{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2026:6ZOYHLED34BI2P6LES7LB62QVH","short_pith_number":"pith:6ZOYHLED","canonical_record":{"source":{"id":"2604.02216","kind":"arxiv","version":2},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"astro-ph.CO","submitted_at":"2026-04-02T16:08:29Z","cross_cats_sorted":[],"title_canon_sha256":"a8caa4b8575609a95e1bd1060f2f7693a908f728353ccfc850e363a140812a85","abstract_canon_sha256":"f10eca927d1b5f88b404a7c729587d70f7ed00346c206d04050de63958db225b"},"schema_version":"1.0"},"canonical_sha256":"f65d83ac83df028d3fcb24beb0fb50a9fb988c48fd0414d8d648f7d1d93e6d54","source":{"kind":"arxiv","id":"2604.02216","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2604.02216","created_at":"2026-07-07T01:16:11Z"},{"alias_kind":"arxiv_version","alias_value":"2604.02216v2","created_at":"2026-07-07T01:16:11Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2604.02216","created_at":"2026-07-07T01:16:11Z"},{"alias_kind":"pith_short_12","alias_value":"6ZOYHLED34BI","created_at":"2026-07-07T01:16:11Z"},{"alias_kind":"pith_short_16","alias_value":"6ZOYHLED34BI2P6L","created_at":"2026-07-07T01:16:11Z"},{"alias_kind":"pith_short_8","alias_value":"6ZOYHLED","created_at":"2026-07-07T01:16:11Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2026:6ZOYHLED34BI2P6LES7LB62QVH","target":"record","payload":{"canonical_record":{"source":{"id":"2604.02216","kind":"arxiv","version":2},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"astro-ph.CO","submitted_at":"2026-04-02T16:08:29Z","cross_cats_sorted":[],"title_canon_sha256":"a8caa4b8575609a95e1bd1060f2f7693a908f728353ccfc850e363a140812a85","abstract_canon_sha256":"f10eca927d1b5f88b404a7c729587d70f7ed00346c206d04050de63958db225b"},"schema_version":"1.0"},"canonical_sha256":"f65d83ac83df028d3fcb24beb0fb50a9fb988c48fd0414d8d648f7d1d93e6d54","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-07T01:16:11.525849Z","signature_b64":"jbGaOWwt1DyF1jY441xWZLtq7rLWNwc1vQ2X/VxRzpYQ+NskJvo3FCE+IuMZIMh8HN3VEWb9WCPRSQiK00iwCg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"f65d83ac83df028d3fcb24beb0fb50a9fb988c48fd0414d8d648f7d1d93e6d54","last_reissued_at":"2026-07-07T01:16:11.525026Z","signature_status":"signed_v1","first_computed_at":"2026-07-07T01:16:11.525026Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2604.02216","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":"2026-07-07T01:16:11Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"tVukI70qjI/g+QO1ZHPYKG4hLk4p30yOhTU3ZWY3YFd9yLJRfkGEEQes8yFtMEaY5qRBqkBXhOb0R0/SJcEqAw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-08T22:51:37.500100Z"},"content_sha256":"61ee6fa2c3af5e7f301bacf964b53f8a0e27ce91a7cef30fab4d5d68e64f2824","schema_version":"1.0","event_id":"sha256:61ee6fa2c3af5e7f301bacf964b53f8a0e27ce91a7cef30fab4d5d68e64f2824"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2026:6ZOYHLED34BI2P6LES7LB62QVH","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Consistency relations of amplitude and phase fluctuations of gravitational waves magnified by strong gravitational lensing","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"astro-ph.CO","authors_text":"Teruaki Suyama, Yuta Nakazono","submitted_at":"2026-04-02T16:08:29Z","abstract_excerpt":"We discuss the amplitude and phase fluctuations of gravitational waves due to wave optics lensing in the presence of both a strong lens and cosmological weak lenses. By applying the geometric optics approximation to the strong lens and treating the weak lensing potential perturbatively, we obtain the amplification factor up to the second order in the weak lensing potential. Additionally, we establish a methodology to systematically evaluate the weak lensing effects based on diagrammatic rules. Based on the derived amplification factor, we evaluate the statistics of the fluctuations and demonst"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2604.02216","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/2604.02216/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":"2026-07-07T01:16:11Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"l88GUK9nChfRZsguXBP42GKrcqC33hVoLpFnqHghmjdccU3beSHUxLbj4GexJKOHEbYOgnGxN4ZBZbJpJYj8Cg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-08T22:51:37.501034Z"},"content_sha256":"d4c6b8c7ab79165fa1123d483da969de6618e75e5034b33a0d4ec07890e47b2f","schema_version":"1.0","event_id":"sha256:d4c6b8c7ab79165fa1123d483da969de6618e75e5034b33a0d4ec07890e47b2f"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/6ZOYHLED34BI2P6LES7LB62QVH/bundle.json","state_url":"https://pith.science/pith/6ZOYHLED34BI2P6LES7LB62QVH/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/6ZOYHLED34BI2P6LES7LB62QVH/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":"2026-08-08T22:51:37Z","links":{"resolver":"https://pith.science/pith/6ZOYHLED34BI2P6LES7LB62QVH","bundle":"https://pith.science/pith/6ZOYHLED34BI2P6LES7LB62QVH/bundle.json","state":"https://pith.science/pith/6ZOYHLED34BI2P6LES7LB62QVH/state.json","well_known_bundle":"https://pith.science/.well-known/pith/6ZOYHLED34BI2P6LES7LB62QVH/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2026:6ZOYHLED34BI2P6LES7LB62QVH","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":"f10eca927d1b5f88b404a7c729587d70f7ed00346c206d04050de63958db225b","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"astro-ph.CO","submitted_at":"2026-04-02T16:08:29Z","title_canon_sha256":"a8caa4b8575609a95e1bd1060f2f7693a908f728353ccfc850e363a140812a85"},"schema_version":"1.0","source":{"id":"2604.02216","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2604.02216","created_at":"2026-07-07T01:16:11Z"},{"alias_kind":"arxiv_version","alias_value":"2604.02216v2","created_at":"2026-07-07T01:16:11Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2604.02216","created_at":"2026-07-07T01:16:11Z"},{"alias_kind":"pith_short_12","alias_value":"6ZOYHLED34BI","created_at":"2026-07-07T01:16:11Z"},{"alias_kind":"pith_short_16","alias_value":"6ZOYHLED34BI2P6L","created_at":"2026-07-07T01:16:11Z"},{"alias_kind":"pith_short_8","alias_value":"6ZOYHLED","created_at":"2026-07-07T01:16:11Z"}],"graph_snapshots":[{"event_id":"sha256:d4c6b8c7ab79165fa1123d483da969de6618e75e5034b33a0d4ec07890e47b2f","target":"graph","created_at":"2026-07-07T01:16:11Z","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/2604.02216/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We discuss the amplitude and phase fluctuations of gravitational waves due to wave optics lensing in the presence of both a strong lens and cosmological weak lenses. By applying the geometric optics approximation to the strong lens and treating the weak lensing potential perturbatively, we obtain the amplification factor up to the second order in the weak lensing potential. Additionally, we establish a methodology to systematically evaluate the weak lensing effects based on diagrammatic rules. Based on the derived amplification factor, we evaluate the statistics of the fluctuations and demonst","authors_text":"Teruaki Suyama, Yuta Nakazono","cross_cats":[],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"astro-ph.CO","submitted_at":"2026-04-02T16:08:29Z","title":"Consistency relations of amplitude and phase fluctuations of gravitational waves magnified by strong gravitational lensing"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2604.02216","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":"sha256:61ee6fa2c3af5e7f301bacf964b53f8a0e27ce91a7cef30fab4d5d68e64f2824","target":"record","created_at":"2026-07-07T01:16:11Z","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":"f10eca927d1b5f88b404a7c729587d70f7ed00346c206d04050de63958db225b","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"astro-ph.CO","submitted_at":"2026-04-02T16:08:29Z","title_canon_sha256":"a8caa4b8575609a95e1bd1060f2f7693a908f728353ccfc850e363a140812a85"},"schema_version":"1.0","source":{"id":"2604.02216","kind":"arxiv","version":2}},"canonical_sha256":"f65d83ac83df028d3fcb24beb0fb50a9fb988c48fd0414d8d648f7d1d93e6d54","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"f65d83ac83df028d3fcb24beb0fb50a9fb988c48fd0414d8d648f7d1d93e6d54","first_computed_at":"2026-07-07T01:16:11.525026Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-07T01:16:11.525026Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"jbGaOWwt1DyF1jY441xWZLtq7rLWNwc1vQ2X/VxRzpYQ+NskJvo3FCE+IuMZIMh8HN3VEWb9WCPRSQiK00iwCg==","signature_status":"signed_v1","signed_at":"2026-07-07T01:16:11.525849Z","signed_message":"canonical_sha256_bytes"},"source_id":"2604.02216","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:61ee6fa2c3af5e7f301bacf964b53f8a0e27ce91a7cef30fab4d5d68e64f2824","sha256:d4c6b8c7ab79165fa1123d483da969de6618e75e5034b33a0d4ec07890e47b2f"],"state_sha256":"c00bd0126bcae0b25f11ad513922dbc180ad476fcbfa197792bb294ed056944f"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"cMwucRGokz3ljuTUZ3FPD5EG7ypvlMKStjJbQHfL+e8aSGS4gBlVtJCBbTTmcFlykB5tJhyxoFfkJSKdcdWuBw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-08T22:51:37.562437Z","bundle_sha256":"b62e77117ba8aa27fd898effda6a3c32d77d03462702aa00c0b0a2c9d4407c99"}}