Part XIII of the 6N project. The Goldbach comet -- the scatter plot of r (2N), the number of ways to write 2N = p1 + p2 with both prime -- shows pronounced bands and heavy oscillation. We apply the omega-stratified, factor-resolved viewpoint developed for the twin skeleton in Parts I-XII to the sum 2N, and show the comet's scatter is, pointwise, the classical Hardy-Littlewood conditional singular series. Writing SG (N) = 2*Pi₂ * prodₐ|₍, ₐ>₂ (q-1) / (q-2), with Pi₂ = prodₐ>₂ (1 - 1/ (q-1) ²) the twin constant, and base (2N) = 2N/ln² (2N), the ratio R (N) = r (2N) / (base (2N) * SG (N) ) is constant: mean 0. 566, pointwise coefficient of variation 0. 22% across the ~1. 25e7 even numbers with N in 1. 25e7, 2. 5e7, and at most 0. 24% within each omega>₂ (N) band. The comet's vertical structure is exactly the values of SG (N) ; dividing by it collapses the comet to a single line. The measured Pi₂ = 0. 66016182 matches the literature value to eight figures, confirming SG is used with no free normalisation. The factor prodₐ|₍, ₐ>₂ (q-1) / (q-2) is the sum-analogue of the twin-difference enrichment prod (q-1) / (q-3) found in Part I: divisibility of 2N by a small prime q raises the number of admissible residue pairs, lifting the representation count. The same factor-resolved mechanism evaluated on the two arithmetic constraints (difference and sum) accounts for both. ATTRIBUTION. SG is the classical Hardy-Littlewood Goldbach singular series (1923), NOT a new formula. The contribution here is methodological and empirical: the omega-stratified viewpoint that reads the comet's bands directly as prod (q-1) / (q-2), and the pointwise verification at the 5e7 scale (CV 0. 22%), carrying the factor-resolved framework of Parts I-XII from the prime difference to the prime sum. SCOPE. This concerns only the shape of the conditional count. It makes NO statement about the Goldbach conjecture, i. e. that r (2N) >= 1 for every even 2N >= 4. RESIDUAL TREND. R drifts monotonically by decile of 2N, from 0. 5674 to 0. 5647 (about 0. 5%). This is the known logarithmic correction: the crude weight N/ln² N differs from the sharper integral weight, and the difference varies with N. It is a deficiency of the chosen base, not of SG, and is absorbed into R; a logarithmically exact weight flattens it. We report it rather than hide it, as the natural entry point for a finer post-main-term analysis.
Ruqing Chen (Wed,) studied this question.