{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2021:FGQ7GW5IPGNSKYYVRA24YYNXMQ","short_pith_number":"pith:FGQ7GW5I","canonical_record":{"source":{"id":"2106.09630","kind":"arxiv","version":3},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"gr-qc","submitted_at":"2021-06-17T16:15:08Z","cross_cats_sorted":["astro-ph.HE"],"title_canon_sha256":"37f3fbc760be93675e4fc5fda3059d934c5c23c2c78355665b2641eb01c9a4f3","abstract_canon_sha256":"53b44aed1ec7102c33e85d9d2298bc3ce9e75e862c2b7e4cb8127844c59d0f55"},"schema_version":"1.0"},"canonical_sha256":"29a1f35ba8799b2563158835cc61b7641a701f6a8ea5974c2b6513610a18c6b8","source":{"kind":"arxiv","id":"2106.09630","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2106.09630","created_at":"2026-07-05T03:43:02Z"},{"alias_kind":"arxiv_version","alias_value":"2106.09630v3","created_at":"2026-07-05T03:43:02Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2106.09630","created_at":"2026-07-05T03:43:02Z"},{"alias_kind":"pith_short_12","alias_value":"FGQ7GW5IPGNS","created_at":"2026-07-05T03:43:02Z"},{"alias_kind":"pith_short_16","alias_value":"FGQ7GW5IPGNSKYYV","created_at":"2026-07-05T03:43:02Z"},{"alias_kind":"pith_short_8","alias_value":"FGQ7GW5I","created_at":"2026-07-05T03:43:02Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2021:FGQ7GW5IPGNSKYYVRA24YYNXMQ","target":"record","payload":{"canonical_record":{"source":{"id":"2106.09630","kind":"arxiv","version":3},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"gr-qc","submitted_at":"2021-06-17T16:15:08Z","cross_cats_sorted":["astro-ph.HE"],"title_canon_sha256":"37f3fbc760be93675e4fc5fda3059d934c5c23c2c78355665b2641eb01c9a4f3","abstract_canon_sha256":"53b44aed1ec7102c33e85d9d2298bc3ce9e75e862c2b7e4cb8127844c59d0f55"},"schema_version":"1.0"},"canonical_sha256":"29a1f35ba8799b2563158835cc61b7641a701f6a8ea5974c2b6513610a18c6b8","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T03:43:02.709846Z","signature_b64":"F0+KukC2nABfYtrgceyMVkLZkLHdP2KA+NniUYWVw6H7bepUAE8HLgznWdnxXqraT+i1+W/gUpC4P2GRLJxLAA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"29a1f35ba8799b2563158835cc61b7641a701f6a8ea5974c2b6513610a18c6b8","last_reissued_at":"2026-07-05T03:43:02.709347Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T03:43:02.709347Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2106.09630","source_version":3,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-05T03:43:02Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"QBBLdLYU5yT5MAwsH9kM1WIUJ0VYM8NpBjQ+x1IKDBg3daDYTmTpaiClSEJARjqaM5TEdZah4pUjo3hpn7tjBQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-06T00:18:06.546811Z"},"content_sha256":"d1498b815d86065ed49f216f57b5fd35552e66e2a2db765888529320286ae024","schema_version":"1.0","event_id":"sha256:d1498b815d86065ed49f216f57b5fd35552e66e2a2db765888529320286ae024"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2021:FGQ7GW5IPGNSKYYVRA24YYNXMQ","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Lensing of Gravitational Waves as a Novel Probe of Graviton Mass","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["astro-ph.HE"],"primary_cat":"gr-qc","authors_text":"Ka-Wai Chung, Tjonnie Guang Feng Li","submitted_at":"2021-06-17T16:15:08Z","abstract_excerpt":"The diffraction patterns of lensed gravitational waves encode information about their propagation speeds. If gravitons have mass, the dispersion relation and speed of gravitational waves will be affected in a frequency-dependent manner, which would leave traces in the diffraction pattern if the waves are lensed. In this paper, we study how the alternative dispersion relation induced by massive gravitons affects gravitational waves lensed by point-mass lenses, such as intermediate-mass black holes. We find that the waveform morphology of lensed dispersive gravitational waves depends on the grav"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2106.09630","kind":"arxiv","version":3},"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/2106.09630/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":"2026-07-05T03:43:02Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"olLowKHF44XkGHD0R5gOrKVxQjh7WpUA3OXVNC2NtQVE0o05gBlpDY9aAiorzqG/3RtvlOr2onJ8hWf6pPNsDg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-06T00:18:06.547291Z"},"content_sha256":"8a3b844a7feb11ab4b10cdccbda4b004f9fc583a521d19dc556cc123f484c22e","schema_version":"1.0","event_id":"sha256:8a3b844a7feb11ab4b10cdccbda4b004f9fc583a521d19dc556cc123f484c22e"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/FGQ7GW5IPGNSKYYVRA24YYNXMQ/bundle.json","state_url":"https://pith.science/pith/FGQ7GW5IPGNSKYYVRA24YYNXMQ/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/FGQ7GW5IPGNSKYYVRA24YYNXMQ/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":"2026-08-06T00:18:06Z","links":{"resolver":"https://pith.science/pith/FGQ7GW5IPGNSKYYVRA24YYNXMQ","bundle":"https://pith.science/pith/FGQ7GW5IPGNSKYYVRA24YYNXMQ/bundle.json","state":"https://pith.science/pith/FGQ7GW5IPGNSKYYVRA24YYNXMQ/state.json","well_known_bundle":"https://pith.science/.well-known/pith/FGQ7GW5IPGNSKYYVRA24YYNXMQ/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2021:FGQ7GW5IPGNSKYYVRA24YYNXMQ","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":"53b44aed1ec7102c33e85d9d2298bc3ce9e75e862c2b7e4cb8127844c59d0f55","cross_cats_sorted":["astro-ph.HE"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"gr-qc","submitted_at":"2021-06-17T16:15:08Z","title_canon_sha256":"37f3fbc760be93675e4fc5fda3059d934c5c23c2c78355665b2641eb01c9a4f3"},"schema_version":"1.0","source":{"id":"2106.09630","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2106.09630","created_at":"2026-07-05T03:43:02Z"},{"alias_kind":"arxiv_version","alias_value":"2106.09630v3","created_at":"2026-07-05T03:43:02Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2106.09630","created_at":"2026-07-05T03:43:02Z"},{"alias_kind":"pith_short_12","alias_value":"FGQ7GW5IPGNS","created_at":"2026-07-05T03:43:02Z"},{"alias_kind":"pith_short_16","alias_value":"FGQ7GW5IPGNSKYYV","created_at":"2026-07-05T03:43:02Z"},{"alias_kind":"pith_short_8","alias_value":"FGQ7GW5I","created_at":"2026-07-05T03:43:02Z"}],"graph_snapshots":[{"event_id":"sha256:8a3b844a7feb11ab4b10cdccbda4b004f9fc583a521d19dc556cc123f484c22e","target":"graph","created_at":"2026-07-05T03:43:02Z","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/2106.09630/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"The diffraction patterns of lensed gravitational waves encode information about their propagation speeds. If gravitons have mass, the dispersion relation and speed of gravitational waves will be affected in a frequency-dependent manner, which would leave traces in the diffraction pattern if the waves are lensed. In this paper, we study how the alternative dispersion relation induced by massive gravitons affects gravitational waves lensed by point-mass lenses, such as intermediate-mass black holes. We find that the waveform morphology of lensed dispersive gravitational waves depends on the grav","authors_text":"Ka-Wai Chung, Tjonnie Guang Feng Li","cross_cats":["astro-ph.HE"],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"gr-qc","submitted_at":"2021-06-17T16:15:08Z","title":"Lensing of Gravitational Waves as a Novel Probe of Graviton Mass"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2106.09630","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:d1498b815d86065ed49f216f57b5fd35552e66e2a2db765888529320286ae024","target":"record","created_at":"2026-07-05T03:43:02Z","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":"53b44aed1ec7102c33e85d9d2298bc3ce9e75e862c2b7e4cb8127844c59d0f55","cross_cats_sorted":["astro-ph.HE"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"gr-qc","submitted_at":"2021-06-17T16:15:08Z","title_canon_sha256":"37f3fbc760be93675e4fc5fda3059d934c5c23c2c78355665b2641eb01c9a4f3"},"schema_version":"1.0","source":{"id":"2106.09630","kind":"arxiv","version":3}},"canonical_sha256":"29a1f35ba8799b2563158835cc61b7641a701f6a8ea5974c2b6513610a18c6b8","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"29a1f35ba8799b2563158835cc61b7641a701f6a8ea5974c2b6513610a18c6b8","first_computed_at":"2026-07-05T03:43:02.709347Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T03:43:02.709347Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"F0+KukC2nABfYtrgceyMVkLZkLHdP2KA+NniUYWVw6H7bepUAE8HLgznWdnxXqraT+i1+W/gUpC4P2GRLJxLAA==","signature_status":"signed_v1","signed_at":"2026-07-05T03:43:02.709846Z","signed_message":"canonical_sha256_bytes"},"source_id":"2106.09630","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:d1498b815d86065ed49f216f57b5fd35552e66e2a2db765888529320286ae024","sha256:8a3b844a7feb11ab4b10cdccbda4b004f9fc583a521d19dc556cc123f484c22e"],"state_sha256":"e25e58e2b4818d57973c59c55eec0edeacebca42ecba99f0a251e167e913e522"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ONOGiTXWyzY85JvehA7Xr+wtUIkuojbSOLIX+L0SmWiQm98izS+thlm9Dkz4qsDZKQyvuUBB+xEL4KDQGNnuCQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-06T00:18:06.550547Z","bundle_sha256":"a2620ca91f0d44b1ec902cdfd871ca7dbdce65e28971d2ffa600a95332f8bf31"}}