{"paper":{"title":"Convergence of Lorentzian spaces and curvature bounds for generalized cones","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"Timelike curvature and curvature-dimension bounds are stable under ℓ-convergence for Lorentzian pre-length spaces, with sharp bounds holding for generalized cones.","cross_cats":["math-ph","math.MG","math.MP"],"primary_cat":"math.DG","authors_text":"Christian Ketterer","submitted_at":"2026-05-11T21:50:56Z","abstract_excerpt":"The goal of this article is twofold. We introduce a notion of convergence for Lorentzian pre-length spaces, $\\ell$-convergence, that extends previous convergence notions in this context. We show that timelike curvature and timelike curvature-dimension bounds are stable under (measured) $\\ell$-convergence. Then, we show that $\\ell$-convergence is well adapted for generalized Lorentzian cones: a sequence of generalized cones $-I_i\\times_{f_i}X_i$ converges in $\\ell$ sense if the base $I_i$ and the fiber $X_i$ converge in GH sense and the functions $f_i$ converge uniformly. We use this to show sh"},"claims":{"count":4,"items":[{"kind":"strongest_claim","text":"timelike curvature and timelike curvature-dimension bounds are stable under (measured) ℓ-convergence; a sequence of generalized cones −I_i ×_{f_i} X_i converges in ℓ-sense if the base I_i and fiber X_i converge in GH sense and f_i converge uniformly; sharp timelike curvature and CD bounds hold for such cones; pre-compactness theorem for smooth generalized cones with uniform lower bound on full Ricci or Riemann curvature.","source":"verdict.strongest_claim","status":"machine_extracted","claim_id":"C1","attestation":"unclaimed"},{"kind":"weakest_assumption","text":"The spaces under consideration are Lorentzian pre-length spaces for which the new ℓ-convergence can be defined and for which timelike curvature bounds make sense; the uniform convergence of warping functions f_i and GH convergence of bases and fibers are sufficient to control the Lorentzian distance and curvature in the cone construction.","source":"verdict.weakest_assumption","status":"machine_extracted","claim_id":"C2","attestation":"unclaimed"},{"kind":"one_line_summary","text":"Introduces ℓ-convergence for Lorentzian pre-length spaces, establishes stability of timelike curvature and CD bounds under it, and derives sharp bounds plus precompactness for generalized cones via GH convergence of bases and fibers.","source":"verdict.one_line_summary","status":"machine_extracted","claim_id":"C3","attestation":"unclaimed"},{"kind":"headline","text":"Timelike curvature and curvature-dimension bounds are stable under ℓ-convergence for Lorentzian pre-length spaces, with sharp bounds holding for generalized cones.","source":"verdict.pith_extraction.headline","status":"machine_extracted","claim_id":"C4","attestation":"unclaimed"}],"snapshot_sha256":"ad61124ee0f494fad73c7bb8463391a0372fe0a29a7d4138e07a8aa6a4f8c101"},"source":{"id":"2605.11271","kind":"arxiv","version":2},"verdict":{"id":"94f89ba7-193c-4818-ade7-65252cfb0246","model_set":{"reader":"grok-4.3"},"created_at":"2026-05-13T00:55:28.436181Z","strongest_claim":"timelike curvature and timelike curvature-dimension bounds are stable under (measured) ℓ-convergence; a sequence of generalized cones −I_i ×_{f_i} X_i converges in ℓ-sense if the base I_i and fiber X_i converge in GH sense and f_i converge uniformly; sharp timelike curvature and CD bounds hold for such cones; pre-compactness theorem for smooth generalized cones with uniform lower bound on full Ricci or Riemann curvature.","one_line_summary":"Introduces ℓ-convergence for Lorentzian pre-length spaces, establishes stability of timelike curvature and CD bounds under it, and derives sharp bounds plus precompactness for generalized cones via GH convergence of bases and fibers.","pipeline_version":"pith-pipeline@v0.9.0","weakest_assumption":"The spaces under consideration are Lorentzian pre-length spaces for which the new ℓ-convergence can be defined and for which timelike curvature bounds make sense; the uniform convergence of warping functions f_i and GH convergence of bases and fibers are sufficient to control the Lorentzian distance and curvature in the cone construction.","pith_extraction_headline":"Timelike curvature and curvature-dimension bounds are stable under ℓ-convergence for Lorentzian pre-length spaces, with sharp bounds holding for generalized cones."},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2605.11271/integrity.json","findings":[],"available":true,"detectors_run":[{"name":"claim_evidence","ran_at":"2026-05-20T04:42:00.765555Z","status":"completed","version":"1.0.0","findings_count":0},{"name":"ai_meta_artifact","ran_at":"2026-05-19T12:39:20.836941Z","status":"completed","version":"1.0.0","findings_count":0},{"name":"doi_title_agreement","ran_at":"2026-05-19T10:01:17.248379Z","status":"completed","version":"1.0.0","findings_count":0},{"name":"doi_compliance","ran_at":"2026-05-19T08:36:55.348810Z","status":"completed","version":"1.0.0","findings_count":0}],"snapshot_sha256":"7d0c4abdbf814cd4dc8ebaec94a5d299419b0f3f44008b07bb7b4e142aaee1f8"},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","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"}