The Adeniyi Spiral, Continued: Reading the Next Prime from its Worldline

A continuation of The Adeniyi Spiral: A Structural Framework for Prime Distribution. Given a prime, the next is located by reading the relationship of the current prime to all primes before it — the first forward position no prior prime’s reach forbids. The construction uses only prime divisors up to the square root of the region ahead. A streamlined form carries the relational state forward by subtraction alone, conserving it across each step. The reach vector is the primary object; the next prime is one reading of it. The twin condition is stated within it. Verified across the primes below ten million.