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,Q_p) for every prime p), and a D(4,4,4) arithmetic chain to zeta(s) times L(s,chi_8). (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 RP^1.

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 Algebra & Number Theory (April 2026)