{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2000:7EFUPJC4QUX4X3P67BJ5QJNCFB","short_pith_number":"pith:7EFUPJC4","canonical_record":{"source":{"id":"gr-qc/0004047","kind":"arxiv","version":2},"metadata":{"license":"","primary_cat":"gr-qc","submitted_at":"2000-04-14T19:33:44Z","cross_cats_sorted":["astro-ph"],"title_canon_sha256":"ace2cccf9b5e4b77290535188dfca002db8c513a475d5a573f6ebf7b3860edc4","abstract_canon_sha256":"ffee7d94834098fcf74ba04f2d13ee66901d4f521a982c0f6ec7f46c098fa702"},"schema_version":"1.0"},"canonical_sha256":"f90b47a45c852fcbedfef853d825a22870adcf57a85a3fd8a09c544ee72b6356","source":{"kind":"arxiv","id":"gr-qc/0004047","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"gr-qc/0004047","created_at":"2026-07-04T16:19:38Z"},{"alias_kind":"arxiv_version","alias_value":"gr-qc/0004047v2","created_at":"2026-07-04T16:19:38Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.gr-qc/0004047","created_at":"2026-07-04T16:19:38Z"},{"alias_kind":"pith_short_12","alias_value":"7EFUPJC4QUX4","created_at":"2026-07-04T16:19:38Z"},{"alias_kind":"pith_short_16","alias_value":"7EFUPJC4QUX4X3P6","created_at":"2026-07-04T16:19:38Z"},{"alias_kind":"pith_short_8","alias_value":"7EFUPJC4","created_at":"2026-07-04T16:19:38Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2000:7EFUPJC4QUX4X3P67BJ5QJNCFB","target":"record","payload":{"canonical_record":{"source":{"id":"gr-qc/0004047","kind":"arxiv","version":2},"metadata":{"license":"","primary_cat":"gr-qc","submitted_at":"2000-04-14T19:33:44Z","cross_cats_sorted":["astro-ph"],"title_canon_sha256":"ace2cccf9b5e4b77290535188dfca002db8c513a475d5a573f6ebf7b3860edc4","abstract_canon_sha256":"ffee7d94834098fcf74ba04f2d13ee66901d4f521a982c0f6ec7f46c098fa702"},"schema_version":"1.0"},"canonical_sha256":"f90b47a45c852fcbedfef853d825a22870adcf57a85a3fd8a09c544ee72b6356","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-04T16:19:38.024531Z","signature_b64":"ihkRc/kPV8yI8GN2sbHsgv11ZCLyFlf1yQmprrhnzcbO7Q7KzMBrD5hlBF04DHa2joZiGgDvOTgQmq3E2b9YBw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"f90b47a45c852fcbedfef853d825a22870adcf57a85a3fd8a09c544ee72b6356","last_reissued_at":"2026-07-04T16:19:38.024119Z","signature_status":"signed_v1","first_computed_at":"2026-07-04T16:19:38.024119Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"gr-qc/0004047","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-04T16:19:38Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"5Srz7MBh1AreU09G7zsNOeh4XppT65r0SsfhwrgqrxxIPJ7fR4B8Cp0nzbHY+me5aUO4WTSnQZMWGW0JXXQvDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-09T08:24:00.768780Z"},"content_sha256":"9ab5eb186d664a248f9067601355bc36ffa9c1bd0fea33c1303f6f3aaa1f7707","schema_version":"1.0","event_id":"sha256:9ab5eb186d664a248f9067601355bc36ffa9c1bd0fea33c1303f6f3aaa1f7707"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2000:7EFUPJC4QUX4X3P67BJ5QJNCFB","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"On the Mass Neutrino Phase calculations along the geodesic line and the null line","license":"","headline":"","cross_cats":["astro-ph"],"primary_cat":"gr-qc","authors_text":"A.Beesham, C.M. Zhang","submitted_at":"2000-04-14T19:33:44Z","abstract_excerpt":"On the mass neutrino phase calculations along both the particle geodesic line and the photon null line, there exists a double counting error--factor of 2 when comparing the geodesic phase with the null phase. For the mass neutrino propagation in the flat spacetime, we study the neutrino interference phase calculation in the Minkowski diagram and find that the double counting effect originates from despising the velocity difference between two mass neutrinos. Moreover, we compare the phase calculations among the same energy description, the same momentum description and same velocity descriptio"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"gr-qc/0004047","kind":"arxiv","version":2},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/gr-qc/0004047/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-04T16:19:38Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"flJ6wW7PlMnBLEd+GvkdddrojC5ZnG5NJw0h33GIJATveQ2BeRc6LNCYGtKF9CCZylXhwiGT2DtOzV80cUCBDw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-09T08:24:00.769375Z"},"content_sha256":"299ca296c24185d3601f6d1736b0eb6c20b3ac039951adf0254b3516b840f85d","schema_version":"1.0","event_id":"sha256:299ca296c24185d3601f6d1736b0eb6c20b3ac039951adf0254b3516b840f85d"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/7EFUPJC4QUX4X3P67BJ5QJNCFB/bundle.json","state_url":"https://pith.science/pith/7EFUPJC4QUX4X3P67BJ5QJNCFB/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/7EFUPJC4QUX4X3P67BJ5QJNCFB/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-08-09T08:24:00Z","links":{"resolver":"https://pith.science/pith/7EFUPJC4QUX4X3P67BJ5QJNCFB","bundle":"https://pith.science/pith/7EFUPJC4QUX4X3P67BJ5QJNCFB/bundle.json","state":"https://pith.science/pith/7EFUPJC4QUX4X3P67BJ5QJNCFB/state.json","well_known_bundle":"https://pith.science/.well-known/pith/7EFUPJC4QUX4X3P67BJ5QJNCFB/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2000:7EFUPJC4QUX4X3P67BJ5QJNCFB","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":"ffee7d94834098fcf74ba04f2d13ee66901d4f521a982c0f6ec7f46c098fa702","cross_cats_sorted":["astro-ph"],"license":"","primary_cat":"gr-qc","submitted_at":"2000-04-14T19:33:44Z","title_canon_sha256":"ace2cccf9b5e4b77290535188dfca002db8c513a475d5a573f6ebf7b3860edc4"},"schema_version":"1.0","source":{"id":"gr-qc/0004047","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"gr-qc/0004047","created_at":"2026-07-04T16:19:38Z"},{"alias_kind":"arxiv_version","alias_value":"gr-qc/0004047v2","created_at":"2026-07-04T16:19:38Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.gr-qc/0004047","created_at":"2026-07-04T16:19:38Z"},{"alias_kind":"pith_short_12","alias_value":"7EFUPJC4QUX4","created_at":"2026-07-04T16:19:38Z"},{"alias_kind":"pith_short_16","alias_value":"7EFUPJC4QUX4X3P6","created_at":"2026-07-04T16:19:38Z"},{"alias_kind":"pith_short_8","alias_value":"7EFUPJC4","created_at":"2026-07-04T16:19:38Z"}],"graph_snapshots":[{"event_id":"sha256:299ca296c24185d3601f6d1736b0eb6c20b3ac039951adf0254b3516b840f85d","target":"graph","created_at":"2026-07-04T16:19:38Z","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/gr-qc/0004047/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"On the mass neutrino phase calculations along both the particle geodesic line and the photon null line, there exists a double counting error--factor of 2 when comparing the geodesic phase with the null phase. For the mass neutrino propagation in the flat spacetime, we study the neutrino interference phase calculation in the Minkowski diagram and find that the double counting effect originates from despising the velocity difference between two mass neutrinos. Moreover, we compare the phase calculations among the same energy description, the same momentum description and same velocity descriptio","authors_text":"A.Beesham, C.M. Zhang","cross_cats":["astro-ph"],"headline":"","license":"","primary_cat":"gr-qc","submitted_at":"2000-04-14T19:33:44Z","title":"On the Mass Neutrino Phase calculations along the geodesic line and the null line"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"gr-qc/0004047","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":"sha256:9ab5eb186d664a248f9067601355bc36ffa9c1bd0fea33c1303f6f3aaa1f7707","target":"record","created_at":"2026-07-04T16:19:38Z","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":"ffee7d94834098fcf74ba04f2d13ee66901d4f521a982c0f6ec7f46c098fa702","cross_cats_sorted":["astro-ph"],"license":"","primary_cat":"gr-qc","submitted_at":"2000-04-14T19:33:44Z","title_canon_sha256":"ace2cccf9b5e4b77290535188dfca002db8c513a475d5a573f6ebf7b3860edc4"},"schema_version":"1.0","source":{"id":"gr-qc/0004047","kind":"arxiv","version":2}},"canonical_sha256":"f90b47a45c852fcbedfef853d825a22870adcf57a85a3fd8a09c544ee72b6356","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"f90b47a45c852fcbedfef853d825a22870adcf57a85a3fd8a09c544ee72b6356","first_computed_at":"2026-07-04T16:19:38.024119Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-04T16:19:38.024119Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"ihkRc/kPV8yI8GN2sbHsgv11ZCLyFlf1yQmprrhnzcbO7Q7KzMBrD5hlBF04DHa2joZiGgDvOTgQmq3E2b9YBw==","signature_status":"signed_v1","signed_at":"2026-07-04T16:19:38.024531Z","signed_message":"canonical_sha256_bytes"},"source_id":"gr-qc/0004047","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:9ab5eb186d664a248f9067601355bc36ffa9c1bd0fea33c1303f6f3aaa1f7707","sha256:299ca296c24185d3601f6d1736b0eb6c20b3ac039951adf0254b3516b840f85d"],"state_sha256":"91f9571a8945dfd2647fe9eb51116408417b82530e7a9d0acbc3fb09feabc760"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"fUmK18lgDAb8Dfr0ht9BNjmVyEH40UOUPw19jkE24Sv0UKF9rtOinTU0Z1ZN5TPy8dqRSRk+ORzfQOirz17tCQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-09T08:24:00.773810Z","bundle_sha256":"12d74e1b407c1f3d0fd4834ca14e1a5fb45bc4e68d80c6ac3bdfd620f694edbf"}}