This manuscript presents a referee-oriented candidate route toward the twin prime conjecture. It is not framed as a publicly accepted proof, but as a complete and explicitly checkable proof chain. The method studies the symmetric pairs 6r-1, 6r+1 through a two-column residual metronome: each prime p>=5 removes two periodic phases of rows. The main reduction takes place in a terminal population of rows surviving the sieve up to Y=X^1/3. At this threshold, each surviving endpoint is prime or semiprime, up to projected squarefull errors. The rows are classified as prime-prime, mixed, or semiprime-semiprime, with counts T, U, V. The decisive identity is T-V = eta₃ LY - EY, eta₃= (1-log 2) / (1+log 2) >0. Thus terminal positivity follows formally from EY=o (LY). The analytic burden is transferred to an oscillating defect DY through the centered accounting relation DY=EY+o (LY), and then to an autonomous terminal transfer statement, UniformTDT, asserting DY=o (LY). The central part of UniformTDT is reduced to three branches: A-15, controlled by a gcd-sensitive vertical large sieve under local geometric hypotheses for trace functions; A-16, matched to the Fouvry-Kowalski-Michel-Sawin bilinear theorem for trace functions in a near-prime modulus range; and A-17, controlled by sparsity of dominant prime powers. The manuscript isolates the remaining verification tasks in a referee checklist: local geometric catalogue, sheaf non-isomorphy, FKMS range, absorption of projectors, and absence of residual Oₒut terms.
Stefano Rivis (Sat,) studied this question.