Part XIV of the 6N project. Part XIII collapsed the Goldbach comet (prime sums 2N = p1 + p2) onto the Hardy-Littlewood conditional singular series. Here we treat the dual object: prime differences of arbitrary even gap d (Polignac). For each even gap d, let pi_d(X) = #{n <= X : n, n+d both prime}; plotting pi_d against d gives a "Polignac comet" banded by the odd-factor structure of d. With the Hardy-Littlewood prime-pair singular series S(d) = 2*Pi_2 * prod_{p|d, p>2} (p-1)/(p-2), Pi_2 = prod_{p>2}(1 - 1/(p-1)^2), and base(X) = X/ln^2(X), we find C(d) = pi_d(X) / (base(X) * S(d)) collapses to a single constant across ALL gaps. Over the 500 even gaps d <= 1000 at X = 10^8, C(d) has mean 1.131 and coefficient of variation 0.068%, with no trend in d (quartile means agree to 0.015%) and clean stratification by omega_odd(d) (band CV at most 0.11%). The measured Pi_2 = 0.66016186 matches the literature to eight figures, so S carries no free normalisation. The difference side thus mirrors the sum side: dividing by the singular series collapses the comet, and here the collapse constant is moreover shared across all gaps. Gaps with wildly different absolute counts -- pi_2 = 440,312, pi_6 = 879,908, pi_210 = 1,409,148 at X = 10^8 -- all reduce to C ~ 1.131 once S(d) is removed. (For d=6=2*3 the odd factor 3 contributes (3-1)/(3-2)=2, the familiar doubling of gap-6 pairs.) SUM-DIFFERENCE SYMMETRY. Parts I-XII resolved the prime difference at fixed gap (twins d=2; cousins and sexy d=4,6). Part XIII collapsed the prime sum. The present paper completes the pair: across all even gaps, the difference-side comet collapses onto S(d) with a gap-independent constant. The sum-side enrichment prod(q-1)/(q-2) in N and the difference-side prod(q-1)/(q-2) in d are the same singular-series mechanism read on the two linear constraints p1+p2=2N and p1-p2=d. ATTRIBUTION. S(d) is the classical Hardy-Littlewood prime-pair singular series, NOT a new formula. The contribution is the omega-stratified reading of the comet's bands as S(d), the verification of pointwise collapse to CV 0.068% over 500 gaps at X = 10^8, and the empirical cross-gap constancy of C(d) -- a falsifiable statement (the quartile test) that the data confirm. SCOPE. This concerns only the conditional count's shape and constant; it makes NO statement about Polignac's conjecture (that each even gap is attained by infinitely many prime pairs). The constant C ~ 1.131 carries the logarithmic correction of the crude weight X/ln^2 X (it shifts with X: 1.147 at X = 2e7, 1.131 at X = 1e8), but -- unlike the Goldbach decile drift -- this does not break the cross-gap constancy, since X is fixed while d varies.