Making the decadic shells continuous turns the static cores of the 6N programme into a flow. The natural depth coordinate is the proper depth ℓ = ln ln X, in which both governing fields linearise: the twin-centre density obeys d ln ρ/dℓ = −2 and the mean factor count obeys d ω̄/dℓ = 1, so that for a prime m-tuple d ln ρ_m/dℓ → −m — the tuple size is the stratum decay rate. We verify this for the twin (m=2) and the triplet (6N−1, 6N+1, 6N+5) (m=3). The S10 triplet count, recomputed entirely from sieve primitives, reproduces the Part XV total (2,333,839) to 0.0000%. Deep-shell slopes are −2.072 and −3.111; extrapolated against 1/ln X they reach −2.085 and −3.065, consistent with −2 and −3 (the residual is the uncaptured higher-order logarithmic tail). The scale-free statement is their ratio, 3.111/2.072 = 1.5011 ≈ 3/2, in which the shared ω̄-clock distortion and the shared singular-series tail cancel. Provenance is explicit (the (ln X)^−m law is Hardy–Littlewood; ln ln X + B is Hardy–Ramanujan/Mertens; ρ and the 0.2604 enrichment shift are Parts I and XII), as are the limits (first moments only; the ω-variance / Erdős–Kac law on twin centres remains open; no infinitude is claimed). We close with a falsifiable prediction: the prime quadruplet (6N−1, 6N+1, 6N+5, 6N+7) (m=4) must give slope −4 and ratio 2:1 against the twin.