{"id":"palomar/PALOMAR-2026-09-20-000005","url":"https://github.com/DiarHaidary/Improved-SparseStack-Constants/tree/782e60fd7cd8382ac45fbbe13c706b949387acb8","json":"https://data.palomar-registry.org/entries/PALOMAR-2026-09-20-000005-v1.json","repo":"https://github.com/DiarHaidary/Improved-SparseStack-Constants","tags":["math.PR","math.NA","msc:60B20","msc:68W20","msc:65F55","randomized-linear-algebra","sketching","lean","probability"],"score":0,"title":"Improved SparseStack Constants","trust":"high","domain":"math.PR","source":"palomar","authors":["Diar Heidary"],"reviews":0,"subject":"math.PR","summary":"Complete Lean proof of the revised SparseStack main theorem through its retained-count route. For every fixed real isometry, the actual independent uniform signed-bucket sketch with the rounded C=80, B=169/20 prescription has Gram-norm failure probability at most delta. The same prescription satisfies s<26.35 q/eps and m<176.9(d+q)/eps^2. All physical channel estimates and the all-order scalar certificate are proved.","category":"research","comments":0,"disputed":false,"division":"math","mentions":0,"verified":true,"discussed":0,"published":"2026-09-20","reactions":{},"formalized":true,"formalizes":[{"title":"SparseStack Is an Optimal Oblivious Subspace Embedding, Version 3.0, retained-count revision","identifier":"","relationship":"formalizes"},{"title":"SparseStack hybrid constants template, updated retained-count manuscript","identifier":"","relationship":"adapts"}]}