{"id":"palomar/PALOMAR-2026-10-28-000033","url":"https://github.com/Arthur742Ramos/Math-Formalization/tree/9e5b57dba2ba9423cc8f12ff934bd07d86394c47/topology/furstenberg-weak-mixing","json":"https://data.palomar-registry.org/entries/PALOMAR-2026-10-28-000033-v1.json","repo":"https://github.com/Arthur742Ramos/Math-Formalization","tags":["math.DS","math.GN","msc:37B05","msc:37B02"],"score":0,"title":"Furstenberg weak mixing and finite diagonal powers","trust":"high","domain":"math.DS","source":"palomar","authors":["Arthur Freitas Ramos","David Barros Hulak","Ruy Jose Guerra Barretto de Queiroz"],"reviews":0,"subject":"math.DS","summary":"For a continuous self-map of a nonempty topological space, square transitivity implies transitivity of every finite diagonal power, including power zero. A genuine open-pair refinement and finite induction give a common natural forward hitting time for any finite family of nonempty open pairs. The literal two-pair condition is proved equivalent to actual square transitivity.","category":"research","comments":0,"disputed":false,"division":"math","mentions":0,"verified":true,"discussed":0,"published":"2026-10-28","reactions":{},"formalized":true,"formalizes":[{"title":"Notes on Topological Dynamics","identifier":"https://math.huji.ac.il/~mhochman/courses/TD2022/notes-v3.pdf","relationship":"formalizes"},{"title":"Revisiting Variations in Topological Transitivity","identifier":"arXiv:1906.00712v4","relationship":"formalizes"}]}