{"paper":{"title":"Reference-renormalized curvature-primitive Gauss-Bonnet formalism for finite-distance weak gravitational lensing in static spherical spacetimes","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"Reference renormalization of the curvature primitive computes finite-distance weak lensing deflection angles without photon spheres.","cross_cats":["hep-th"],"primary_cat":"gr-qc","authors_text":"Ali \\\"Ovg\\\"un, Reggie C. Pantig","submitted_at":"2026-04-18T03:29:59Z","abstract_excerpt":"We develop a reference-renormalized (photon-sphere-free) normalization scheme for Gauss-Bonnet gravitational lensing at finite distance in static, spherically symmetric spacetimes. The method treats the curvature primitive used to reduce the Gauss-Bonnet curvature-area integral as a quantity defined only modulo an additive constant (an additive gauge freedom). We fix this gauge by matching to a physically chosen reference optical geometry in an outer regime where the physical geometry approaches that reference, thereby defining a unique renormalized discrepancy primitive $\\mathcal{P}_e(r)$ by "},"claims":{"count":4,"items":[{"kind":"strongest_claim","text":"The resulting master formula yields the Ishihara-Li finite-distance deflection angle without invoking any circular null orbit, while remaining fully compatible with orbit-normalized prescriptions whenever a suitable photon sphere exists (the two gauges differ only by a constant shift and give identical α).","source":"verdict.strongest_claim","status":"machine_extracted","claim_id":"C1","attestation":"unclaimed"},{"kind":"weakest_assumption","text":"That a physically chosen reference optical geometry exists in an outer regime where the physical geometry approaches that reference, thereby defining a unique renormalized discrepancy primitive P_e(r) by reference subtraction.","source":"verdict.weakest_assumption","status":"machine_extracted","claim_id":"C2","attestation":"unclaimed"},{"kind":"one_line_summary","text":"A reference-renormalized curvature-primitive Gauss-Bonnet formalism computes finite-distance weak deflection angles in static spherical spacetimes without invoking photon spheres.","source":"verdict.one_line_summary","status":"machine_extracted","claim_id":"C3","attestation":"unclaimed"},{"kind":"headline","text":"Reference renormalization of the curvature primitive computes finite-distance weak lensing deflection angles without photon spheres.","source":"verdict.pith_extraction.headline","status":"machine_extracted","claim_id":"C4","attestation":"unclaimed"}],"snapshot_sha256":"9c3cbcabd3ebe0e89c01f6d445ceec9441213079d64882ab8da9a229ecc298df"},"source":{"id":"2604.16807","kind":"arxiv","version":1},"verdict":{"id":"85b2934b-b87c-4105-8fa5-3707b7d26a27","model_set":{"reader":"grok-4.3"},"created_at":"2026-05-10T07:30:00.853051Z","strongest_claim":"The resulting master formula yields the Ishihara-Li finite-distance deflection angle without invoking any circular null orbit, while remaining fully compatible with orbit-normalized prescriptions whenever a suitable photon sphere exists (the two gauges differ only by a constant shift and give identical α).","one_line_summary":"A reference-renormalized curvature-primitive Gauss-Bonnet formalism computes finite-distance weak deflection angles in static spherical spacetimes without invoking photon spheres.","pipeline_version":"pith-pipeline@v0.9.0","weakest_assumption":"That a physically chosen reference optical geometry exists in an outer regime where the physical geometry approaches that reference, thereby defining a unique renormalized discrepancy primitive P_e(r) by reference subtraction.","pith_extraction_headline":"Reference renormalization of the curvature primitive computes finite-distance weak lensing deflection angles without photon spheres."},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2604.16807/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"references":{"count":43,"sample":[{"doi":"","year":1992,"title":"P. Schneider, J. Ehlers, and E. E. Falco,Gravitational Lenses, Astronomy and Astrophysics Library (Springer, 1992)","work_id":"","ref_index":1,"cited_arxiv_id":"","is_internal_anchor":false},{"doi":"","year":2004,"title":"Perlick, Gravitational lensing from a spacetime perspec- tive, Living Rev","work_id":"","ref_index":2,"cited_arxiv_id":"","is_internal_anchor":false},{"doi":"","year":2016,"title":"Gravitational bending angle of light for finite distance and the Gauss-Bonnet theorem","work_id":"7aca9491-fdf3-4017-bb79-cc6c9c74bd13","ref_index":3,"cited_arxiv_id":"1604.08308","is_internal_anchor":false},{"doi":"","year":2018,"title":"Light deflection and Gauss–Bonnet theorem: definition of total deflection angle and its applications","work_id":"e1f7f9b0-a4b7-4553-8d46-5b20504fe922","ref_index":4,"cited_arxiv_id":"1708.04011","is_internal_anchor":false},{"doi":"","year":2020,"title":"K. Takizawa, T. Ono, and H. Asada, Gravitational deflection angle of light: Definition by an observer and its application to an asymptotically nonflat spacetime, Phys. Rev. D101, 104032 (2020), arXiv:","work_id":"7bffdd7f-9aa9-4121-9f85-e22a81ef1ea0","ref_index":5,"cited_arxiv_id":"","is_internal_anchor":false}],"resolved_work":33,"snapshot_sha256":"8ab67abcf323f4454f8f921ff9f6b8069e029b01f453dd287e894a52f49c154e","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"}