{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2021:Z5L43ZFPDUTSMD5BAZRFSTTDWG","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":"aebf6a5a716d716ed83e128d7fa63bfe2d2fee276d7830713d43e0d7f45d4b7c","cross_cats_sorted":["astro-ph.CO"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"gr-qc","submitted_at":"2021-09-03T09:44:21Z","title_canon_sha256":"35b9c06b5f2ddf11bc625ee96257d8d7db5c455f2d3ac668e33c160665e74137"},"schema_version":"1.0","source":{"id":"2109.01398","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2109.01398","created_at":"2026-05-17T23:38:14Z"},{"alias_kind":"arxiv_version","alias_value":"2109.01398v2","created_at":"2026-05-17T23:38:14Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2109.01398","created_at":"2026-05-17T23:38:14Z"},{"alias_kind":"pith_short_12","alias_value":"Z5L43ZFPDUTS","created_at":"2026-05-18T12:33:33Z"},{"alias_kind":"pith_short_16","alias_value":"Z5L43ZFPDUTSMD5B","created_at":"2026-05-18T12:33:33Z"},{"alias_kind":"pith_short_8","alias_value":"Z5L43ZFP","created_at":"2026-05-18T12:33:33Z"}],"graph_snapshots":[{"event_id":"sha256:09175b81a795531091776f61d4fc4e9e9f8e9f88504ffeaa381b5aa0b5aec390","target":"graph","created_at":"2026-05-17T23:38:14Z","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":4,"items":[{"attestation":"unclaimed","claim_id":"C1","kind":"strongest_claim","source":"verdict.strongest_claim","status":"machine_extracted","text":"We revisit and unify the general analytical formulation. We then present general formulas in a compact form, ready to be applied."},{"attestation":"unclaimed","claim_id":"C2","kind":"weakest_assumption","source":"verdict.weakest_assumption","status":"machine_extracted","text":"That the literature formulas can be unified without hidden inconsistencies or that the compact expressions remain accurate when applied to arbitrary expansion histories not explicitly checked in the review."},{"attestation":"unclaimed","claim_id":"C3","kind":"one_line_summary","source":"verdict.one_line_summary","status":"machine_extracted","text":"A review that unifies analytical expressions for scalar-induced gravitational waves and emphasizes calculations for non-radiation-dominated cosmologies."},{"attestation":"unclaimed","claim_id":"C4","kind":"headline","source":"verdict.pith_extraction.headline","status":"machine_extracted","text":"Scalar-induced gravitational waves have unified compact formulas valid for any early-universe expansion history."}],"snapshot_sha256":"cb30216e8e547d2085923a05af5cacc63f79e59b086fff34524450bf6baacf1f"},"formal_canon":{"evidence_count":2,"snapshot_sha256":"f183de39d0e0f6f7c1c5188c5f58827df1d0bbc4483dc62a365a1408a8132b79"},"paper":{"abstract_excerpt":"We provide a review on the state-of-the-art of gravitational waves induced by primordial fluctuations, so-called induced gravitational waves. We present the intuitive physics behind induced gravitational waves and we revisit and unify the general analytical formulation. We then present general formulas in a compact form, ready to be applied. This review places emphasis on the open possibility that the primordial universe experienced a different expansion history than the often assumed radiation dominated cosmology. We hope that anyone interested in the topic will become aware of current advanc","authors_text":"Guillem Dom\\`enech","cross_cats":["astro-ph.CO"],"headline":"Scalar-induced gravitational waves have unified compact formulas valid for any early-universe expansion history.","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"gr-qc","submitted_at":"2021-09-03T09:44:21Z","title":"Scalar induced gravitational waves review"},"references":{"count":300,"internal_anchors":144,"resolved_work":300,"sample":[{"cited_arxiv_id":"","doi":"","is_internal_anchor":false,"ref_index":1,"title":"Allahverdiet al., The First Three Seconds: a Re- view of Possible Expansion Histories of the Early Uni- verse, Open J","work_id":"6e63fb46-9be1-49e3-a08a-9db5ca298be8","year":2021},{"cited_arxiv_id":"1807.06209","doi":"","is_internal_anchor":true,"ref_index":2,"title":"Planck 2018 results. VI. Cosmological parameters","work_id":"eeae0089-7b56-4c63-ace2-a31de468f6c5","year":2018},{"cited_arxiv_id":"1807.06211","doi":"","is_internal_anchor":true,"ref_index":3,"title":"Planck 2018 results. X. Constraints on inflation","work_id":"ac5d2133-b998-4b22-878d-b78fb5623e08","year":2018},{"cited_arxiv_id":"","doi":"","is_internal_anchor":false,"ref_index":4,"title":"R. Brout, F. Englert and E. Gunzig,The Creation of the Universe as a Quantum Phenomenon, Annals Phys.115 (1978) 78","work_id":"0990c674-8c68-425f-9b68-c865bdadffc0","year":1978},{"cited_arxiv_id":"","doi":"","is_internal_anchor":false,"ref_index":5,"title":"Starobinsky,Spectrum of relict gravitational radiation and the early state of the universe, JETP Lett.30 (1979) 682","work_id":"42c72c69-61f0-4abc-82fa-017facfaee94","year":1979}],"snapshot_sha256":"bb931656a17cb216e1c8a7b26eade94fb78388980288d32dec8b1b0f10b3947c"},"source":{"id":"2109.01398","kind":"arxiv","version":2},"verdict":{"created_at":"2026-05-17T07:52:12.491988Z","id":"5f4b872e-b8df-4622-85c4-c70d27177283","model_set":{"reader":"grok-4.3"},"one_line_summary":"A review that unifies analytical expressions for scalar-induced gravitational waves and emphasizes calculations for non-radiation-dominated cosmologies.","pipeline_version":"pith-pipeline@v0.9.0","pith_extraction_headline":"Scalar-induced gravitational waves have unified compact formulas valid for any early-universe expansion history.","strongest_claim":"We revisit and unify the general analytical formulation. We then present general formulas in a compact form, ready to be applied.","weakest_assumption":"That the literature formulas can be unified without hidden inconsistencies or that the compact expressions remain accurate when applied to arbitrary expansion histories not explicitly checked in the review."}},"verdict_id":"5f4b872e-b8df-4622-85c4-c70d27177283"}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:09970ec1787c6a66e5c0f638f4d877f7c43b2bd3f118691ddd5fa892b640d772","target":"record","created_at":"2026-05-17T23:38:14Z","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":"aebf6a5a716d716ed83e128d7fa63bfe2d2fee276d7830713d43e0d7f45d4b7c","cross_cats_sorted":["astro-ph.CO"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"gr-qc","submitted_at":"2021-09-03T09:44:21Z","title_canon_sha256":"35b9c06b5f2ddf11bc625ee96257d8d7db5c455f2d3ac668e33c160665e74137"},"schema_version":"1.0","source":{"id":"2109.01398","kind":"arxiv","version":2}},"canonical_sha256":"cf57cde4af1d27260fa10662594e63b1b63bd6e33325bfb9a582848bd2c05d39","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"cf57cde4af1d27260fa10662594e63b1b63bd6e33325bfb9a582848bd2c05d39","first_computed_at":"2026-05-17T23:38:14.656975Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:38:14.656975Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"iB368RCjXd9+FYviySMl8coBbvvLfKWHWKZuGwn99Hq2cBrLOZ01o4t84Zk7j0LvO9A8nGcHEOJ7VBkrVsBbAA==","signature_status":"signed_v1","signed_at":"2026-05-17T23:38:14.657587Z","signed_message":"canonical_sha256_bytes"},"source_id":"2109.01398","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:09970ec1787c6a66e5c0f638f4d877f7c43b2bd3f118691ddd5fa892b640d772","sha256:09175b81a795531091776f61d4fc4e9e9f8e9f88504ffeaa381b5aa0b5aec390"],"state_sha256":"316c55cd6c5d5fdcd25972ef1c32802afb8240455da06192ef5fe6f362c9f7c7"}