Three Structural Results on the Riemann Hypothesis via the Projective Blow-Up of the Probability Simplex

We prove three structural results on the Riemann Hypothesis using the projective blow-up of the probability simplex (Spencer 2026f, doi: 10. 5281/zenodo. 19188284). We do not claim a proof of the Riemann Hypothesis. (1) The characteristic-zero obstruction to extending Weil's proof is circumvented by a canonical involution of the blow-up — the Seam Consistency Condition (SCC) — which plays an analogous role to the Frobenius in characteristic zero. (2) The blow-up tower establishes an arithmetic-geometry dictionary at three independent levels: the Turing Tower Theorem, the Weyl element identification (the map sending xi to 1/xi is the Weyl element of GL (2, Qₚ) for every prime p), and a D (4, 4, 4) arithmetic chain to zeta (s) times L (s, chi₈). (3) The SCC is Pi-0-2-complete, so no elementary proof of the Riemann Hypothesis is possible: any proof must use the two-chart structure of RP¹. These results establish the blow-up geometry as the minimal correct framework for the Riemann Hypothesis and position the problem within the Langlands landscape at three independent levels. Companion paper: Spencer 2026i (The Riemann Hypothesis as a Necessary Consequence of Self-Consistency). Submitted to Proceedings of the American Mathematical Society.