The Prime Triplet as a Three-Member Two-Centre CRT Pattern: A Non-Monotone omega-Distortion on the 6N Skeleton

Part XV of the 6N project. Parts IX-X showed that prime pairs straddling two consecutive centres of the 6N skeleton (cousins, sexy pairs) exhibit omega-distortions reproduced by a two-centre Chinese-Remainder mechanism with no fitted parameters. We extend this from two members to three: the prime triplet (6N-1, 6N+1, 6N+5). The only admissible triplet patterns within a span of six are (0,2,6) and its mirror (0,4,6); (0,2,4) is inadmissible (it occupies all residues mod 3). On the 6N skeleton, (p,p+2,p+6) with p=6N-1 becomes (6N-1, 6N+1, 6(N+1)-1), so its three members sit at (centre-offset, wing) = (0,-1), (0,+1), (1,-1): two wings on centre N, one on the neighbour N+1. Like cousins and sexy pairs, and unlike the single-centre twin, the triplet straddles two consecutive centres, so its omega-dependence is a two-centre distortion rather than the monotone single-centre enrichment of the twin. Binned by omega>3(N) and normalised to omega=1, the triplet rate is NON-MONOTONE: it rises to a peak near omega=3 and then falls. This is the sexy-B signature of two competing effects: the twin component (6N +- 1) on the conditioned centre N enriches with omega, while the third member on the neighbour N+1 (like the cousin's partner) suppresses the rate at high omega; the balance produces the peak. The three-member two-centre CRT factor, with dead(q,s) = -s*6⁻¹ mod q and the three members {(0,-1),(0,+1),(1,-1)}, is deterministic when q|N and an admissible-residue average when q does not divide N. With no fitted parameters, the model reproduces the non-monotone shape on two shells: error at most 2.4% for omega <= 6 on S10 (~2.3x10^6 triplets). The lone large residual at omega=6 on S9 (6.5%, 56 triplets) tightens to 0.5% on S10 (1832 triplets), identifying it as small-sample; the omega=7 stratum has only 11 triplets on S10 and is not interpretable, so the result is stated for omega <= 6. The triplet is thus a three-member instance of the same two-centre mechanism as cousins and sexy pairs. ATTRIBUTION: the Hardy-Littlewood triplet singular series S(0,2,6) = 2.858 is classical (our sieve reproduces it to the literature value); this paper proposes no new constant. The contribution is the identification of the triplet's omega-dependence as a non-monotone two-centre distortion and its quantitative reproduction by the parameter-free CRT model. This is NOT a "divide by the singular series and collapse to a constant" result (that is the Goldbach/Polignac case): the triplet straddles two centres and is a distortion, like cousins and sexy pairs. SCOPE. No statement is made about the infinitude of prime triplets or any prime k-tuple conjecture. This is a measured, factor-resolved account of the triplet's conditional rate.