00052v2","created_at":"2026-05-18T01:19:48Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1508.00052","created_at":"2026-05-18T01:19:48Z"},{"alias_kind":"pith_short_12","alias_value":"VMS2NTSFBI5I","created_at":"2026-05-18T12:29:47Z"},{"alias_kind":"pith_short_16","alias_value":"VMS2NTSFBI5IX74N","created_at":"2026-05-18T12:29:47Z"},{"alias_kind":"pith_short_8","alias_value":"VMS2NTSF","created_at":"2026-05-18T12:29:47Z"}],"graph_snapshots":[{"event_id":"sha256:d921f9f40b06320e5bad39dc5bf16ae611b7483a1e6172a6f0fdc2839f721ac0","target":"graph","created_at":"2026-05-18T01:19:48Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"graph_snapshot":{"author_claims":{"count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","strong_count":0},"builder_version":"pith-number-builder-2026-05-17-v1","claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"paper":{"abstract_excerpt":"In the presence of both direct and indirect unitarity violation in the lepton mixing matrix, we derive a complete set of series expansion formulas for neutrino oscillation probabilities in matter of constant density. Expansions in the mass hierarchy parameter $\\alpha \\equiv \\Delta m_{21}^{2} / \\Delta m_{31}^{2}$ and those unitarity violation parameters $s^{2}_{ij}$ (for i = 1, 2, 3 and j = 4, 5, 6) up to the first order are studied in this paper. We analyse the accuracy of the analytical series expansion formulas in different regions of L / E. A detailed numerical analysis is also performed, o","authors_text":"Shu Luo, Yu-Feng Li","cross_cats":["hep-ex"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-ph","submitted_at":"2015-07-31T23:33:41Z","title":"Neutrino Oscillation Probabilities in Matter with Direct and Indirect Unitarity Violation in the Lepton Mixing Matrix"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1508.00052","kind":"arxiv","version":2},"verdict":{"created_at":null,"id":null,"model_set":{},"one_line_summary":"","pipeline_version":null,"pith_extraction_headline":"","strongest_claim":"","weakest_assumption":""}},"verdict_id":null}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:a3c1ef75ffb74b0c6f987405f8cdc85b08e7c0e125838aaae7d60d80b8128bc0","target":"record","created_at":"2026-05-18T01:19:48Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"attestation_state":"computed","canonical_record":{"metadata":{"abstract_canon_sha256":"5db0c9d81c9003263110ce78b7573057b74c4098f5d8cfc63bf08e161dac5d82","cross_cats_sorted":["hep-ex"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-ph","submitted_at":"2015-07-31T23:33:41Z","title_canon_sha256":"cc4be6f262a82cb7e8536d16ec95c565280501a3eb92321ef943bf368d99b5d3"},"schema_version":"1.0","source":{"id":"1508.00052","kind":"arxiv","version":2}},"canonical_sha256":"ab25a6ce450a3a8bff8dd80c30483fb8ae4e944393c547de2459ef35fbebd8ba","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"ab25a6ce450a3a8bff8dd80c30483fb8ae4e944393c547de2459ef35fbebd8ba","first_computed_at":"2026-05-18T01:19:48.350934Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:19:48.350934Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"V3bMNogJeRdgz1Vxd2aH/hcuQu8jcUqhTQKe4t6oUhYwDZgz+LvSHO/q+Vjdr64TFLwOhu1RhnjO0TK6aWWUDQ==","signature_status":"signed_v1","signed_at":"2026-05-18T01:19:48.351488Z","signed_message":"canonical_sha256_bytes"},"source_id":"1508.00052","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:a3c1ef75ffb74b0c6f987405f8cdc85b08e7c0e125838aaae7d60d80b8128bc0","sha256:d921f9f40b06320e5bad39dc5bf16ae611b7483a1e6172a6f0fdc2839f721ac0"],"state_sha256":"13f8722832502110d3e2d35d35c60bc7ed11eb720e8345005de9c72eafac2109"}