The Riemann zeta world through one conformal lens, z = 1 − 1/s (the Li map — the Smith-chart move for arithmetic):
the pole s = 1 lands at dead center; the number line becomes the gold spoke, its integers marching toward the rim;
the critical line becomes the rim itself, carrying the zeros; and infinity is tamed to a single point on the right edge.
Where the gold spoke touches the rim is the point at infinity — the number line and the critical line meet there.
The Riemann Hypothesis, on this disc, is one sentence: every zero sits exactly on the rim. Inside the rim or outside it — anywhere off it —
is what a counterexample would look like. None has ever been found.
Motion — the flow x ↦ eᵗx
flow time t = 0.0prime meetings: 0
Gold tracers ride the number line toward infinity. Twelve prime orbits turn — the p-th at angular speed log p
(the Kronecker winding on the character torus). A white chord flashes when two primes realign; pair (p, q) realigns every
2π / log(p/q) — neighbours almost never, distant pairs constantly. The rim shimmers at the zero frequencies γ.
All twelve started aligned at t = 0; by unique factorization they will never all align again.
Layers
Inspector — tap any dot
Tap a zero, a prime milestone, a red ring, a fan spoke, or an orbiting prime.
How to read it
Center: the pole — the always-on term that gives the staircase its main growth.
Gold spoke: n ↦ 1 − 1/n. Solid ticks are prime powers — the only events the explicit formula sees. Red rings are the doubled primes 2p — on the number line, but the zero-choir is provably silent there (Λ(2p) = 0).
Rim: ρ = ½ + iγ ↦ 1 − 1/ρ, which has |z| = 1 exactly when β = ½. The zeros crowd toward the infinity point like milestones toward a horizon — that crowding is the taming. The strip below un-compresses the rim.
In motion: the orbit side (primes turning) and the spectral side (zeros shimmering) move under one clock — the explicit formula is the statement that those two motions are Fourier duals.