{"id":"palomar/PALOMAR-2026-08-29-000017","url":"https://github.com/shaikidris/prime-star-spectra-formalization/tree/fe3fe9fa41f5c69d9e1e16abc6da144511f778b0","json":"https://data.palomar-registry.org/entries/PALOMAR-2026-08-29-000017-v2.json","repo":"https://github.com/shaikidris/prime-star-spectra-formalization","tags":["math.CO","math.NT","msc:05C50","msc:11N05","spectral-graph-theory","prime-numbers","lean-formalization","adjacency-spectrum"],"score":0,"title":"shaikidris/prime-star-spectra-formalization","trust":"high","domain":"math.CO","source":"palomar","authors":["Idris Ali Shaik"],"reviews":0,"subject":"math.CO","summary":"A Lean 4 formalization of the ordered adjacency spectrum of finite prime-cover graphs. Its root-centred specialization proves that the square of the largest ordered eigenvalue equals pi(X) plus four times the finite prime sum of 1/(p-1), up to o(1). More generally, for every fixed finite set S of deleted primes and epsilon > 0, the same law with the explicit centre correction c(a) holds uniformly over allowed centres a <= (log X)^(1/2-epsilon). The same window admits a uniform centre--shell evolution theorem at the explicit first-exit frequency, with a finite localization-plus-phase error…","category":"research","comments":0,"disputed":false,"division":"math","mentions":0,"verified":true,"discussed":0,"published":"2026-08-31","reactions":{},"formalized":true,"formalizes":[{"title":"Prime-Star Localization and Second-Order Spectra of Finite Divisibility Cover Graphs","identifier":"https://doi.org/10.5281/zenodo.22163492","relationship":"formalizes"}]}