{"paper":{"title":"The two-boost problem and Lagrangian Rabinowitz Floer homology","license":"http://creativecommons.org/licenses/by/4.0/","headline":"Two boosts of given energy connect any two points in phase space for a class of systems related to the restricted three-body problem.","cross_cats":[],"primary_cat":"math.SG","authors_text":"Eva Miranda, Jagna Wi\\'sniewska, Kai Cieliebak, Urs Frauenfelder","submitted_at":"2024-12-11T14:33:44Z","abstract_excerpt":"The two-boost problem in space mission design asks whether two points of phase space can be connected with the help of two boosts of given energy. We provide a positive answer for a class of systems related to the restricted three-body problem by defining and computing its Lagrangian Rabinowitz Floer homology. The main technical work goes into dealing with the noncompactness of the corresponding energy hypersurfaces."},"claims":{"count":4,"items":[{"kind":"strongest_claim","text":"We provide a positive answer for a class of systems related to the restricted three-body problem by defining and computing its Lagrangian Rabinowitz Floer homology.","source":"verdict.strongest_claim","status":"machine_extracted","claim_id":"C1","attestation":"unclaimed"},{"kind":"weakest_assumption","text":"The energy hypersurfaces for the chosen class of systems admit a well-defined Lagrangian Rabinowitz Floer homology despite their noncompactness, allowing the computation to yield the positive connectivity result.","source":"verdict.weakest_assumption","status":"machine_extracted","claim_id":"C2","attestation":"unclaimed"},{"kind":"one_line_summary","text":"Defines and computes Lagrangian Rabinowitz Floer homology to prove positive solvability of the two-boost problem for certain restricted three-body systems by addressing noncompact energy hypersurfaces.","source":"verdict.one_line_summary","status":"machine_extracted","claim_id":"C3","attestation":"unclaimed"},{"kind":"headline","text":"Two boosts of given energy connect any two points in phase space for a class of systems related to the restricted three-body problem.","source":"verdict.pith_extraction.headline","status":"machine_extracted","claim_id":"C4","attestation":"unclaimed"}],"snapshot_sha256":"9b4752fc6c364031f17347c2fa5161bc53352a5f6e1978f3817664c114e518cc"},"source":{"id":"2412.08415","kind":"arxiv","version":2},"verdict":{"id":"59614582-90db-4336-8db2-46fc027441f4","model_set":{"reader":"grok-4.3"},"created_at":"2026-05-23T07:33:50.039659Z","strongest_claim":"We provide a positive answer for a class of systems related to the restricted three-body problem by defining and computing its Lagrangian Rabinowitz Floer homology.","one_line_summary":"Defines and computes Lagrangian Rabinowitz Floer homology to prove positive solvability of the two-boost problem for certain restricted three-body systems by addressing noncompact energy hypersurfaces.","pipeline_version":"pith-pipeline@v0.9.0","weakest_assumption":"The energy hypersurfaces for the chosen class of systems admit a well-defined Lagrangian Rabinowitz Floer homology despite their noncompactness, allowing the computation to yield the positive connectivity result.","pith_extraction_headline":"Two boosts of given energy connect any two points in phase space for a class of systems related to the restricted three-body problem."},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2412.08415/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"references":{"count":16,"sample":[{"doi":"","year":2009,"title":"Estimates and computations in Rabinowitz- Floer homology","work_id":"e10c5002-c494-4c4d-a83d-571dd6c1f5b1","ref_index":1,"cited_arxiv_id":"","is_internal_anchor":false},{"doi":"","year":2014,"title":"M. 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