{"paper":{"title":"Untwisting the double copy: the zeroth copy as an optical seed","license":"http://creativecommons.org/licenses/by/4.0/","headline":"A complex optical seed organizes stationary Kerr-Schild geometries and represents the zeroth copy in the double-copy framework.","cross_cats":["gr-qc"],"primary_cat":"hep-th","authors_text":"Damien A. Easson, Michael J. Falato","submitted_at":"2026-04-06T19:08:35Z","abstract_excerpt":"We present a historical optical foundation for stationary vacuum Kerr--Schild spacetimes on a flat background and interpret it in modern double-copy language. In this setting, a complex optical seed \\(\\rho=-\\theta-i\\omega\\), built from the expansion and signed twist of the Kerr--Schild congruence, is harmonic, while its inverse obeys an eikonal equation and reconstructs the congruence algebraically. Thus the local stationary geometry is organized by a single complex seed. In the overlap of the stationary Kerr--Schild and Petrov type--D Weyl double-copy framework, this seed furnishes a normaliz"},"claims":{"count":4,"items":[{"kind":"strongest_claim","text":"In the overlap of the stationary Kerr-Schild and Petrov type-D Weyl double-copy framework, this seed furnishes a normalized representative of the zeroth-copy data, while its real part yields the Kerr-Schild profile and its gradient generates the single-copy gauge-field strength.","source":"verdict.strongest_claim","status":"machine_extracted","claim_id":"C1","attestation":"unclaimed"},{"kind":"weakest_assumption","text":"The construction assumes that the spacetime is a stationary vacuum Kerr-Schild solution on a flat background and lies in the overlap region with the Petrov type-D Weyl double-copy framework; the abstract does not specify how restrictive this overlap is or whether the seed remains well-defined outside it.","source":"verdict.weakest_assumption","status":"machine_extracted","claim_id":"C2","attestation":"unclaimed"},{"kind":"one_line_summary","text":"A single complex optical seed built from expansion and twist organizes stationary Kerr-Schild geometries, reconstructs the congruence, and encodes the zeroth-copy data that generates both the gravitational profile and the single-copy gauge field.","source":"verdict.one_line_summary","status":"machine_extracted","claim_id":"C3","attestation":"unclaimed"},{"kind":"headline","text":"A complex optical seed organizes stationary Kerr-Schild geometries and represents the zeroth copy in the double-copy framework.","source":"verdict.pith_extraction.headline","status":"machine_extracted","claim_id":"C4","attestation":"unclaimed"}],"snapshot_sha256":"789843af74d93f90dec84ac31d751c97eccffaaee227218104a4044af575b927"},"source":{"id":"2604.05103","kind":"arxiv","version":1},"verdict":{"id":"b70d4cc0-5f30-4952-a5fc-77e94feea733","model_set":{"reader":"grok-4.3"},"created_at":"2026-05-10T18:50:16.076739Z","strongest_claim":"In the overlap of the stationary Kerr-Schild and Petrov type-D Weyl double-copy framework, this seed furnishes a normalized representative of the zeroth-copy data, while its real part yields the Kerr-Schild profile and its gradient generates the single-copy gauge-field strength.","one_line_summary":"A single complex optical seed built from expansion and twist organizes stationary Kerr-Schild geometries, reconstructs the congruence, and encodes the zeroth-copy data that generates both the gravitational profile and the single-copy gauge field.","pipeline_version":"pith-pipeline@v0.9.0","weakest_assumption":"The construction assumes that the spacetime is a stationary vacuum Kerr-Schild solution on a flat background and lies in the overlap region with the Petrov type-D Weyl double-copy framework; the abstract does not specify how restrictive this overlap is or whether the seed remains well-defined outside it.","pith_extraction_headline":"A complex optical seed organizes stationary Kerr-Schild geometries and represents the zeroth copy in the double-copy framework."},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2604.05103/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"references":{"count":37,"sample":[{"doi":"","year":null,"title":"Since the optical equations are for the congruencekµ, they are insensitive to whether the scalar prefactor is stored inVor inl0. Rather than defining twist by a square root (and leaving a sign ambigui","work_id":"abb7394b-0769-4ed2-b85e-7e30abb827c3","ref_index":1,"cited_arxiv_id":"","is_internal_anchor":false},{"doi":"","year":1986,"title":"H. Kawai, D. C. Lewellen, and S. H. H. Tye, A Relation Between Tree Amplitudes of Closed and Open Strings, Nucl. Phys. B269, 1 (1986)","work_id":"f40be55b-fe20-4f6e-b706-e38520e1447c","ref_index":2,"cited_arxiv_id":"","is_internal_anchor":false},{"doi":"","year":2008,"title":"New Relations for Gauge-Theory Amplitudes","work_id":"a25526c6-1166-46fb-87d7-cba60d9d1fd8","ref_index":3,"cited_arxiv_id":"0805.3993","is_internal_anchor":false},{"doi":"","year":2010,"title":"Perturbative Quantum Gravity as a Double Copy of Gauge Theory","work_id":"fa884d2f-8720-484f-a4b9-803ad37cccbf","ref_index":4,"cited_arxiv_id":"1004.0476","is_internal_anchor":false},{"doi":"","year":2018,"title":"C. D. White, The double copy: gravity from gluons, Con- temp. Phys.59, 109 (2018), arXiv:1708.07056 [hep-th]","work_id":"1d081059-d5d2-440a-9525-f1c066b90105","ref_index":5,"cited_arxiv_id":"","is_internal_anchor":false}],"resolved_work":37,"snapshot_sha256":"0118ae16265572d4d40dddb069b6cfc86047f91e4e2f139fe58b337224f855b8","internal_anchors":1},"formal_canon":{"evidence_count":2,"snapshot_sha256":"ac854f65539b7e2d71fbfa6e2190c3a70ceabfac5c254aa3395a8f1e6dd96487"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}