{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:O6A2GMOESOCSLS3G6FIIMJFDFT","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":"2aac97bce209188bfcd5f0c9140194d209286e2fb6bc84d86856f61788b3e7ae","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-ph","submitted_at":"2016-10-13T15:41:59Z","title_canon_sha256":"a07192317e2ff48c87ed58700952cdc528233c4217f05c8a976cc16648023a46"},"schema_version":"1.0","source":{"id":"1610.04133","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1610.04133","created_at":"2026-05-18T00:53:58Z"},{"alias_kind":"arxiv_version","alias_value":"1610.04133v2","created_at":"2026-05-18T00:53:58Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1610.04133","created_at":"2026-05-18T00:53:58Z"},{"alias_kind":"pith_short_12","alias_value":"O6A2GMOESOCS","created_at":"2026-05-18T12:30:36Z"},{"alias_kind":"pith_short_16","alias_value":"O6A2GMOESOCSLS3G","created_at":"2026-05-18T12:30:36Z"},{"alias_kind":"pith_short_8","alias_value":"O6A2GMOE","created_at":"2026-05-18T12:30:36Z"}],"graph_snapshots":[{"event_id":"sha256:96760fe19b209fe809fe0d787f440854c4a6ac8079cd85d01dadb3fd2de48fd8","target":"graph","created_at":"2026-05-18T00:53:58Z","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":"Motivated by tremendous progress in neutrino oscillation experiments, we derive a new set of simple and compact formulas for three-flavor neutrino oscillation probabilities in matter of a constant density. A useful definition of the $\\eta$-gauge neutrino mass-squared difference $\\Delta^{}_* \\equiv \\eta \\Delta^{}_{31} + (1-\\eta) \\Delta^{}_{32}$ is introduced, where $\\Delta^{}_{ji} \\equiv m^2_j - m^2_i$ for $ji = 21, 31, 32$ are the ordinary neutrino mass-squared differences and $0 \\leq \\eta \\leq 1$ is a real and positive parameter. Expanding neutrino oscillation probabilities in terms of $\\alph","authors_text":"Jing-yu Zhu, Jue Zhang, Shun Zhou, Yu-Feng Li","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-ph","submitted_at":"2016-10-13T15:41:59Z","title":"Looking into Analytical Approximations for Three-flavor Neutrino Oscillation Probabilities in Matter"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1610.04133","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":"sha256:95af52b188d8037e59607b93eabc620df3087c5702fffd2f1ce855cd9b3607d5","target":"record","created_at":"2026-05-18T00:53:58Z","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":"2aac97bce209188bfcd5f0c9140194d209286e2fb6bc84d86856f61788b3e7ae","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-ph","submitted_at":"2016-10-13T15:41:59Z","title_canon_sha256":"a07192317e2ff48c87ed58700952cdc528233c4217f05c8a976cc16648023a46"},"schema_version":"1.0","source":{"id":"1610.04133","kind":"arxiv","version":2}},"canonical_sha256":"7781a331c4938525cb66f1508624a32cd061b2a399c3fd78a03026eb1dbeb896","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"7781a331c4938525cb66f1508624a32cd061b2a399c3fd78a03026eb1dbeb896","first_computed_at":"2026-05-18T00:53:58.295587Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:53:58.295587Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"DTqy7J1PPrp7C13jbRwy8HzcLA0zdT7Tj1SZJrLtPxHFDx4UqL8PevyPao5U0JG4wiGYjCnCXkVHo9SpfpnLDw==","signature_status":"signed_v1","signed_at":"2026-05-18T00:53:58.296158Z","signed_message":"canonical_sha256_bytes"},"source_id":"1610.04133","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:95af52b188d8037e59607b93eabc620df3087c5702fffd2f1ce855cd9b3607d5","sha256:96760fe19b209fe809fe0d787f440854c4a6ac8079cd85d01dadb3fd2de48fd8"],"state_sha256":"2c01e3c3f128e44d10d468951a6768a381d5dc6a77ec1a4af6b08aa9bdac03f5"}