{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2023:AI2X3DDN2XTDU6PXYTVHYBISFF","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":"893b2529121d261cea63c473df34b8ee9cf884975437cec7581fd8f9174890d3","cross_cats_sorted":["hep-th"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-ph","submitted_at":"2023-08-28T11:21:25Z","title_canon_sha256":"cc1f72a881af64f065778195c8ec6a960c444c8d7b3cffda0bd690f58c694f1a"},"schema_version":"1.0","source":{"id":"2308.14501","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2308.14501","created_at":"2026-07-05T07:32:22Z"},{"alias_kind":"arxiv_version","alias_value":"2308.14501v3","created_at":"2026-07-05T07:32:22Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2308.14501","created_at":"2026-07-05T07:32:22Z"},{"alias_kind":"pith_short_12","alias_value":"AI2X3DDN2XTD","created_at":"2026-07-05T07:32:22Z"},{"alias_kind":"pith_short_16","alias_value":"AI2X3DDN2XTDU6PX","created_at":"2026-07-05T07:32:22Z"},{"alias_kind":"pith_short_8","alias_value":"AI2X3DDN","created_at":"2026-07-05T07:32:22Z"}],"graph_snapshots":[{"event_id":"sha256:ac9dbb86944fba581b2ae700337ef5e67e66aa7dc3f360a0243fcb1fe93cd74e","target":"graph","created_at":"2026-07-05T07:32:22Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2308.14501/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"The $S$ matrix rephasing invariance is one of the fundamental principles of quantum mechanics that originates in its probabilistic interpretation. For a given $S$ matrix which describes neutrino oscillation, one can define the two different rephased amplitudes $S_{\\alpha \\beta}^{ \\text{Reph-1} } \\equiv e^{ i (\\lambda_{1} / 2E) x} S_{\\alpha \\beta}$ and $S_{\\alpha \\beta}^{ \\text{Reph-2} } \\equiv e^{ i (\\lambda_{2} / 2E) x} S_{\\alpha \\beta}$, which are physically equivalent to each other, where $\\lambda_{k} / 2E$ denotes the energy eigenvalue of the $k$-th mass eigenstate. We point out that the t","authors_text":"Hisakazu Minakata","cross_cats":["hep-th"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-ph","submitted_at":"2023-08-28T11:21:25Z","title":"Neutrino amplitude decomposition, $S$ matrix rephasing invariance, and reparametrization symmetry"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2308.14501","kind":"arxiv","version":3},"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:ebca0408742b811c04909fa8492980c4397726f26b7cb3c6461711e0a8e97125","target":"record","created_at":"2026-07-05T07:32:22Z","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":"893b2529121d261cea63c473df34b8ee9cf884975437cec7581fd8f9174890d3","cross_cats_sorted":["hep-th"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-ph","submitted_at":"2023-08-28T11:21:25Z","title_canon_sha256":"cc1f72a881af64f065778195c8ec6a960c444c8d7b3cffda0bd690f58c694f1a"},"schema_version":"1.0","source":{"id":"2308.14501","kind":"arxiv","version":3}},"canonical_sha256":"02357d8c6dd5e63a79f7c4ea7c051229652e105a7d6ffb659fb0a96659277577","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"02357d8c6dd5e63a79f7c4ea7c051229652e105a7d6ffb659fb0a96659277577","first_computed_at":"2026-07-05T07:32:22.225854Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T07:32:22.225854Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"o2NYKxsLY+lCZKulAGpCByqSbjlBWLY7znWPng7EisnRML7nPCjXq/mtjAiQezyATD0dm4H1ZpLbcm1fEmYuCg==","signature_status":"signed_v1","signed_at":"2026-07-05T07:32:22.226267Z","signed_message":"canonical_sha256_bytes"},"source_id":"2308.14501","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:ebca0408742b811c04909fa8492980c4397726f26b7cb3c6461711e0a8e97125","sha256:ac9dbb86944fba581b2ae700337ef5e67e66aa7dc3f360a0243fcb1fe93cd74e"],"state_sha256":"9b98046d1ac185e5d33e994bfb068fe37e7fb40c0fde7b07f0e734f74984129f"}