Closure Points and Forced Residues: An Index-Line Sieve for Twin Primes

I formulate the twin-prime sieve on the index line, where a closure point 6𝑘 has flanks 6𝑘 −1 and 6𝑘 +1. For a prime 𝑝 = 6𝑚 𝑝 +𝑠 𝑝 , divisibility removes exactly the two index classes ±𝑚 𝑝 (mod 𝑝). From this law I derive the exact survivor count over a complete period, an alignment rati