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Authors
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Funding
Funding for this research was provided by:
Schweizerischer Nationalfonds zur Förderung der Wissenschaftlichen Forschung (SNF 200020 219429)
Narodowa Agencja Wymiany Akademickiej (BPN/PPO/2021/1/00019/U/00001)
Narodowe Centrum Nauki (2023/51/D/ST1/02907)
National Science Foundation (NSF Career DMS-2044898)
Alexander von Humboldt-Stiftung
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Article History
Received: 19 January 2026
Accepted: 22 June 2026
First Online: 3 July 2026
Declarations
Notation.: Throughout the paper, B ( x , r ) denotes the (open) ball of radius centred at x . When the ambient space is , this is the Euclidean ball; when the ambient space is , it is the geodesic ball. The meaning will always be clear from the context.
Conflicts of Interest: The authors have no conflict of interests to declare.
