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Our main result yields information on the size of the sumset <jats:inline-formula><jats:alternatives><jats:tex-math>$$\\lambda X + \\eta Y$$<\/jats:tex-math><mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n                  <mml:mrow>\n                    <mml:mi>\u03bb<\/mml:mi>\n                    <mml:mi>X<\/mml:mi>\n                    <mml:mo>+<\/mml:mo>\n                    <mml:mi>\u03b7<\/mml:mi>\n                    <mml:mi>Y<\/mml:mi>\n                  <\/mml:mrow>\n                <\/mml:math><\/jats:alternatives><\/jats:inline-formula> uniformly across a compact set of parameters at fixed scales. The proof is combinatorial and avoids the machinery of local entropy averages and CP-processes, relying instead on a quantitative, discrete Marstrand projection theorem and a subtree regularity theorem that may be of independent interest.<\/jats:p>","DOI":"10.1007\/s00493-023-00008-9","type":"journal-article","created":{"date-parts":[[2023,6,14]],"date-time":"2023-06-14T07:02:12Z","timestamp":1686726132000},"page":"299-328","update-policy":"http:\/\/dx.doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["A combinatorial proof of a sumset conjecture of Furstenberg"],"prefix":"10.1007","volume":"43","author":[{"given":"Daniel","family":"Glasscock","sequence":"first","affiliation":[]},{"given":"Joel","family":"Moreira","sequence":"additional","affiliation":[]},{"given":"Florian K.","family":"Richter","sequence":"additional","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2023,6,14]]},"reference":[{"key":"8_CR1","doi-asserted-by":"publisher","first-page":"1","DOI":"10.3934\/jmd.2022001","volume":"18","author":"T Austin","year":"2022","unstructured":"Austin, T.: A new dynamical proof of the Shmerkin-Wu theorem. 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