{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2021:CITQ54O357TCTOAUFY6KZLEHU6","short_pith_number":"pith:CITQ54O3","canonical_record":{"source":{"id":"2111.09163","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"gr-qc","submitted_at":"2021-11-17T14:54:12Z","cross_cats_sorted":["astro-ph.CO","hep-th"],"title_canon_sha256":"87800c0a822f3c73aef17601babf98a97fbff4dbd8be84e536508e5a65ad28db","abstract_canon_sha256":"3bb9c4e47607cbd157685dc316108dec7a7b3cd798f269d897d30a10b0aadeb7"},"schema_version":"1.0"},"canonical_sha256":"12270ef1dbefe629b8142e3cacac87a7b27ceb9d66c168cd8eae8c13ca5f968d","source":{"kind":"arxiv","id":"2111.09163","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2111.09163","created_at":"2026-07-05T05:03:20Z"},{"alias_kind":"arxiv_version","alias_value":"2111.09163v2","created_at":"2026-07-05T05:03:20Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2111.09163","created_at":"2026-07-05T05:03:20Z"},{"alias_kind":"pith_short_12","alias_value":"CITQ54O357TC","created_at":"2026-07-05T05:03:20Z"},{"alias_kind":"pith_short_16","alias_value":"CITQ54O357TCTOAU","created_at":"2026-07-05T05:03:20Z"},{"alias_kind":"pith_short_8","alias_value":"CITQ54O3","created_at":"2026-07-05T05:03:20Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2021:CITQ54O357TCTOAUFY6KZLEHU6","target":"record","payload":{"canonical_record":{"source":{"id":"2111.09163","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"gr-qc","submitted_at":"2021-11-17T14:54:12Z","cross_cats_sorted":["astro-ph.CO","hep-th"],"title_canon_sha256":"87800c0a822f3c73aef17601babf98a97fbff4dbd8be84e536508e5a65ad28db","abstract_canon_sha256":"3bb9c4e47607cbd157685dc316108dec7a7b3cd798f269d897d30a10b0aadeb7"},"schema_version":"1.0"},"canonical_sha256":"12270ef1dbefe629b8142e3cacac87a7b27ceb9d66c168cd8eae8c13ca5f968d","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T05:03:20.145428Z","signature_b64":"NEo9IJlTZvbfxbnRg+BLK6ZkOzJDbuGNDN67u1meTPLKfN7/QdygRvyUhur7SVwq7GYei+Kv03KZRqWIhsnmCA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"12270ef1dbefe629b8142e3cacac87a7b27ceb9d66c168cd8eae8c13ca5f968d","last_reissued_at":"2026-07-05T05:03:20.145026Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T05:03:20.145026Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2111.09163","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":"2026-07-05T05:03:20Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"hUQ58XUW+YBE/LQ/N3S7od4yA74WNm9aaBxOc7AlnUpr7dA28DcNM66ph6IDWGgE9dmm+dBvsv+f0KhBLcRHAA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-03T20:19:30.451444Z"},"content_sha256":"1655ae24b1c56a63f8bfd620a3bea03ef4adc313b8b26c4650c956cab8d2e808","schema_version":"1.0","event_id":"sha256:1655ae24b1c56a63f8bfd620a3bea03ef4adc313b8b26c4650c956cab8d2e808"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2021:CITQ54O357TCTOAUFY6KZLEHU6","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Covariant transverse-traceless projection for secondary gravitational waves","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["astro-ph.CO","hep-th"],"primary_cat":"gr-qc","authors_text":"Atsuhisa Ota, Hayley J. Macpherson, William R. Coulton","submitted_at":"2021-11-17T14:54:12Z","abstract_excerpt":"Second-order tensor modes induced by nonlinear gravity are a key component of the cosmological background of gravitational waves. A detection of this background would allow us to probe the primordial power spectrum at otherwise inaccessible scales. Usually, the energy density of these gravitational waves is studied within perturbation theory in a particular gauge -- a connection between our physical spacetime and a fictitious background. It is a widely recognized issue that the second-order, scalar-induced gravitational waves are gauge dependent. This issue arises because they are not well-def"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2111.09163","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/2111.09163/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":"2026-07-05T05:03:20Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"0lAy8rZyYPyFpKWv4Je8V/04RRSxTpWlR3/yOofHC8YuhQzINjJ26sFib1bu2NEICqxIpnx1yYTup2J4Jv25AA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-03T20:19:30.451869Z"},"content_sha256":"24a8f16d0cceab916b46068a46ce481445d14df6abda838688c3b965990e57b8","schema_version":"1.0","event_id":"sha256:24a8f16d0cceab916b46068a46ce481445d14df6abda838688c3b965990e57b8"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/CITQ54O357TCTOAUFY6KZLEHU6/bundle.json","state_url":"https://pith.science/pith/CITQ54O357TCTOAUFY6KZLEHU6/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/CITQ54O357TCTOAUFY6KZLEHU6/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":"2026-08-03T20:19:30Z","links":{"resolver":"https://pith.science/pith/CITQ54O357TCTOAUFY6KZLEHU6","bundle":"https://pith.science/pith/CITQ54O357TCTOAUFY6KZLEHU6/bundle.json","state":"https://pith.science/pith/CITQ54O357TCTOAUFY6KZLEHU6/state.json","well_known_bundle":"https://pith.science/.well-known/pith/CITQ54O357TCTOAUFY6KZLEHU6/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2021:CITQ54O357TCTOAUFY6KZLEHU6","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":"3bb9c4e47607cbd157685dc316108dec7a7b3cd798f269d897d30a10b0aadeb7","cross_cats_sorted":["astro-ph.CO","hep-th"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"gr-qc","submitted_at":"2021-11-17T14:54:12Z","title_canon_sha256":"87800c0a822f3c73aef17601babf98a97fbff4dbd8be84e536508e5a65ad28db"},"schema_version":"1.0","source":{"id":"2111.09163","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2111.09163","created_at":"2026-07-05T05:03:20Z"},{"alias_kind":"arxiv_version","alias_value":"2111.09163v2","created_at":"2026-07-05T05:03:20Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2111.09163","created_at":"2026-07-05T05:03:20Z"},{"alias_kind":"pith_short_12","alias_value":"CITQ54O357TC","created_at":"2026-07-05T05:03:20Z"},{"alias_kind":"pith_short_16","alias_value":"CITQ54O357TCTOAU","created_at":"2026-07-05T05:03:20Z"},{"alias_kind":"pith_short_8","alias_value":"CITQ54O3","created_at":"2026-07-05T05:03:20Z"}],"graph_snapshots":[{"event_id":"sha256:24a8f16d0cceab916b46068a46ce481445d14df6abda838688c3b965990e57b8","target":"graph","created_at":"2026-07-05T05:03:20Z","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/2111.09163/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Second-order tensor modes induced by nonlinear gravity are a key component of the cosmological background of gravitational waves. A detection of this background would allow us to probe the primordial power spectrum at otherwise inaccessible scales. Usually, the energy density of these gravitational waves is studied within perturbation theory in a particular gauge -- a connection between our physical spacetime and a fictitious background. It is a widely recognized issue that the second-order, scalar-induced gravitational waves are gauge dependent. This issue arises because they are not well-def","authors_text":"Atsuhisa Ota, Hayley J. Macpherson, William R. Coulton","cross_cats":["astro-ph.CO","hep-th"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"gr-qc","submitted_at":"2021-11-17T14:54:12Z","title":"Covariant transverse-traceless projection for secondary gravitational waves"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2111.09163","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":"sha256:1655ae24b1c56a63f8bfd620a3bea03ef4adc313b8b26c4650c956cab8d2e808","target":"record","created_at":"2026-07-05T05:03:20Z","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":"3bb9c4e47607cbd157685dc316108dec7a7b3cd798f269d897d30a10b0aadeb7","cross_cats_sorted":["astro-ph.CO","hep-th"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"gr-qc","submitted_at":"2021-11-17T14:54:12Z","title_canon_sha256":"87800c0a822f3c73aef17601babf98a97fbff4dbd8be84e536508e5a65ad28db"},"schema_version":"1.0","source":{"id":"2111.09163","kind":"arxiv","version":2}},"canonical_sha256":"12270ef1dbefe629b8142e3cacac87a7b27ceb9d66c168cd8eae8c13ca5f968d","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"12270ef1dbefe629b8142e3cacac87a7b27ceb9d66c168cd8eae8c13ca5f968d","first_computed_at":"2026-07-05T05:03:20.145026Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T05:03:20.145026Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"NEo9IJlTZvbfxbnRg+BLK6ZkOzJDbuGNDN67u1meTPLKfN7/QdygRvyUhur7SVwq7GYei+Kv03KZRqWIhsnmCA==","signature_status":"signed_v1","signed_at":"2026-07-05T05:03:20.145428Z","signed_message":"canonical_sha256_bytes"},"source_id":"2111.09163","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:1655ae24b1c56a63f8bfd620a3bea03ef4adc313b8b26c4650c956cab8d2e808","sha256:24a8f16d0cceab916b46068a46ce481445d14df6abda838688c3b965990e57b8"],"state_sha256":"ac2022262e0636f69f8ab15919a7ddb97c1b5419dbfcd6edec49ef33376838a0"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"KgWiaPj1aYagu2YFcESsj2G2ZYtSbtTmTZvOdhdIrhecwLgFJOGGt+12qDzy2mMWw4MPPK6R4lVq6xlsWSASAg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-03T20:19:30.454537Z","bundle_sha256":"31b228342216ba26be115960d57209f1c9dc4ffd424c10ba6b0789dfe6f7701a"}}