Split Support Geometry on the Absolute Arithmetic Curve: Universal Zero Fibres, Arithmetic Curves, and Frobenius-Perfect Quantization

Version 10 pre-publication draft of a side mathematics note on split support geometry and support-amplitude semirings. The note starts from the distinction between absence and a present datum of zero amplitude. For a bounded distributive lattice L and a nonzero commutative ring R, it studies the semiring G_L(R) whose ordinary amplitudes come from R while its ring-null fibre records support states in L. The draft develops explicit algebraic and geometric consequences of this separation: universal maps to rings, localization at support-zero elements, ideal and prime-ideal classification, spectral ordinal sums, projective support profiles, finite-field point counts, split determinants, monomial matrix normal forms, weighted-cycle Euler factors, adelic support localization, weighted height descent, arithmetic Jacobians, Frobenius-perfect denominator towers, finite gerbe/theta quantization, UHF-limit data, monomial spectral charts, and a Beurling/Nyman--Baez-Duarte reciprocal-root skeleton. The reason for the construction is to test how much geometry is lost when classical zero conflates absence with supported zero-amplitude data. The draft treats split support as a bookkeeping and geometry-building device across algebra, arithmetic geometry, adelic heights, phase/carry phenomena, and monomial spectral charts. This is a pre-publication mathematical draft and side research note, not part of the public-domain manuscript translation archive and not a certified or refereed result.