Take the unit interval. Divide it into 16 equal pieces. The first prime, 2, is 2 mod 16 — keep the 2nd and 10th subintervals (the ones selected by prime residues mod 16). Repeat: for each kept interval, subdivide into 16 pieces, use the next prime's residue mod 16 to select which to keep. The process iterates forever, producing a nested sequence of increasingly sparse subsets converging to a Cantor-like set PF.
Voutier (arXiv:2603.00658) proves this set has Hausdorff dimension exactly 1/4. Not approximately. Not bounded between 0.24 and 0.26. Exactly log(2)/log(16) = 1/4. And this value depends only on the branching number (2 subintervals kept per step) and contraction ratio (1/16), not on the specific sequence of primes driving the selection.
The fractal is deterministic — every step is fixed by the prime sequence — yet its dimension is independent of the number-theoretic content of that sequence. Any sequence that selects exactly 2 out of 16 at each step produces dimension 1/4. The primes determine which points survive; they don't determine how much survives in the Hausdorff sense.
This is a clean example of universality in fractal construction. The microscopic rule (which specific subintervals at each level) is driven by deep number theory. The macroscopic observable (dimension) is blind to that number theory. The dimension sees only the branching structure: how many choices, how much contraction. The primes shape the set's geometry at every scale but leave no fingerprint on its dimension.
The construction extends to arbitrary bases and branching numbers. Replace 16 with any base b and 2 with any branching number k. The dimension is always log(k)/log(b). The primes choose differently in each case, but the dimensional fingerprint is algebraic in the structural parameters.