A Relational Forward-Cast Walk Common to Prime Location and Electromagnetic Propagation

A forward-cast walk locates each prime by its relations: a prime registers a remainder against each earlier prime, these cast a determined pattern of forbidden positions forward, and the next prime is the first position left open. The same structure, applied to the coupled electric and magnetic fields, is the propagation of a plane electromagnetic wave, with the speed of light as the cadence of the walk and the d’Alembert form as its closed solution. The walk is indifferent to what travels, keyed to the worldline of its entity, and runs in reverse as readily as forward. The index is unbounded in both directions; the field is a function of that index, not an enumeration over it. The odd-square decomposition bounds prime gaps at the order of the square root, and by von Koch (1901) this is the statement that the non-trivial zeros of the Riemann zeta function lie on the critical line. The primes are read exactly from the worldline; the odd-square interval is never empty, the index being unbounded; the location of the zeros follows as the deviation of the square-root-bounded primes from the logarithmic integral.