{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2020:XHCY4DXK455B7L5LGHTWAMYRF3","short_pith_number":"pith:XHCY4DXK","canonical_record":{"source":{"id":"2005.12306","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"gr-qc","submitted_at":"2020-05-25T18:00:30Z","cross_cats_sorted":["astro-ph.CO","hep-th"],"title_canon_sha256":"37cf977b0d75c50222907fb890b7fcc57a504eee9b0825b1615d4f5b99b58045","abstract_canon_sha256":"31e1758b23b2d3f3cd3a4fba8de9ee7c49ce7496684042ed4463b85bd4a764ce"},"schema_version":"1.0"},"canonical_sha256":"b9c58e0eeae77a1fafab31e76033112ec1d84689727cf3370bd38f01a3c2d8b4","source":{"kind":"arxiv","id":"2005.12306","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2005.12306","created_at":"2026-07-05T01:38:37Z"},{"alias_kind":"arxiv_version","alias_value":"2005.12306v2","created_at":"2026-07-05T01:38:37Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2005.12306","created_at":"2026-07-05T01:38:37Z"},{"alias_kind":"pith_short_12","alias_value":"XHCY4DXK455B","created_at":"2026-07-05T01:38:37Z"},{"alias_kind":"pith_short_16","alias_value":"XHCY4DXK455B7L5L","created_at":"2026-07-05T01:38:37Z"},{"alias_kind":"pith_short_8","alias_value":"XHCY4DXK","created_at":"2026-07-05T01:38:37Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2020:XHCY4DXK455B7L5LGHTWAMYRF3","target":"record","payload":{"canonical_record":{"source":{"id":"2005.12306","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"gr-qc","submitted_at":"2020-05-25T18:00:30Z","cross_cats_sorted":["astro-ph.CO","hep-th"],"title_canon_sha256":"37cf977b0d75c50222907fb890b7fcc57a504eee9b0825b1615d4f5b99b58045","abstract_canon_sha256":"31e1758b23b2d3f3cd3a4fba8de9ee7c49ce7496684042ed4463b85bd4a764ce"},"schema_version":"1.0"},"canonical_sha256":"b9c58e0eeae77a1fafab31e76033112ec1d84689727cf3370bd38f01a3c2d8b4","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T01:38:37.433535Z","signature_b64":"sVVQ8RE5btXMAyfOfRudzHEU6TSrCoBsBD1mhf1zrcqeUYr3abDY8jnPtFLB3khIal8e9Zbg4wLgIhh0IsJ8Dw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"b9c58e0eeae77a1fafab31e76033112ec1d84689727cf3370bd38f01a3c2d8b4","last_reissued_at":"2026-07-05T01:38:37.433056Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T01:38:37.433056Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2005.12306","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":"2026-07-05T01:38:37Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"tGFLbT4jNOOs+EG+my0omxVt7IAKG+qnA+9fEmzns1L1PgANFdIeUipJ6NFfUcNwTooNQIMLSAi+c+/EuMfPCw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-04T07:18:09.186383Z"},"content_sha256":"cf4b48fd658c85c0e19c53fb1a007a274a77f0eff2765cbdc7d8cea1e45eb11f","schema_version":"1.0","event_id":"sha256:cf4b48fd658c85c0e19c53fb1a007a274a77f0eff2765cbdc7d8cea1e45eb11f"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2020:XHCY4DXK455B7L5LGHTWAMYRF3","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Gravitational Waves Induced by Scalar Perturbations with a Lognormal Peak","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["astro-ph.CO","hep-th"],"primary_cat":"gr-qc","authors_text":"Misao Sasaki, Shi Pi","submitted_at":"2020-05-25T18:00:30Z","abstract_excerpt":"We study the stochastic gravitational wave (GW) background induced by the primordial scalar perturbation with the spectrum having a lognormal peak of width $\\Delta$ at $k=k_*$. We derive an analytical formula for the GW spectrum $\\Omega_\\text{GW}$ for both narrow ($\\Delta\\ll1$) and broad ($\\Delta\\gtrsim1$) peaks. In the narrow-peak case, the spectrum has a double peak feature with the sharper peak at $k= 2k_*/\\sqrt{3}$. On the infrared (IR) side of the spectrum, we find power-law behavior with a break at $k=k_b$ in the power-law index where it chages from $k^3$ on the far IR side to $k^2$ on t"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2005.12306","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/2005.12306/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":"2026-07-05T01:38:37Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"H0kqMiJFGMpAShNt/8tk7uZU1lc1wf+rzgoAvIl05TXhOizq4ppIVYI7BP8GPRwd4qlI6IBiAuFtJvKUG54BAQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-04T07:18:09.186783Z"},"content_sha256":"cf1aedcfcbea8d0fb172760998b4f2cab257c89a4730e067dd74889015ba9380","schema_version":"1.0","event_id":"sha256:cf1aedcfcbea8d0fb172760998b4f2cab257c89a4730e067dd74889015ba9380"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/XHCY4DXK455B7L5LGHTWAMYRF3/bundle.json","state_url":"https://pith.science/pith/XHCY4DXK455B7L5LGHTWAMYRF3/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/XHCY4DXK455B7L5LGHTWAMYRF3/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":"2026-08-04T07:18:09Z","links":{"resolver":"https://pith.science/pith/XHCY4DXK455B7L5LGHTWAMYRF3","bundle":"https://pith.science/pith/XHCY4DXK455B7L5LGHTWAMYRF3/bundle.json","state":"https://pith.science/pith/XHCY4DXK455B7L5LGHTWAMYRF3/state.json","well_known_bundle":"https://pith.science/.well-known/pith/XHCY4DXK455B7L5LGHTWAMYRF3/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2020:XHCY4DXK455B7L5LGHTWAMYRF3","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":"31e1758b23b2d3f3cd3a4fba8de9ee7c49ce7496684042ed4463b85bd4a764ce","cross_cats_sorted":["astro-ph.CO","hep-th"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"gr-qc","submitted_at":"2020-05-25T18:00:30Z","title_canon_sha256":"37cf977b0d75c50222907fb890b7fcc57a504eee9b0825b1615d4f5b99b58045"},"schema_version":"1.0","source":{"id":"2005.12306","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2005.12306","created_at":"2026-07-05T01:38:37Z"},{"alias_kind":"arxiv_version","alias_value":"2005.12306v2","created_at":"2026-07-05T01:38:37Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2005.12306","created_at":"2026-07-05T01:38:37Z"},{"alias_kind":"pith_short_12","alias_value":"XHCY4DXK455B","created_at":"2026-07-05T01:38:37Z"},{"alias_kind":"pith_short_16","alias_value":"XHCY4DXK455B7L5L","created_at":"2026-07-05T01:38:37Z"},{"alias_kind":"pith_short_8","alias_value":"XHCY4DXK","created_at":"2026-07-05T01:38:37Z"}],"graph_snapshots":[{"event_id":"sha256:cf1aedcfcbea8d0fb172760998b4f2cab257c89a4730e067dd74889015ba9380","target":"graph","created_at":"2026-07-05T01:38:37Z","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/2005.12306/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We study the stochastic gravitational wave (GW) background induced by the primordial scalar perturbation with the spectrum having a lognormal peak of width $\\Delta$ at $k=k_*$. We derive an analytical formula for the GW spectrum $\\Omega_\\text{GW}$ for both narrow ($\\Delta\\ll1$) and broad ($\\Delta\\gtrsim1$) peaks. In the narrow-peak case, the spectrum has a double peak feature with the sharper peak at $k= 2k_*/\\sqrt{3}$. On the infrared (IR) side of the spectrum, we find power-law behavior with a break at $k=k_b$ in the power-law index where it chages from $k^3$ on the far IR side to $k^2$ on t","authors_text":"Misao Sasaki, Shi Pi","cross_cats":["astro-ph.CO","hep-th"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"gr-qc","submitted_at":"2020-05-25T18:00:30Z","title":"Gravitational Waves Induced by Scalar Perturbations with a Lognormal Peak"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2005.12306","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:cf4b48fd658c85c0e19c53fb1a007a274a77f0eff2765cbdc7d8cea1e45eb11f","target":"record","created_at":"2026-07-05T01:38:37Z","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":"31e1758b23b2d3f3cd3a4fba8de9ee7c49ce7496684042ed4463b85bd4a764ce","cross_cats_sorted":["astro-ph.CO","hep-th"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"gr-qc","submitted_at":"2020-05-25T18:00:30Z","title_canon_sha256":"37cf977b0d75c50222907fb890b7fcc57a504eee9b0825b1615d4f5b99b58045"},"schema_version":"1.0","source":{"id":"2005.12306","kind":"arxiv","version":2}},"canonical_sha256":"b9c58e0eeae77a1fafab31e76033112ec1d84689727cf3370bd38f01a3c2d8b4","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"b9c58e0eeae77a1fafab31e76033112ec1d84689727cf3370bd38f01a3c2d8b4","first_computed_at":"2026-07-05T01:38:37.433056Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T01:38:37.433056Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"sVVQ8RE5btXMAyfOfRudzHEU6TSrCoBsBD1mhf1zrcqeUYr3abDY8jnPtFLB3khIal8e9Zbg4wLgIhh0IsJ8Dw==","signature_status":"signed_v1","signed_at":"2026-07-05T01:38:37.433535Z","signed_message":"canonical_sha256_bytes"},"source_id":"2005.12306","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:cf4b48fd658c85c0e19c53fb1a007a274a77f0eff2765cbdc7d8cea1e45eb11f","sha256:cf1aedcfcbea8d0fb172760998b4f2cab257c89a4730e067dd74889015ba9380"],"state_sha256":"fa100ce7e9d2b9bcdd64028be0c1679a94b8b5f81bf318934cf1194897b7b108"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Kn2bCj4MRzKEyyIu+op/poMZsWEW+anqz36V/9YbXOANQzlrLF/XY5nLUKnPM89XEkbVyu667zNwyKod4QI2DA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-04T07:18:09.189627Z","bundle_sha256":"4a94690848f1d06f0314448422926ee2b8d237927e2d34f133d4e45dfd817476"}}