The Rail–Phase Hypothesis for Twin Primes: Five Structural Ingredients to Proving Twin Prime Infinitude Unconditionally

In this version, I demonstrate an unconditional proof of twin prime infinitude. Previous dangling conjecture has been fully resolved/removed.

I propose the Rail–Phase Hypothesis, which asserts that any unconditional proof of the Twin Prime Conjecture must operate within a bounded modular framework that studies primes and composites together, in direct relation to one another. The hypothesis identifies five structural necessities: (i) a bounded modular phase system (our example is on the 6k ±1 rails with 28-phase synchronization via mod 7 drift, but we leave open the possibility of other options) providing the finite control arena, (ii) a prime–composite rail balance that guarantees survivors in every bounded window, (iii) a dispersion ceiling preventing larger primes from erasing those survivors, (iv) a slot alignment mechanism ensuring survivors repeatedly form complete twin slots, and (v) a height condition ensuring survivors are genuine primes.