Infinite Twin Primes by Rail Exclusion: Capacity, Dispersion, Drift–Lock Alignment, and Non-Persistence

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 phase
alignment 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