Split Support on the Absolute Arithmetic Curve: Invariant Coordinates, Adelic Height Descent, Frobenius Perfection, and Monomial Spectral Charts

Version 9 pre-publication draft of a side mathematics note on the split-zero globalization G(R)=R∪{τ} of a nonzero commutative ring, separating the actual semiring zero from the supported ring zero. The draft develops the geometry retained by this separation through semiring spectra, Boolean character coordinates, Arakelov geometry over adelic curves, the Connes--Consani absolute F_1-curve, Frobenius-perfect denominator towers, finite gerbe theories, theta quantization, and monomial spectral charts. The draft constructs lattice-valued split-zero extensions G_L(R), records Boolean localization and invariant-coordinate consequences, analyzes weighted heights over proper Chen--Moriwaki adelic curves, describes split support in arithmetic Picard/Jacobian settings, and relates denominator towers, cyclotomic phase, finite Heisenberg extensions, UHF limits, and reciprocal-root skeletons. Status. This is a pre-publication mathematical draft and side research note, not part of the public-domain manuscript translation archive and not a certified critical edition. This version fronts the Version 9 PDF and includes the corresponding LaTeX source. The draft explicitly distinguishes its formal constructions from any claim that F_1 is the Boolean semiring, any perfectoid-space claim, or any proof of the Riemann hypothesis.