{"id":"palomar/PALOMAR-2026-09-08-000005","url":"https://github.com/DiarHaidary/Sharp-Bounds-for-Graph-Matrices/tree/01994362f8543743d556e7544d2538e93c62c02b","json":"https://data.palomar-registry.org/entries/PALOMAR-2026-09-08-000005-v1.json","repo":"https://github.com/DiarHaidary/Sharp-Bounds-for-Graph-Matrices","tags":["math.PR","math.CO","msc:60B20","msc:05C80","msc:03B35","random-matrices","graph-theory","probability","lean"],"score":0,"title":"Sharp Bounds for Graph Matrices","trust":"high","domain":"math.PR","source":"palomar","authors":["Diar Heidary"],"reviews":0,"subject":"math.PR","summary":"A Lean formalization of matching polynomial and logarithmic orders for the norm of every fixed finite simple graph matrix in the globally injective dense independent-sign model. For each fixed positive real moment order p, the pth norm moment to the power 1/p is bounded above and below by positive shape-dependent constants times n^((h+i0-s)/2) log(2n)^(b*/2). Here h is the number of graph roles, i0 counts isolated interior roles, s is the minimum boundary-separator size, and b* is the maximum number of attached floating components over minimum separators. The expected-norm specialization and…","category":"research","comments":0,"disputed":false,"division":"math","mentions":0,"verified":true,"discussed":0,"published":"2026-09-08","reactions":{},"formalized":true,"formalizes":[{"title":"The polynomial and logarithmic order of every fixed dense sign graph matrix","identifier":"Graph Matrices technical report 96, 8 September 2026","relationship":"formalizes"},{"title":"Critical separator operators and connected creation commutators","identifier":"Graph Matrices technical report 97, 8 September 2026","relationship":"adapts"},{"title":"Separator extremes survive in the graph-matrix norm","identifier":"Graph Matrices technical report 98, 8 September 2026","relationship":"adapts"},{"title":"Connected floating fields and the critical occupation operators","identifier":"Graph Matrices technical report 90","relationship":"adapts"},{"title":"Maximum exponents of all connected floating components","identifier":"Graph Matrices technical report 95","relationship":"adapts"}]}