{"paper":{"title":"Geodesic currents of coarse negative curvature","license":"http://creativecommons.org/licenses/by/4.0/","headline":"Geodesic currents with strongly hyperbolic dual pseudometrics are dense in the full space of currents.","cross_cats":[],"primary_cat":"math.GT","authors_text":"D\\'idac Mart\\'inez-Granado, Meenakshy Jyothis","submitted_at":"2026-05-14T07:04:20Z","abstract_excerpt":"Strong hyperbolicity is a coarse notion of negative curvature, stronger than Gromov hyperbolicity, that includes all CAT(-k) metrics for k positive and allows the use of dynamical techniques available in negative curvature, such as thermodynamical formalism. We prove that the subset of geodesic currents whose dual pseudometric is strongly hyperbolic is dense in the space of geodesic currents. The proof combines an elementary finite-cover argument with a characterization of strong hyperbolicity in terms of boundary data for pseudometrics dual to geodesic currents. In contrast, we show that curr"},"claims":{"count":4,"items":[{"kind":"strongest_claim","text":"We prove that the subset of geodesic currents whose dual pseudometric is strongly hyperbolic is dense in the space of geodesic currents.","source":"verdict.strongest_claim","status":"machine_extracted","claim_id":"C1","attestation":"unclaimed"},{"kind":"weakest_assumption","text":"The characterization of strong hyperbolicity in terms of boundary data for pseudometrics dual to geodesic currents is valid and the elementary finite-cover argument applies without further restrictions on the surface or the currents.","source":"verdict.weakest_assumption","status":"machine_extracted","claim_id":"C2","attestation":"unclaimed"},{"kind":"one_line_summary","text":"Strongly hyperbolic geodesic currents are dense in the space of geodesic currents, yielding infinitely many pairwise non-roughly-isometric strongly hyperbolic metrics on the universal cover that are not CAT(0).","source":"verdict.one_line_summary","status":"machine_extracted","claim_id":"C3","attestation":"unclaimed"},{"kind":"headline","text":"Geodesic currents with strongly hyperbolic dual pseudometrics are dense in the full space of currents.","source":"verdict.pith_extraction.headline","status":"machine_extracted","claim_id":"C4","attestation":"unclaimed"}],"snapshot_sha256":"d3b0df4ccc42eecbba0f7ee2ff9604de958199f9da1d73014633adb9ffdf6588"},"source":{"id":"2605.14469","kind":"arxiv","version":1},"verdict":{"id":"64109b7b-dbd1-4ce6-b1a3-631ae8d349e2","model_set":{"reader":"grok-4.3"},"created_at":"2026-05-15T01:34:16.876095Z","strongest_claim":"We prove that the subset of geodesic currents whose dual pseudometric is strongly hyperbolic is dense in the space of geodesic currents.","one_line_summary":"Strongly hyperbolic geodesic currents are dense in the space of geodesic currents, yielding infinitely many pairwise non-roughly-isometric strongly hyperbolic metrics on the universal cover that are not CAT(0).","pipeline_version":"pith-pipeline@v0.9.0","weakest_assumption":"The characterization of strong hyperbolicity in terms of boundary data for pseudometrics dual to geodesic currents is valid and the elementary finite-cover argument applies without further restrictions on the surface or the currents.","pith_extraction_headline":"Geodesic currents with strongly hyperbolic dual pseudometrics are dense in the full space of currents."},"references":{"count":58,"sample":[{"doi":"","year":2015,"title":"The pressure metric for Anosov representations","work_id":"dbfb12fa-3aeb-4ee5-b34d-ae88a6150061","ref_index":1,"cited_arxiv_id":"1301.7459","is_internal_anchor":true},{"doi":"","year":2011,"title":"Bridson and Andre Haefliger, Metric spaces of nonpositive curvature, Springer, 2011","work_id":"56a99169-b1b3-4cfa-b712-831246f46ba9","ref_index":2,"cited_arxiv_id":"","is_internal_anchor":false},{"doi":"","year":2021,"title":"M. Burger, A. Iozzi, A. Parreau, and M. B. Pozzetti, Currents, systoles, and compactifications of character varieties, Proc. Lond. Math. Soc. 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