NSk--Windows Spectral Window Theory: Contracts, Operator Realizations, and the Reference NSk Family

NSk--Windows develops an autonomous theory of spectral windows for nonnegative self-adjoint operators on Hilbert spaces. The module builds a complete window apparatus in four layers: a PRE-PURE language of band axes, window families, partitions, refinement and ACC; a PURE contract of window masses, conditional distributions and refinement consistency; a CORE realization through spectral calculus, Paley--Wiener analysis, the reference Nowak--Stachowiak window family and stability certificates; and an EXEC layer with comparative profiles, torus realizations and parameter diagnostics.The structural parts of the module are proved locally, while classical analytic tools such as the spectral theorem, Paley--Wiener theory, Mosco convergence, Kato--Rellich and KLMN are imported through explicit proof certificates. Kernel and trace statements are exported under elliptic gates, and norm convergence statements remain controlled by separate norm certificates.The NSk reference windows form the distinguished spectral-window family of the NSk/ψ program. Their frequency profiles are smooth, compactly supported and flat at the edges; their time kernels lie in the Paley--Wiener and Schwartz classes; and their operator multipliers have the form m(λ)=G(sqrt(λ)). The module provides the common spectral-window apparatus used downstream by Weyl, Entropy, Spectrum, Wightman, Amplitudes, Clay and related NSk/ψ modules.