{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2015:P5YONZ4EDOYZT7V3XGT2ZIRBC4","short_pith_number":"pith:P5YONZ4E","schema_version":"1.0","canonical_sha256":"7f70e6e7841bb199febbb9a7aca221171142f5dc12549b1fad9a9f9c83782cc6","source":{"kind":"arxiv","id":"1512.03134","version":2},"attestation_state":"computed","paper":{"title":"Vacuum and Gravitons of Relic Gravitational Waves, and Regularization of Spectrum and Energy-Momentum Tensor","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["astro-ph.CO","hep-ph","hep-th"],"primary_cat":"gr-qc","authors_text":"Dong-Gang Wang, Jie-Wen Chen, Yang Zhang","submitted_at":"2015-12-10T03:53:44Z","abstract_excerpt":"The spectrum of relic gravitational wave (RGW) contains high-frequency divergences, which should be removed. We present a systematic study of the issue, based on the exact RGW solution that covers the five stages, from inflation to the acceleration, each being a power law expansion. We show that the present RGW consists of vacuum dominating at $f>10^{11}$Hz and graviton dominating at $f<10^{11}$Hz, respectively. The gravitons are produced by the four cosmic transitions, mostly by the inflation-reheating one. We perform adiabatic regularization to remove vacuum divergences in three schemes: at "},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1512.03134","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"gr-qc","submitted_at":"2015-12-10T03:53:44Z","cross_cats_sorted":["astro-ph.CO","hep-ph","hep-th"],"title_canon_sha256":"071c071f91cf83fb8d468c977250375939413a89f26960cb1efae00c43851ee8","abstract_canon_sha256":"d5160497bb49482868c64f58641941856e9383a5184d6e37950d0b2aa855c364"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:07:58.385150Z","signature_b64":"iotsoeVkBqmPKAC26h8GLSbEV3dC395lSxp7QpKv10xOocyseRJMYyY2R087tAZ/+Rr8sQgaxixCWoqyAsRtAQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"7f70e6e7841bb199febbb9a7aca221171142f5dc12549b1fad9a9f9c83782cc6","last_reissued_at":"2026-05-18T01:07:58.384468Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:07:58.384468Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Vacuum and Gravitons of Relic Gravitational Waves, and Regularization of Spectrum and Energy-Momentum Tensor","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["astro-ph.CO","hep-ph","hep-th"],"primary_cat":"gr-qc","authors_text":"Dong-Gang Wang, Jie-Wen Chen, Yang Zhang","submitted_at":"2015-12-10T03:53:44Z","abstract_excerpt":"The spectrum of relic gravitational wave (RGW) contains high-frequency divergences, which should be removed. We present a systematic study of the issue, based on the exact RGW solution that covers the five stages, from inflation to the acceleration, each being a power law expansion. We show that the present RGW consists of vacuum dominating at $f>10^{11}$Hz and graviton dominating at $f<10^{11}$Hz, respectively. The gravitons are produced by the four cosmic transitions, mostly by the inflation-reheating one. We perform adiabatic regularization to remove vacuum divergences in three schemes: at "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1512.03134","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":""},"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"},"aliases":[{"alias_kind":"arxiv","alias_value":"1512.03134","created_at":"2026-05-18T01:07:58.384591+00:00"},{"alias_kind":"arxiv_version","alias_value":"1512.03134v2","created_at":"2026-05-18T01:07:58.384591+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1512.03134","created_at":"2026-05-18T01:07:58.384591+00:00"},{"alias_kind":"pith_short_12","alias_value":"P5YONZ4EDOYZ","created_at":"2026-05-18T12:29:34.919912+00:00"},{"alias_kind":"pith_short_16","alias_value":"P5YONZ4EDOYZT7V3","created_at":"2026-05-18T12:29:34.919912+00:00"},{"alias_kind":"pith_short_8","alias_value":"P5YONZ4E","created_at":"2026-05-18T12:29:34.919912+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":2,"internal_anchor_count":2,"sample":[{"citing_arxiv_id":"2605.18286","citing_title":"Primary gravitational waves at high frequencies II: Emergence of the exponential cut-off in the power spectrum","ref_index":54,"is_internal_anchor":true},{"citing_arxiv_id":"2512.03959","citing_title":"Primary gravitational waves at high frequencies I: Origin of suppression in the power spectrum","ref_index":56,"is_internal_anchor":true}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/P5YONZ4EDOYZT7V3XGT2ZIRBC4","json":"https://pith.science/pith/P5YONZ4EDOYZT7V3XGT2ZIRBC4.json","graph_json":"https://pith.science/api/pith-number/P5YONZ4EDOYZT7V3XGT2ZIRBC4/graph.json","events_json":"https://pith.science/api/pith-number/P5YONZ4EDOYZT7V3XGT2ZIRBC4/events.json","paper":"https://pith.science/paper/P5YONZ4E"},"agent_actions":{"view_html":"https://pith.science/pith/P5YONZ4EDOYZT7V3XGT2ZIRBC4","download_json":"https://pith.science/pith/P5YONZ4EDOYZT7V3XGT2ZIRBC4.json","view_paper":"https://pith.science/paper/P5YONZ4E","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1512.03134&json=true","fetch_graph":"https://pith.science/api/pith-number/P5YONZ4EDOYZT7V3XGT2ZIRBC4/graph.json","fetch_events":"https://pith.science/api/pith-number/P5YONZ4EDOYZT7V3XGT2ZIRBC4/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/P5YONZ4EDOYZT7V3XGT2ZIRBC4/action/timestamp_anchor","attest_storage":"https://pith.science/pith/P5YONZ4EDOYZT7V3XGT2ZIRBC4/action/storage_attestation","attest_author":"https://pith.science/pith/P5YONZ4EDOYZT7V3XGT2ZIRBC4/action/author_attestation","sign_citation":"https://pith.science/pith/P5YONZ4EDOYZT7V3XGT2ZIRBC4/action/citation_signature","submit_replication":"https://pith.science/pith/P5YONZ4EDOYZT7V3XGT2ZIRBC4/action/replication_record"}},"created_at":"2026-05-18T01:07:58.384591+00:00","updated_at":"2026-05-18T01:07:58.384591+00:00"}