{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2019:MWPTJLVTMFI74VEVTKCAWTJQ3P","short_pith_number":"pith:MWPTJLVT","canonical_record":{"source":{"id":"1905.03272","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"gr-qc","submitted_at":"2019-05-08T18:01:24Z","cross_cats_sorted":[],"title_canon_sha256":"e58d5f037e7489853a027a6afd8cb25ee261e7505d9d40906fb957b03960529c","abstract_canon_sha256":"b13037ab29ce6f7c97dafdbfde03f347613d675acf0d91bdcc683b976d87a7f6"},"schema_version":"1.0"},"canonical_sha256":"659f34aeb36151fe54959a840b4d30dbf9c68321257e3a89417cef412da40ba8","source":{"kind":"arxiv","id":"1905.03272","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1905.03272","created_at":"2026-05-17T23:42:13Z"},{"alias_kind":"arxiv_version","alias_value":"1905.03272v3","created_at":"2026-05-17T23:42:13Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1905.03272","created_at":"2026-05-17T23:42:13Z"},{"alias_kind":"pith_short_12","alias_value":"MWPTJLVTMFI7","created_at":"2026-05-18T12:33:24Z"},{"alias_kind":"pith_short_16","alias_value":"MWPTJLVTMFI74VEV","created_at":"2026-05-18T12:33:24Z"},{"alias_kind":"pith_short_8","alias_value":"MWPTJLVT","created_at":"2026-05-18T12:33:24Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2019:MWPTJLVTMFI74VEVTKCAWTJQ3P","target":"record","payload":{"canonical_record":{"source":{"id":"1905.03272","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"gr-qc","submitted_at":"2019-05-08T18:01:24Z","cross_cats_sorted":[],"title_canon_sha256":"e58d5f037e7489853a027a6afd8cb25ee261e7505d9d40906fb957b03960529c","abstract_canon_sha256":"b13037ab29ce6f7c97dafdbfde03f347613d675acf0d91bdcc683b976d87a7f6"},"schema_version":"1.0"},"canonical_sha256":"659f34aeb36151fe54959a840b4d30dbf9c68321257e3a89417cef412da40ba8","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:42:13.457903Z","signature_b64":"R3ELmiaXYonF0l8uYZ12OlzASIr5fHh7FTfK0dfM8ZS2rLTSVfvyAMTwb2jWi3/EDYgM5AISXRZP/gJXrjWWCQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"659f34aeb36151fe54959a840b4d30dbf9c68321257e3a89417cef412da40ba8","last_reissued_at":"2026-05-17T23:42:13.457431Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:42:13.457431Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1905.03272","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":"2026-05-17T23:42:13Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ghPSIxpMu1qKpM5HTL5PNJV3OX/nzTnzargpjDuyTAe0TsGkjeBmHkjyWU341gWs8+tS1psCYmHfxadiDQTpDw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-06T14:48:51.243723Z"},"content_sha256":"14d1cc32ad5340fe2dae29e8aa7d32e522406d9e37e6082ef4780574336cb5b8","schema_version":"1.0","event_id":"sha256:14d1cc32ad5340fe2dae29e8aa7d32e522406d9e37e6082ef4780574336cb5b8"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2019:MWPTJLVTMFI74VEVTKCAWTJQ3P","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Second-order cosmological perturbations. IV. Produced by scalar-tensor and tensor-tensor couplings during the radiation dominated stage","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"gr-qc","authors_text":"Bo Wang, Yang Zhang","submitted_at":"2019-05-08T18:01:24Z","abstract_excerpt":"We continue to study the 2nd-order cosmological perturbations in synchronous coordinates in the framework of the general relativity (GR) during the radiation dominated (RD) stage, and to focus on the scalar-tensor and tensor-tensor couplings. The 1st-order curl velocity and the associated 1st-order vector metric perturbations are assumed to be vanishing. By analytically solving the 2nd-order Einstein equation and the energy-momentum conservation equations, we obtain the 2nd-order formal solutions (in the integral form) of all the metric perturbations, density contrast and velocity; perform the"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1905.03272","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":""},"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":"2026-05-17T23:42:13Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"mEkV80XqSFFpnsqAtiuudiW+LJkLCRv+GV8rureW2bh8j5sS5P5gDX6QyBSUfocHp2TqpjFIXeObPTr6jnQEDg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-06T14:48:51.244131Z"},"content_sha256":"c09185dfe28701665bf9aa54c5b63a885c1706b080c690184250498f57d020a3","schema_version":"1.0","event_id":"sha256:c09185dfe28701665bf9aa54c5b63a885c1706b080c690184250498f57d020a3"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/MWPTJLVTMFI74VEVTKCAWTJQ3P/bundle.json","state_url":"https://pith.science/pith/MWPTJLVTMFI74VEVTKCAWTJQ3P/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/MWPTJLVTMFI74VEVTKCAWTJQ3P/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":"2026-06-06T14:48:51Z","links":{"resolver":"https://pith.science/pith/MWPTJLVTMFI74VEVTKCAWTJQ3P","bundle":"https://pith.science/pith/MWPTJLVTMFI74VEVTKCAWTJQ3P/bundle.json","state":"https://pith.science/pith/MWPTJLVTMFI74VEVTKCAWTJQ3P/state.json","well_known_bundle":"https://pith.science/.well-known/pith/MWPTJLVTMFI74VEVTKCAWTJQ3P/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2019:MWPTJLVTMFI74VEVTKCAWTJQ3P","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":"b13037ab29ce6f7c97dafdbfde03f347613d675acf0d91bdcc683b976d87a7f6","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"gr-qc","submitted_at":"2019-05-08T18:01:24Z","title_canon_sha256":"e58d5f037e7489853a027a6afd8cb25ee261e7505d9d40906fb957b03960529c"},"schema_version":"1.0","source":{"id":"1905.03272","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1905.03272","created_at":"2026-05-17T23:42:13Z"},{"alias_kind":"arxiv_version","alias_value":"1905.03272v3","created_at":"2026-05-17T23:42:13Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1905.03272","created_at":"2026-05-17T23:42:13Z"},{"alias_kind":"pith_short_12","alias_value":"MWPTJLVTMFI7","created_at":"2026-05-18T12:33:24Z"},{"alias_kind":"pith_short_16","alias_value":"MWPTJLVTMFI74VEV","created_at":"2026-05-18T12:33:24Z"},{"alias_kind":"pith_short_8","alias_value":"MWPTJLVT","created_at":"2026-05-18T12:33:24Z"}],"graph_snapshots":[{"event_id":"sha256:c09185dfe28701665bf9aa54c5b63a885c1706b080c690184250498f57d020a3","target":"graph","created_at":"2026-05-17T23:42:13Z","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"},"paper":{"abstract_excerpt":"We continue to study the 2nd-order cosmological perturbations in synchronous coordinates in the framework of the general relativity (GR) during the radiation dominated (RD) stage, and to focus on the scalar-tensor and tensor-tensor couplings. The 1st-order curl velocity and the associated 1st-order vector metric perturbations are assumed to be vanishing. By analytically solving the 2nd-order Einstein equation and the energy-momentum conservation equations, we obtain the 2nd-order formal solutions (in the integral form) of all the metric perturbations, density contrast and velocity; perform the","authors_text":"Bo Wang, Yang Zhang","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"gr-qc","submitted_at":"2019-05-08T18:01:24Z","title":"Second-order cosmological perturbations. IV. Produced by scalar-tensor and tensor-tensor couplings during the radiation dominated stage"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1905.03272","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":"sha256:14d1cc32ad5340fe2dae29e8aa7d32e522406d9e37e6082ef4780574336cb5b8","target":"record","created_at":"2026-05-17T23:42:13Z","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":"b13037ab29ce6f7c97dafdbfde03f347613d675acf0d91bdcc683b976d87a7f6","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"gr-qc","submitted_at":"2019-05-08T18:01:24Z","title_canon_sha256":"e58d5f037e7489853a027a6afd8cb25ee261e7505d9d40906fb957b03960529c"},"schema_version":"1.0","source":{"id":"1905.03272","kind":"arxiv","version":3}},"canonical_sha256":"659f34aeb36151fe54959a840b4d30dbf9c68321257e3a89417cef412da40ba8","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"659f34aeb36151fe54959a840b4d30dbf9c68321257e3a89417cef412da40ba8","first_computed_at":"2026-05-17T23:42:13.457431Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:42:13.457431Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"R3ELmiaXYonF0l8uYZ12OlzASIr5fHh7FTfK0dfM8ZS2rLTSVfvyAMTwb2jWi3/EDYgM5AISXRZP/gJXrjWWCQ==","signature_status":"signed_v1","signed_at":"2026-05-17T23:42:13.457903Z","signed_message":"canonical_sha256_bytes"},"source_id":"1905.03272","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:14d1cc32ad5340fe2dae29e8aa7d32e522406d9e37e6082ef4780574336cb5b8","sha256:c09185dfe28701665bf9aa54c5b63a885c1706b080c690184250498f57d020a3"],"state_sha256":"d2482d380af069aba16ea77339ca2063cfd590daa991184a05ff988fe59aba6a"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"LPM5n6KnBEh5SVXX6YAEuuwDfby9E7M0FHjqwnQvWzix6aX/oWOoFuhBK1KN9dj2/R7IlAv4Ps5O8czWTj5YDQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-06T14:48:51.247899Z","bundle_sha256":"b8fdab7ae3d7daaa25254c0ed020491cf84b88e3f14f0cea0f64617c809fa7ea"}}