A Gold–Simplex Geometry for Prime Centers in Recursive Dyadic Domains

In this paper we ask whether the center of the prime population inside a finite domain
can be generated recursively from the structure of the domain itself. By prime center we
mean the unique median prime when the prime population is odd, and the midpoint of the two
central primes when the population is even. In either case, equal numbers of primes lie on the
two sides of the center.
We develop a geometric construction in which successive numerical domains are inherited
from earlier states. The construction links repeated simplex accumulation, a diagonal Fibonacci–
Gold recurrence, dyadic power domains, and recursively completed prime-cycle structure

Revision 1: Clarified and made explicit the Recursive memory state.
Revision 2: Revised only the abstract to be more clear and brief.