We study the two prime-candidate rails 6k ± 1 through the modular framework of 28 phases (the least common multiple of moduli 2 and 7). Within this lens we establish universal exclusion laws, drift–lock mechanisms, and dispersion ceilings which together guarantee the persistence of survivor slots after every prime square. Using these survivors, a Hall-type phasealignment argument forces at least one full twin slot within bounded windows. The method avoids reliance on analytic conjectures such as Elliott–Halberstam, instead operating entirely within explicit combinatorial exclusion and modular alignment. All constants are explicit: The fraction of unlocked phases is 20/28 (denoted θunlocked); the small-prime survivor surplus is σS = 2 per block; the large-prime baseline into survivors is < 0.99 per block for p ≥ 47; and a window of W0 = 2 blocks already forces a full survivor, with a Hall-type alignment producing a twin slot in each bounded window. Together these bounds yield an unconditional proof of the infinitude of twin primes